JP2005001013A - Robot positioning error correcting device - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a robot positioning error correcting device which reduces positioning errors of various types caused by various factors. <P>SOLUTION: According to the operation of the robot positioning error correcting device, first, determination is made on a hysteresis error correcting function for offsetting a hysteresis error that is a positioning error depending on locations of respective link elements before movement, and when the hysteresis error is offset, determination is made on a geometrical error correcting function for offsetting a geometrical error caused by locational errors of the respective link elements and an installation error of a robot. Then determination is further made on a non-modeled error correcting function for reducing a non-modeled error that is difficult to be modeled, and an angular transmission error correcting function for reducing an angular transmission error caused by a motion transmission mechanism. <P>COPYRIGHT: (C)2005,JPO&NCIPI

Description

【数２】

【００３２】
ここで、ｋ１１〜ｋ２４は定数である。得られたヒステリシス誤差Δθｈ１，Δθｈ１’．．．の数の分だけ式（１３）を連立し、θｈ１にΔθｈ１，Δθｈ１’．．．の反数を代入し、θ１，θ２，Δθ１，Δθ２にコントローラ８の各指令値を代入して、最小自乗法により多数の連立方程式を解くことにより定数ｋ１１，ｋ１２，ｋ２１，ｋ２２が定まる。同様にして、式（１４）を連立した連立方程式から定数ｋ１３，ｋ１４，ｋ２３，ｋ２４が定まる。
【００３３】
計算機９は、以上のようにして求めたヒステリシス誤差補正関数ｈ１，ｈ２をコントローラ８に通知し、コントローラ８はこれらを内部に記憶する（図４のステップＳＴ３）。これによりコントローラ８はヒステリシス誤差を補正しながら手先軸４の任意の目標位置から各アーム２，３の目標角度位置を換算することが可能になる。つまり、コントローラ８は、アームを移動させるときに、ヒステリシス誤差補正関数ｈ１，ｈ２を用いてヒステリシス誤差補正量θｃ１およびθｃ２を算出し、目標位置Ｐ２に対応する関節角度θ２１およびθ２２にヒステリシス誤差補正量θｃ１およびθｃ２を加算することにより指令角度位置を補正でき、補正された指令角度位置に従ってアーム２，３を駆動することにより、手先軸４の水平方向位置決め誤差からヒステリシス誤差を除去することができる。このようにしてヒステリシス誤差の補正が完了する。
【００３４】
なお、この明細書で、「誤差補正関数をコントローラ８に通知する」とは、関数の種類および係数またはパラメータをすべてコントローラ８に通知することでもよいし、コントローラ８と計算機９とで共通の種類の誤差補正関数を使用することにしておけば、計算機９で求めた係数またはパラメータのみをコントローラ８に通知することでもよい。
【００３５】
ヒステリシス誤差の補正完了後、計算機９は、幾何学誤差算出のために手先軸４の位置を測定し（図４のステップＳＴ４）、幾何学誤差を算出し（ステップＳＴ５）、幾何学誤差補正関数を決定してコントローラ８に通知する（ステップＳＴ６）。
【００３６】
幾何学誤差補正について図６を参照して説明する。手先軸４の目標指令位置としてＰ０（Ｘ０，Ｙ０）を与えても、ロボットの据付誤差Ｐｂとロボット本体の幾何学誤差Ｐｅがあると、基準座標系Ｏ−ＸＹで見た手先軸４の実際の位置Ｐ（Ｘ，Ｙ）は目標指令位置Ｐ０（Ｘ０，Ｙ０）から外れてしまう。ロボットの据付誤差Ｐｂとロボット本体の幾何学誤差Ｐｅを、ここでは幾何学誤差という。
【００３７】
ロボットの据付誤差Ｐｂとは、ロボットベース１つまり回転関節軸２ａの据付誤差、即ちロボットのコントローラ８が位置指令の基準とする理想的な基準座標系Ｏ−ＸＹに対する実際のロボット座標系Ｏ’−Ｘ’Ｙ’の相対的位置ずれを意味する。ロボット座標系Ｏ’−Ｘ’Ｙ’の原点Ｏ’は基準座標系Ｏ−ＸＹ上では（Ｘｂ，Ｙｂ，θｂ）にあり、このためにロボットの据付誤差Ｐｂは、アーム２，３がロボット動作範囲内でどの回転位置にあっても一定の誤差ベクトルとして手先軸４の位置決め精度に影響する。ロボットの据付誤差Ｐｂがある場合に、コントローラ８が目標指令位置Ｐ０に手先軸４を位置決めしようとしても、実際にはモータはロボット座標系Ｏ’−Ｘ’Ｙ’で働くので、コントローラ８はロボット座標系Ｏ’−Ｘ’Ｙ’で目標指令位置Ｐ０に従ってモータを駆動することになる。
【００３８】
ロボット本体の幾何学誤差Ｐｅとは、リンク要素の形状誤差と位置的誤差（アームの長さの誤差およびアームの回転角度誤差）に起因して手先軸４に発生する位置決め誤差を意味する。ロボット本体の幾何学誤差Ｐｅは、アーム２，３の長さと角度位置に依存して変化し、ロボット座標系Ｏ’−Ｘ’Ｙ’の中で表現される。ロボット本体の幾何学誤差Ｐｅがあるために、ロボット座標系Ｏ’−Ｘ’Ｙ’で目標指令位置Ｐ０（Ｘ０，Ｙ０）に従ってモータを駆動しても、ロボット座標系Ｏ’−Ｘ’Ｙ’で手先軸４の位置はＰｒ（Ｘｒ，Ｙｒ）になり、ＰｂとＰｒの結果として基準座標系Ｏ−ＸＹでの手先軸４の位置はＰ（Ｘ，Ｙ）になる。
【００３９】
現実にアーム２，３を制御できるロボット座標系Ｏ’−Ｘ’Ｙ’において、目標指令位置Ｐ０（Ｘ０，Ｙ０）に対応した手先軸４の実際の位置がＰｒ（Ｘｒ，Ｙｒ）であることは、式（１５）で表現できる。
【００４０】
Ｐｒ＝ｇ（Ｐ０，ｖ＋ｅ） （１５）
ここで、ｇはロボット座標系Ｏ’−Ｘ’Ｙ’上で目標指令位置Ｐ０から実際の位置Ｐｒ（Ｘｒ，Ｙｒ）を算出することができる、ロボット本体の幾何学的関係を表した関数である。ｖはリンク要素の理想的な寸法および目標角度、すなわち理想幾何学パラメータを表し、ロボット座標系Ｏ’−Ｘ’Ｙ’上のモデルを規定するパラメータの並びすなわちベクトルで表現できる。ｅはアームの長さの誤差およびアームの回転角度誤差、すなわち前記の幾何学誤差パラメータを表し、ロボット座標系Ｏ’−Ｘ’Ｙ’上のモデルを規定するパラメータのベクトルで表現でき、ロボット本体の幾何学誤差Ｐｅの原因になる。
【００４１】
式（１５）をＸ’方向成分とＹ’方向成分について表現すると、式（１６）および式（１７）のようになる。
Ｘｒ＝ｇｘ（Ｘ０，Ｙ０，ｖ＋ｅ） （１６）
Ｙｒ＝ｇｙ（Ｘ０，Ｙ０，ｖ＋ｅ） （１７）
【００４２】
幾何学誤差のない、即ちロボットの据付誤差Ｐｂとロボット本体の幾何学誤差Ｐｅのない理想的なロボットに目標指令位置Ｐ０（Ｘ０，Ｙ０）を与えた時、手先軸４は目標通りの位置Ｐ０（Ｘ０，Ｙ０）に位置決めされる。この関係は式（１５）の特殊ケースであり、式（１８）のように表現することができる。
Ｐｒ＝Ｐ０＝ｇ（Ｐ０， ｖ） （１８）
【００４３】
図７を参照しながら、理想幾何学パラメータｖおよび幾何学誤差パラメータｅを説明する。図７は図１に示す水平多関節ロボットの要素を簡略化して示す平面図である。図中のＬ１は第１のアーム２の設計上の規定の長さ、ｄＬ１はアーム２の長さの誤差、Ｌ２は第２のアーム３の設計上の規定の長さ、ｄＬ２はアーム３の長さの誤差、θ１は第１のアーム２の指令された回転角度位置（関節角度）、ｄＬθはアーム２の角度位置の誤差（例えば原点Ｏ’の位置ずれに起因する）、θ２は第２のアーム３の指令された回転角度位置（関節角度）、ｄＬθはアーム２の角度位置の誤差（例えば原点Ｏ’の位置ずれと回転関節軸３ａの位置ずれに起因する）である。
【００４４】
理想幾何学パラメータｖは式（１９）のようにベクトルとして表現され、幾何学誤差パラメータｅは式（２０）のようにベクトルとして表現される。
ｖ＝（Ｌ１，Ｌ２，θ１，θ２） （１９）
ｅ＝（ｄＬ１，ｄＬ２，ｄθ１，ｄθ２） （２０）
幾何学誤差パラメータｅのうち、角度位置の誤差ｄθ１，ｄθ２は、アーム２，３の角度位置に依存して変化する。
【００４５】
ロボット本体の幾何学的関係を表す関数ｇは、理想幾何学パラメータｖと幾何学誤差パラメータｅを用いて一意に表現される。
【００４６】
また、リンク要素の機械的な誤差に起因するロボット本体の幾何学誤差Ｐｅに加え、据付誤差Ｐｂがあると、基準座標系Ｏ−ＸＹ上の手先軸４の位置Ｐ（Ｘ，Ｙ）は式（２１）で表される。
Ｐ＝Ｐｂ・Ｐｒ （２１）
【００４７】
ロボットの据付誤差Ｐｂ（Ｘｂ，Ｙｂ，θｂ）、およびロボット座標系Ｏ’−Ｘ’Ｙ’上の手先軸４の実際の位置Ｐｒ（Ｘｒ，Ｙｒ）は、３×３行列による同次変換形式で式（２２）および式（２３）のように表現される。
【数３】

【数４】

【００４８】
式（２２）の第１行および第２行の第１列および第２列の行列成分は、ロボットの据付誤差Ｐｂの回転誤差成分を示し、第１行および第２行の第３列は、ロボットの据付誤差Ｐｂの並進誤差成分を示す。式（２３）では、座標系の回転を考慮しないので、回転誤差成分は２×２の単位行列になる。式（２３）の第１行および第２行の第３列は、ロボット座標系Ｏ’−Ｘ’Ｙ’上の手先軸４の実際の位置Ｐｒの並進誤差成分（Ｘｒ，Ｙｒ）を示す。
【００４９】
式（２１）〜式（２３）に従って、基準座標系Ｏ−ＸＹ上の手先軸４の位置Ｐ（Ｘ，Ｙ）は、同次変換形式で式（２４）のように表現される。
【数５】

【００５０】
基準座標系Ｏ−ＸＹ上の手先軸４の位置Ｐの並進誤差成分は、Ｘ，Ｙであるので、式（２４）の第１行および第２行の第３列から、Ｘ，Ｙは式（２５）および式（２６）のように表現される。

【００５１】
式（２５）および式（２６）から明らかなように、基準座標系Ｏ−ＸＹ上の手先軸４の実測位置Ｐ（Ｘ，Ｙ）は、ロボットの据付誤差Ｐｂ（Ｘｂ，Ｙｂ，θｂ）と、目標指令位置Ｐ０および幾何学誤差パラメータｅ、すなわちｄＬ１，ｄＬ２，ｄθ１，ｄθ２に対して対応関係を持つ。
【００５２】
図４のステップＳＴ４では、計算機９は、手先軸４の多数のランダムな目標位置Ｐ０（Ｘ０，Ｙ０）をコントローラ８に指示し、コントローラ８がヒステリシス誤差補正関数により補正しながら手先軸４を多数のランダムな目標位置Ｐ０（Ｘ０，Ｙ０）に移動するように指令する。一方、計算機９は、各目標位置について移動後の手先軸４の実測位置Ｐ（Ｘ，Ｙ）を測定する。このようにして、多数の目標位置Ｐ０について、手先軸４の各目標位置Ｐ０（Ｘ０，Ｙ０）と測定された位置Ｐ（Ｘ，Ｙ）を記録する。
【００５３】
次に計算機９は、手先軸４の測定された各位置と手先軸４の各目標位置に基づいて、幾何学誤差を算出する（図４のステップＳＴ５）。具体的には、これらの多数の目標位置Ｐ０（Ｘ０，Ｙ０）、基準座標系Ｏ−ＸＹ上の多数の実測位置Ｐ（Ｘ，Ｙ）および理想幾何学パラメータｖ（＝Ｌ１，Ｌ２，θ１，θ２）を式（２３）および式（２４）に代入し、最小自乗法を使用することにより、ロボットの据付誤差Ｐｂ（Ｘｂ，Ｙｂ，θｂ）および幾何学誤差パラメータｅ（＝ｄＬ１，ｄＬ２，ｄθ１，ｄθ２）を算出する。
【００５４】
このようにしてロボットの据付誤差Ｐｂと幾何学誤差パラメータｅが分かれば、幾何学誤差を相殺するために目標位置指令を補正する方式を定めることができる。前述の通り、ロボット座標系Ｏ’−Ｘ’Ｙ’で目標指令位置Ｐ０（Ｘ０，Ｙ０）に従ってモータを駆動しても、ロボット座標系Ｏ’−Ｘ’Ｙ’で手先軸４の位置はＰｒ（Ｘｒ，Ｙｒ）になり、ＰｂとＰｒの結果として基準座標系Ｏ−ＸＹでの手先軸４の位置はＰ（Ｘ，Ｙ）になる。これを別の観点からいえば、ロボット座標系Ｏ’−Ｘ’Ｙ’で手先軸４の位置が図６のＰｒｃであれば、ＰｂとＰｒｃの結果として基準座標系Ｏ−ＸＹでの手先軸４の位置は目標位置Ｐ０（Ｘ０，Ｙ０）になる。つまり、基準座標系Ｏ−ＸＹで目標位置Ｐ０に手先軸４を移動させるべきときには、手先軸４をロボット座標系Ｏ’−Ｘ’Ｙ’で位置Ｐｒｃに実際に移動させればよい。ロボット座標系Ｏ’−Ｘ’Ｙ’において目標指令位置Ｐ０（Ｘ０，Ｙ０）に対応した手先軸４の実際の位置がＰｒ（Ｘｒ，Ｙｒ）であることは、一般式（１５）で表現できるので、一般式（１５）のロボット座標系Ｏ’−Ｘ’Ｙ’上の実際の手先軸４の位置ＰｒをＰｒｃで置き換え、モータに指令するための目標指令位置Ｐ０をＰｃで置き換えると式（２７）が得られる。
Ｐｒｃ＝ｇ（Ｐｃ，ｖ＋ｅ） （２７）
【００５５】
また、式（２１）の基準座標系Ｏ−ＸＹ上の手先軸４の位置Ｐ（Ｘ，Ｙ）を真の目標位置Ｐ０で置き換え、ロボット座標系Ｏ’−Ｘ’Ｙ’上の実際の手先軸４の位置ＰｒをＰｒｃで置き換えると式（２８）が得られる。
Ｐ０＝Ｐｂ・Ｐｒｃ （２８）
【００５６】
従って、ロボットの据付誤差Ｐｂが同定できれば、基準座標系Ｏ−ＸＹ内の手先軸４の真の目標指令位置Ｐ０からロボット座標系Ｏ’−Ｘ’Ｙ’内の目標位置Ｐｒｃを求めることができる。さらに、幾何学誤差パラメータｅが同定できれば、ロボット座標系Ｏ’−Ｘ’Ｙ’内の目標位置Ｐｒｃを実現するための目標指令位置Ｐｃを求めることができる。このように基準座標系Ｏ−ＸＹ内の手先軸４の真の目標指令位置Ｐ０からロボット座標系Ｏ’−Ｘ’Ｙ’上で有効な目標指令位置Ｐｃを得る関数を、ここでは幾何学誤差補正関数という。コントローラ８は、幾何学誤差補正関数に基づいて、真の目標指令位置Ｐ０をロボット座標系Ｏ’−Ｘ’Ｙ’上で有効な目標指令位置Ｐｃに設定し直して、モータを制御すれば、幾何学誤差を相殺することができる。
【００５７】
図４のステップＳＴ６で、計算機９は、ロボットの据付誤差Ｐｂと幾何学誤差パラメータｅに基づいて、幾何学誤差を相殺するための幾何学誤差補正関数を決定し、コントローラ８に通知し、コントローラ８はこれを内部に記憶する。これによりコントローラ８はヒステリシス誤差に加えて幾何学誤差を補正しながら手先軸４の任意の目標位置から各アーム２，３の目標角度位置を換算することが可能になる。つまり、コントローラ８は、アームを移動させるときに、幾何学誤差補正関数を用いて幾何学誤差を排除した手先軸４の真の目標指令位置を算出でき、真の目標指令位置に対応する指令角度位置に従ってアーム２，３を駆動することにより、手先軸４の水平方向位置決め誤差から幾何学誤差を除去することができる。このようにしてヒステリシス誤差の補正に加えて幾何学誤差の補正が完了する。
【００５８】
幾何学誤差の補正完了後、計算機９は、残留誤差算出のために手先軸４の位置を測定し（図４のステップＳＴ７）、残留誤差を算出し（ステップＳＴ８）、残留誤差に含まれた非モデル化誤差を相殺するための非モデル化誤差補正関数（残留誤差補正関数）を決定する（ステップＳＴ９）。
【００５９】
実際のロボットで生じるリンク要素の機械的な誤差の要因としては、前述の幾何学誤差パラメータｅとして使用したアームの長さの誤差およびアームの回転角度誤差だけでなく、回転関節軸２ａ，３ａのねじれや偏心などの幾何学的要因が全て含まれうる。理論的には、前述の幾何学誤差に関連する幾何学誤差パラメータｅに、関節軸のねじれや偏心を含めることも考えられる。しかし、一般に、誤差パラメータｅとして関節軸のねじれや偏心まで考慮しても、計算モデルが複雑となり、誤差パラメータの同定精度が向上するわけではない。そこで、この実施の形態では、適当な個数のパラメータによるモデルで表現しやすいアームの長さの誤差およびアームの回転角度誤差のみを前述の幾何学誤差パラメータｅとして考慮した。そして、幾何学誤差パラメータｅから除外した幾何学的な誤差要因による誤差は、非モデル化誤差として補正する。
【００６０】
また、この実施の形態では、非モデル化誤差には、前述の関節軸のねじれまたは偏心といった幾何学誤差に加えて、アームの重力によるたわみによる誤差のほか、例えば減速歯車装置などの運動伝達機構内で生じる明確な規則的変化傾向を呈しない伝達誤差に起因する誤差などが含まれている。ただし、重力によるたわみのようにモデルで表現することが可能な誤差要因については、非モデル化誤差から分離して取扱ってもよい。ロボットの構造強度と負荷の関係によっては、この種の誤差要因を非モデル化誤差から分離する方が好ましい場合も考えられる。
【００６１】
ステップＳＴ７では、計算機９は、手先軸４のランダムな複数の目標指令位置Ｐｃ（Ｘｃ，Ｙｃ）をコントローラ８に指示し、コントローラ８は、ヒステリシス誤差補正関数および幾何学誤差補正関数により補正しながら手先軸４をランダムな複数の目標指令位置Ｐｃ（Ｘｃ，Ｙｃ）に移動するように指令する。計算機９は、手先軸４の各目標位置Ｐｃ（Ｘｃ，Ｙｃ）に対応する各アーム２，３の各目標角度位置θ１ｃ，θ２ｃを記録する一方、各目標位置Ｐｃについて移動後の各アーム２，３の各角度位置θ１ａ，θ２ａを測定し、各角度位置θ１ａ，θ２ａを記録する。このようにして、多数の目標位置Ｐｃについて、アーム２，３の各目標角度位置θ１ｃ，θ２ｃと測定された角度位置θ１ａ，θ２ａを記録する。
【００６２】
目標指令位置Ｐｃ（Ｘｃ，Ｙｃ）をロボットに与えた時の手先軸４の水平方向実測位置がＰａ（Ｘａ，Ｙａ）であったとすると、ＰｃおよびＰａに対応する関節角度は、式（２９）および式（３０）のように表される。
（θ１ｃ，θ２ｃ）＝ｆ（Ｘｃ，Ｙｃ） （２９）
（θ１ａ，θ２ａ）＝ｆ（Ｘａ，Ｙａ） （３０）
【００６３】
ステップＳＴ８では、計算機９は、各アーム２，３の移動後の測定された各角度位置θ１ａ，θ２ａと各アーム２，３の各目標角度位置θ１ｃ，θ２ｃとの相違をいまだに残留している残留誤差（第１の残留誤差）θｅ１，θｅ２として算出する。各アーム２，３の関節角度に換算した残留誤差θｅ１，θｅ２は式（３１）および式（３２）のように表すことができる。
θｅ１＝θ１ａ−θ１ｃ （３１）
θｅ２＝θ２ａ−θ２ｃ （３２）
【００６４】
ステップＳＴ８で算出された残留誤差θｅ１，θｅ２は、非モデル化誤差と角度伝達誤差を含んでいる。前述のように、非モデル化誤差はモデルで表現するのが困難な誤差であり、ロボット動作範囲内でアームの個々の角度位置に依存するが、角度伝達誤差とは異なり明確な規則的変化傾向は呈しない。他方、角度伝達誤差は、運動伝達機構の部品の寸法精度およびそれらの部品の取付精度に起因する位置決め誤差であり、アームの角度位置に依存した規則的変化傾向を呈する。
また、一般に角度伝達誤差は非モデル化誤差よりもかなり小さい場合が多い。
【００６５】
図４のステップＳＴ９では、計算機９は、ステップＳＴ８で算出された残留誤差θｅ１，θｅ２の集合に基づいて、残留誤差θｅ１，θｅ２に含まれた非モデル化誤差θｍ１，θｍ２を相殺するための非モデル化誤差補正関数（残留誤差補正関数）を決定する。非モデル化誤差は、一般に角度伝達誤差よりもかなり大きく、角度伝達誤差よりも角度に対する変化が少ないので、この段階では、残留誤差θｅ１，θｅ２を非モデル化誤差θｍ１，θｍ２であると仮定して取り扱う。そして、非モデル化誤差を表す数式モデルは、式（３３）および式（３４）に示すようなアーム２，３の目標関節角θ１ｃ，θ２ｃに関する関数で表現する。
【００６６】
θｅ１＝θｍ１＝ｆｍ１（θ１ｃ，θ２ｃ） （３３）
θｅ２＝θｍ２＝ｆｍ２（θ１ｃ，θ２ｃ） （３４）
ここでｆｍ１およびｆｍ２は、それぞれアーム２，３の目標関節角θ１ｃ，θ２ｃから非モデル化誤差θｍ１，θｍ２を算出できる非モデル化誤差補正関数である。非モデル化誤差補正関数ｆｍ１およびｆｍ２は、多項式で表現することができ、多項式の次数は所望の補正効果に応じて決定すればよいが、例えば式（３５）および式（３６）のような２元３次多項式で表現することが可能である。
【００６７】

【００６８】
ここで、ｋ１０１〜ｋ２１０は実測結果に基づき同定される係数である。係数ｋ１０１〜ｋ２１０を求めることにより非モデル化誤差補正関数ｆｍ１およびｆｍ２が確定する。式（３５）の係数ｋ１０１〜ｋ１１０については、多数の（ｎ個の）目標位置について得られた残留誤差θｅ１_１〜θｅ１_ｎの数（ｎ個）分だけ、式（３５）を連立する。これを行列の乗算で表現すると式（３７）のようになる。
【数６】

【００６９】
ここでθ１ｃ_１〜θ１ｃ_ｎはｎ個の目標位置についての第１のアーム２の目標関節角、θ２ｃ_１〜θ２ｃ_ｎはｎ個の目標位置についての第２のアーム３の目標関節角である。残留誤差θｅ１_１〜θｅ１_ｎ（すなわち非モデル化誤差θｍ１_１〜θｍ１_ｎ）と記録されたアーム２の目標関節角θ１ｃ_１〜θ１ｃ_ｎおよびアーム３の目標関節角θ２ｃ_１〜θ２ｃ_ｎを式（３５）に代入すると、一般的な線形表現になる。従って、多数の連立方程式から最小自乗法により、未知の係数ｋ１０１〜ｋ１１０を求めることができる。
【００７０】
すなわち式（３７）は式（３８）の形式で表現でき、式（３９）によりｐ１の最小自乗解を求めることができる。
θｍ１＝Ｍ１・ｐ１ （３８）
ｐ１＝［（Ｍ１^Ｔ・Ｍ１）^−１・Ｍ１^Ｔ］・θｍ１ （３９）
ここで、θｍ１は式（３７）の左辺のｎ行ベクトル、Ｍ１は式（３７）の右辺のｎ×１０行列、ｐ１は係数ｋ１０１〜ｋ１１０を表す式（３７）の右辺の１０行ベクトルである。このようにして非モデル化誤差補正関数ｆｍ１が決定される。同様にして式（３７）を連立して解くことにより、係数ｋ２０１〜ｋ２１０を求め、非モデル化誤差補正関数ｆｍ２を決定することができる。
【００７１】
次に、計算機９は、計算上の非モデル化誤差（計算上の各残留誤差）を算出し（図４のステップＳＴ１０）、角度伝達誤差を算出し（ステップＳＴ１１）、角度伝達誤差補正関数を決定して角度伝達誤差補正関数および非モデル化誤差補正関数をコントローラ８に通知し、コントローラ８はこれらを内部に記憶する（ステップＳＴ１２）。
【００７２】
まずステップＳＴ１０で、計算機９は、ステップＳＴ９で求めた非モデル化誤差補正関数ｆｍ１およびｆｍ２を内部に記録し、続いて非モデル化誤差補正関数ｆｍ１およびｆｍ２を用いて、アーム２の各目標関節角θ１ｃ_１〜θ１ｃ_ｎおよびアーム３の各目標関節角θ２ｃ_１〜θ１ｃ_ｎを代入して、計算上の非モデル化誤差（計算上の各残留誤差）θｍ１_１’〜θｍ１_ｎ’，θｍ２_１’〜θｍ２_ｎ’を算出する。続いて計算機９は、ステップＳＴ８で算出された各残留誤差θｅ１_１’〜θｅ１_ｎ’，θｅ２_１’〜θｅ２_ｎ’と計算上の各非モデル化誤差θｍ１_１’〜θｍ１_ｎ’，θｍ２_１’〜θｍ２_ｎ’との相違である各角度伝達誤差（第２の残留誤差）θｇ１_１〜θｇ１_ｎ，θｇ２_１〜θｇ２_ｎを算出する（ステップＳＴ１１）。一般的に角度伝達誤差θｇ１，θｇ２を表現すると、式（４０）および式（４１）のようになる。
θｇ１＝θｅ１−θｍ１’ （４０）
θｇ２＝θｅ２−θｍ２’ （４１）
【００７３】
上記の通り、非モデル化誤差補正関数ｆｍ１およびｆｍ２を決定するときには、式（３３）〜式（３６）のように、ステップＳＴ８で求めた残留誤差θｅ１，θｅ２を非モデル化誤差θｍ１，θｍ２と等しいと仮定して取り扱うが、非モデル化誤差補正関数ｆｍ１およびｆｍ２は、多項式表現および最小自乗法による解法により、角度伝達誤差の規則的変化が平均化されている。このため、非モデル化誤差補正関数ｆｍ１およびｆｍ２から算出された計算上の非モデル化誤差θｍ１’，θｍ２’も、規則的に変化する角度伝達誤差成分を含まないと考えられる。実際に、非モデル化誤差θｍ１’，θｍ２’は、ステップＳＴ８で求めた残留誤差θｅ１，θｅ２と一致せず、式（４０）および式（４１）で求められた角度伝達誤差θｇ１_１〜θｇ１_ｎ，θｇ２_１〜θｇ２_ｎは規則性を有する。
【００７４】
図４のステップＳＴ１２で計算機９は、各角度伝達誤差に基づいて、角度伝達誤差補正関数を決定する。上記の通り、角度伝達誤差は、運動伝達機構の精度（部品の寸法精度および部品の取付精度）の誤差に起因し、各アーム２，３の位置に依存して変化する規則性の高い位置決め誤差である。規則性の高い角度伝達誤差θｇ１，θｇ２は、運動伝達機構の精度の誤差に依存するため、運動伝達機構の回転要素の回転角度の関数として、式（４２）および式（４３）で表現できる。
【００７５】
θｇ１＝Ａ１・ｓｉｎ（ω・θ１０＋φ１） （４２）
θｇ２＝Ａ２・ｓｉｎ（ω・θ２０＋φ２） （４３）
ここで、Ａ１，Ａ２，φ１，φ２は係数であり、ωは運動伝達機構（例えば減速歯車装置）の入力軸回転周期と角度伝達誤差の発生周期の比である。比ωは式（４４）で求められる。
【００７６】
ω＝ｎ・Ｎｇ （４４）
ここでｎは、角度伝達誤差の発生周期に対応して決まる整数であり、Ｎｇは運動伝達機構の減速比である。例えば、減速歯車装置の入力軸回転と同じ周期で発生する角度伝達誤差であればｎ＝１となりω＝Ｎｇであり、入力回転周期の半分の周期で発生する角度伝達誤差であればｎ＝２となりω＝２Ｎｇである。
【００７７】
係数Ａ１，Ａ２，φ１，φ２を求めることにより角度伝達誤差補正関数が確定する。式（４２）の係数Ａ１，φ１については、多数の（ｎ個の）目標位置について得られた角度伝達誤差θｇ１_１〜θｇ１_ｎの数（ｎ個）分だけ、式（４２）を連立する。式（４２）は非線形表現であるため、例えばガウス・ニュートン法により、係数Ａ１，φ１の最小自乗解を求めることができる。同様にして、式（４３）の係数Ａ２，φ２の最小自乗解を求めることができる。このようにして角度伝達誤差補正関数を決定する。
【００７８】
角度伝達誤差補正関数の決定終了後、計算機９はコントローラ８に非モデル化誤差補正関数ｆｍ１，ｆｍ２と角度伝達誤差補正関数を通知し、コントローラ８はこれらを内部に記憶する。これによりコントローラ８は、ヒステリシス誤差と幾何学誤差に加えて、非モデル化誤差と角度伝達誤差を補正しながら手先軸４の目標位置から各アーム２，３の目標角度位置を換算することが可能になる。つまり、コントローラ８は、アームを移動させるときに、非モデル化誤差補正関数ｆｍ１，ｆｍ２を用いて非モデル化誤差θｍ１，θｍ２を算出し、角度伝達誤差補正関数を用いて角度伝達誤差θｇ１，θｇ２を算出し、目標指令位置に対応するアーム２，３の関節角度の各々から非モデル化誤差θｍ１，θｍ２と角度伝達誤差θｇ１，θｇ２を減算することにより指令角度位置を補正でき、補正された指令角度位置に従ってアーム２，３を駆動することにより、手先軸４の水平方向位置決め誤差から非モデル化誤差と角度伝達誤差を除去することができる。このようにしてヒステリシス誤差と幾何学誤差の補正に加えて非モデル化誤差と角度伝達誤差の補正が完了する。
【００７９】
以上のように、この実施の形態１では、誤差要因の同定に際して極力他の誤差要因の影響が含まれないようにするため、動作の方向や移動量に対して規則性のあるヒステリシス誤差を最初に補正し、次に誤差の絶対値が大きく平面幾何学的関係としてモデル化が容易な幾何学誤差を補正し、最後に絶対値が小さくモデル化が困難な非モデル化誤差および角度伝達誤差を補正する手順を踏んでいる。このような順番で４種類の誤差要因を補正することにより、減速歯車装置のような運動伝達機構を含む構成であっても、同定したい誤差要因に他の誤差要因が含まれる影響を小さくできるため、高い精度で所望の誤差を補正することが可能となり、その結果高い位置決め精度のロボットを実現することができる。
【００８０】
この実施の形態１では、非モデル化誤差と運動伝達機構の角度伝達誤差という異なる２つの誤差を同じデータ（残留誤差θｅ１，θｅ２）を用いて同定しているが、次の理由により同定結果に与える影響は無視できる。すなわち、非モデル化誤差の方が角度伝達誤差に比べて関節角度に対する誤差変動は緩やかであり、角度伝達誤差を含んだデータから非モデル化誤差を同定しても、角度伝達誤差の周期的誤差が非モデル化誤差では平均化され、同定結果はほとんど影響を受けないからである。
【００８１】
また、この実施の形態では、位置測定に光学式平面グリッドエンコーダを使用することにより極めて高い精度の測定データが得られ、前記の誤差同定手順と組合わせることにより、簡便な構成で正確な同定結果を得ることが可能となる。特に微小な誤差要因も正確に測定し同定することが可能となる。また全ての誤差要因を単一の測定手段により実施するので、計測装置を安価に構成でき誤差補正の自動化も容易となる。
【００８２】
実施の形態２．
実施の形態１では、残留誤差θｅ１，θｅ２から非モデル化誤差補正関数ｆｍ１，ｆｍ２を求めた後、非モデル化誤差補正関数ｆｍ１，ｆｍ２を用いて算出された計算上の非モデル化誤差θｍ１’，θｍ２’を残留誤差θｅ１，θｅ２から差し引くことにより、角度伝達誤差θｇ１，θｇ２を算出する（式（４０）および式（４１））。しかし、この発明の実施の形態２として、次の手順を採用してもよい。
【００８３】
図８のフローチャートに従って、この実施の形態２で実行するロボット位置決め誤差補正方法を説明する。ここでも簡略化のため図１に示す水平多関節ロボットの手先軸４の水平方向位置のみについて説明する。まず、実施の形態１と同様に、計算機９はヒステリシス誤差補正関数、幾何学誤差補正関数および非モデル化誤差補正関数を決定する（ステップＳＴ１〜ステップＳＴ９）。
【００８４】
ただし、実施の形態１と異なり、ステップＳＴ９の後、補正関数の決定終了後、計算機９はコントローラ８に非モデル化誤差補正関数ｆｍ１，ｆｍ２を通知し、コントローラ８はこれらを内部に記憶する。これによりコントローラ８は、ヒステリシス誤差と幾何学誤差に加えて、非モデル化誤差を補正しながら手先軸４の目標位置から各アーム２，３の目標角度位置を換算することが可能になる。つまり、コントローラ８は、アームを移動させるときに、非モデル化誤差補正関数ｆｍ１，ｆｍ２を用いて非モデル化誤差θｍ１，θｍ２を算出し、目標指令位置に対応するアーム２，３の関節角度の各々から非モデル化誤差θｍ１，θｍ２を減算することにより指令角度位置を補正でき、補正された指令角度位置に従ってアーム２，３を駆動することにより、手先軸４の水平方向位置決め誤差から非モデル化誤差を除去することができる。このようにしてヒステリシス誤差と幾何学誤差の補正に加えて非モデル化誤差の補正が完了する。
【００８５】
非モデル化誤差の補正完了後、計算機９は、角度伝達誤差算出のために手先軸４の位置を測定し（ステップＳＴ１３）、角度伝達誤差（第２の残留誤差）を算出し（ステップＳＴ１４）、角度伝達誤差を相殺するための角度伝達誤差補正関数（残留誤差補正関数）を決定する（ステップＳＴ１５）。
【００８６】
ステップＳＴ１３では、ステップＳＴ７と同様に、計算機９は、手先軸４のランダムな複数の目標指令位置Ｐｃ（Ｘｃ，Ｙｃ）をコントローラ８に指示し、コントローラ８は、手先軸４をランダムな複数の目標指令位置Ｐｃ（Ｘｃ，Ｙｃ）に移動するように指令する。ただし、コントローラは、目標指令位置Ｐｃ（Ｘｃ，Ｙｃ）を、ヒステリシス誤差補正関数、幾何学誤差補正関数および非モデル化誤差補正関数により補正する。計算機９は、手先軸４の各目標位置Ｐｃ（Ｘｃ，Ｙｃ）に対応する各アーム２，３の各目標角度位置θ１ｃ，θ２ｃを算出する一方、各目標位置Ｐｃについて移動後の各アーム２，３の各角度位置θ１ａ，θ２ａを測定し、各角度位置θ１ａ，θ２ａを記録する。このようにして、多数の目標位置Ｐｃについて、アーム２，３の各目標角度位置θ１ｃ，θ２ｃと測定された角度位置θ１ａ，θ２ａを記録する。
【００８７】
ステップＳＴ１４では、計算機９は、各アーム２，３の移動後の測定された各角度位置θ１ａ，θ２ａと各アーム２，３の各目標角度位置θ１ｃ，θ２ｃとの相違をいまだに残留している第２の残留誤差として算出する。ステップＳＴ１４で算出された第２の残留誤差は、角度伝達誤差θｇ１，θｇ２である。各アーム２，３の関節角度に換算した角度伝達誤差θｇ１，θｇ２は式（４５）および式（４６）のように表すことができる。
θｇ１＝θ１ａ−θ１ｃ （４５）
θｇ２＝θ２ａ−θ２ｃ （４６）
【００８８】
ステップＳＴ１５では、実施の形態１のステップＳＴ１２と同様に、計算機９は、多数の目標位置について得られた各角度伝達誤差θｇ１，θｇ２に基づいて、角度伝達誤差補正関数を決定する。角度伝達誤差補正関数の決定終了後、計算機９はコントローラ８に角度伝達誤差補正関数を通知し、コントローラ８はこれを内部に記憶する。このようにしてヒステリシス誤差と幾何学誤差と非モデル化誤差の補正に加えて、角度伝達誤差の補正が完了する。
【００８９】
この実施の形態２の手順によれば、最後に補正する角度伝達誤差を残留誤差から計算上の非モデル化誤差を差引いて得るのではなく、新たな位置測定に基づいて単独で決定するため、角度伝達誤差の補正の精度を高める効果が期待できる。
【００９０】
実施の形態３．
また、平面グリッドエンコーダによる位置測定においてグリッドプレート６の領域を超える広い範囲にわたって手先軸４を移動させてその位置を測定し、その結果に基づき誤差補正を行うことも可能である。この場合は、グリッドプレート６を移動させて停止した位置で、手先軸４の位置測定を行えばよい。
【００９１】
具体的には、グリッドプレート６のロボットベース１に対する位置、即ち据付誤差Ｐｂはグリッドプレート６の各停止位置で個別に同定し、それ以外の誤差についてのパラメータ、即ちロボット本体の幾何学誤差ｅ、ヒステリシス誤差補正関数の係数、非モデル化誤差補正関数の係数、および角度伝達誤差補正関数の係数としては、グリッドプレート６の複数の停止位置での測定結果から同定された係数の平均値を用いればよい。なお、ヒステリシス誤差補正関数については、関節角に依存せず式（１１）および式（１２）のように移動角のみの関数として表現できると仮定すれば、グリッドプレート６の一つの停止位置で同定すればよい。
【００９２】
実施の形態３に係る方法によれば、平面グリッドエンコーダの有限な位置測定範囲を超える広い動作範囲わたって高精度なロボットの位置決め誤差補正を行うことが可能となる。
【００９３】
前述の実施の形態では、４自由度水平多関節ロボットの手先軸４の水平方向位置の誤差補正を行っているが、前述の実施の形態はこの発明の理解を容易にするために例示したに過ぎない。前述の実施の形態を変形および修正した方法により、垂直多関節ロボットまたはその他の多関節ロボット、さらには回転関節型に限らずボールネジ送り機構を用いた直動型のロボットのエンドエフェクタの位置決め誤差を補正することができる。
【００９４】
また、前述の実施の形態では、光学式平面グリッドエンコーダを好ましい測定手段の例として使用しているが、他の高精度の測定手段、例えば３次元位置計測装置等を使用してもよい。
【００９５】
また、前述の実施の形態では、ヒステリシス誤差補正関数から幾何学誤差補正関数、非モデル化誤差補正関数を経て、角度伝達誤差補正関数に至る順序で補正関数を決定するが、ヒステリシス誤差が無視できるロボットである場合には、幾何学誤差補正関数から非モデル化誤差補正関数を経て、角度伝達誤差補正関数に至る順序で補正関数を決定してもよい。
【００９６】
【発明の効果】
以上説明したように、本発明によれば、様々な要因に起因する様々な種類の位置決め誤差を減少させることが可能である。
【図面の簡単な説明】
【図１】この発明の実施の形態１に係るロボット位置決め誤差補正装置が使用されるロボットの例を示す斜視図である。
【図２】ロボットのアームを連続的に回転移動させながらその角度位置を測定した結果の集合である移動特性曲線を示すグラフである。
【図３】図２の移動特性曲線から抽出された角度伝達誤差の変化を示すグラフである。
【図４】実施の形態１で実行するロボット位置決め誤差補正方法を示すフローチャートである。
【図５】図１に示す水平多関節ロボットの要素を簡略化して示す平面図であり、（ａ）は移動開始位置、（ｂ）は目標位置、（ｃ）は実際の移動後の位置、（ｄ）は（ｂ）と同じ目標位置に他の移動開始位置移動させた場合の実際の移動後の位置を示す図である。
【図６】この発明の実施の形態で行う幾何学誤差補正を説明するために、図１に示す水平多関節ロボットの手先位置を示す図である。
【図７】この発明の実施の形態で使用する理想幾何学パラメータおよび幾何学誤差パラメータを説明するために、図１に示す水平多関節ロボットの要素を簡略化して示す平面図である。
【図８】実施の形態２で実行するロボット位置決め誤差補正方法を示すフローチャートである。
【符号の説明】
１ ロボットベース、２ 第１のアーム（リンク要素）、２ａ 回転関節軸、３ 第２のアーム（リンク要素）、３ａ 回転関節軸、３ｂ 回転関節軸、４ 手先軸（リンク要素）、５ 読取りヘッド、６ グリッドプレート、６ａ プレートベース、７ 作業台、８ コントローラ、９ 計算機（ロボット位置決め誤差補正装置）、１０ 通信回線。[0001]
BACKGROUND OF THE INVENTION
The present invention relates to a robot positioning error correction apparatus for teaching a robot information necessary for correcting a command value based on a measured position of the robot.
[0002]
[Prior art]
As a conventional robot positioning error correction method, for example, there is one disclosed in Patent Document 1. In the method described in this document, the hand positioning error calculated by the static stiffness analysis model is separated into a geometric error and a deflection error, and after correcting the geometric error, the deflection error is corrected.
[0003]
[Patent Document 1]
JP-A-4-33006 (pages 3 to 5, FIGS. 14 and 16)
[0004]
[Problems to be solved by the invention]
The above-mentioned robot positioning error correction method may be effective when geometric errors and deflection errors are the majority as positioning error components, but in general real robots, it is sufficient for other error factors. An error correction effect cannot be obtained. For example, in a robot including a transmission element such as a reduction gear device for driving the arm, there are various other error factors due to the transmission element.
[0005]
The present invention has been made to solve the above-described problems, and an object of the present invention is to provide a robot positioning error correction apparatus capable of reducing various types of positioning errors caused by various factors. .
[0006]
[Means for Solving the Problems]
A robot positioning error correction device according to the present invention includes at least two link elements coupled to each other, a drive device that drives the link element, and a motion transmission mechanism that transmits motion from the drive device to each link element. In the robot positioning error correction apparatus for correcting the positioning error of the robot, the movement of each link element recorded for a number of target positions is repeated by repeatedly moving each link element from the different direction to the same target position. Based on each measured position and each position before movement, a hysteresis error correction function that is a function related to the position change of the link element to cancel the hysteresis error that is a positioning error depending on the position before movement of each link element And a hysteresis error correction function determination unit for determining the hysteresis error correction function. The hysteresis error differs from each measured position and each target position after movement of the link element recorded by moving at least one link element to a plurality of positions in a state corrected by And a second error correction function determining unit that determines a second error correction function for reducing the error.
[0007]
DETAILED DESCRIPTION OF THE INVENTION
Hereinafter, various embodiments according to the present invention will be described with reference to the drawings.
Embodiment 1 FIG.
FIG. 1 is a perspective view showing an example of a robot in which the robot positioning error correction apparatus according to Embodiment 1 of the present invention is used. This robot is a four-degree-of-freedom horizontal articulated robot, a columnar robot base 1 fixed to a horizontal flat work table 7 and a horizontal base connected to the robot base 1 so as to be rotatable around a rotary joint axis 2a. A first arm (link element) 2 extending horizontally, a second arm (link element) 3 extending horizontally connected to the first arm 2 so as to be rotatable about a rotary joint axis 3a, and a second arm 3 And a vertically extending hand shaft (link element) 4. The hand shaft 4 can move up and down along the rotary joint axis 3b and can rotate around the rotary joint axis 3b.
[0008]
Although not shown, the arms 2 and 3 are driven by a dedicated motor as a driving device, and motion is transmitted from each motor to each arm by a reduction gear device or a belt transmission device as a motion transmission mechanism. The hand shaft 4 is moved up and down by a motor for vertical movement and a ball screw feed mechanism (motion transmission mechanism), and is rotated by a motor for rotational movement and a reduction gear device or a belt transmission device.
[0009]
These motors are driven in accordance with a command given from the controller 8. The controller 8 is a control device attached to the robot, and operates according to instructions for operating the robot. For example, when a command to move the hand axis 4 in the horizontal direction is given, the controller 8 causes the target angle position (target joint angle) of the arms 2 and 3 expressed as joint angles for moving the hand axis 4 in a two-dimensional plane. Is calculated, each motor is commanded based on each target designation position, and the arms 2 and 3 are rotated. Thus, when the controller 8 moves the hand shaft 4 in the horizontal direction, it actually gives a command to the motor in accordance with the target angular position of the arms 2 and 3.
[0010]
This embodiment uses an optical planar grid encoder to perform measurements that are used for positioning error correction. The optical planar grid encoder includes a grid plate 6 having a grid pattern with different reflectivities, and a read head 5 that irradiates the grid plate 6 with light and optically reads the reflected light from the grid plate 6. The position of the read head 5 relative to the grid plate 6 can be converted according to the intensity of the reflected light read by the head 5. An end effector is attached to the lower end of the hand shaft 4 during work, but a read head 5 is attached during measurement. A plate base 6 a that horizontally supports the grid plate 6 is installed on the work table 7. With this configuration, as long as the hand axis 4 moves within the range of the grid plate 6, the two-dimensional position of the hand axis 4 can be measured.
[0011]
An output signal of the read head 5 representing the intensity of the reflected light read by the read head 5 is supplied to a computer (robot positioning error correction device) 9. This computer 9 is not a computer attached to the robot but a general-purpose computer, and is used for measuring the robot positioning error, calculating the error correction function, and correcting the robot operation and the measurement result in cooperation. Based on the output signal of the read head 5, the calculator 9 calculates the position of the read head 5, that is, the position of the hand shaft 4, and further, based on the position of the hand shaft 4, the positions of the arms 2 and 3 expressed as joint angles. Is calculated. In this way, the calculator 9 measures the angular position (joint angle) of the arms 2 and 3 every time the position of the hand shaft 4 is measured.
[0012]
The computer 9 is connected to the controller 8 via a communication line 10. The controller 8 moves the hand shaft 4 in the horizontal direction in accordance with an instruction from the computer 9. Further, the computer 9 can notify the controller 8 of various error correction functions to be described later via the communication line 10. When the error correction function is supplied, the controller 8 stores the error correction function therein, and corrects the target position of the hand shaft 4 or the target angular position of each arm 2, 3 according to this.
[0013]
Now, end effector positioning errors that can occur in an articulated robot can be classified into hysteresis errors, angular transmission errors, geometric errors, and non-modeling errors. The hysteresis error is a positioning error that depends on the position of each arm before the movement due to the irreversible motion of the motion transmission mechanism. For example, the hysteresis error is due to backlash or elastic deformation of the reduction gear device or timing belt / timing pulley, or friction of the bearing portion or the like. The hysteresis error appears as a phenomenon in which the stop position fluctuates depending on the direction of movement and the movement distance to reach that position even if the same command position is given. FIG. 2 is a graph showing a concept of a movement characteristic curve that is a set of results obtained by measuring the angular position of the arm while continuously rotating and moving the arm. As shown in FIG. 2, the actual angle when the command angle is decreased due to a hysteresis error is different from the actual angle when the command angle is increased.
[0014]
The angle transmission error is a positioning error caused by an error in the accuracy of the motion transmission mechanism (part dimensional accuracy and component mounting accuracy), and depends on a rotation angle of a rotation element (for example, a gear or a pulley) of the motion transmission mechanism. For example, the angle transmission error is due to the dimensional accuracy and meshing error of the reduction gear device or timing belt / timing pulley teeth. In FIG. 2, an angle transmission error appears as a fluctuation in the waveform that overlaps the gradient of the actual movement characteristic curve. FIG. 3 shows the concept of the angle transmission error obtained by extracting the variation in the gradient of the movement characteristic curve by differentiation. As shown in FIG. 3, the angle transmission error exhibits a regular change tendency depending on the angular position of the arm, specifically, a substantially sinusoidal tendency.
[0015]
Geometric errors include link element shape error and positional error (link element length error and link element rotation angle error resulting therefrom) and robot origin installation error (specifically, the robot shown in FIG. 1). Is a positioning error caused by the installation error of the rotary joint shaft 2a. The geometric error is a large error component compared to other error components.
[0016]
Unmodeled errors are unmodeled errors due to other factors or errors that are difficult to express in the model. For example, when the link mechanism shown in FIG. 1 is expressed by a planar two-dimensional model, errors caused by other twisting or eccentricity of the joint axis, deflection of the arm due to gravity, and other errors occurring in the motion transmission mechanism are included in this. Equivalent to. The non-modeling error depends on the individual angular position of the arm within the robot movement range, but does not exhibit a clear regular change tendency unlike the angular transmission error.
[0017]
In this embodiment, after obtaining an error correction function for correcting an error factor that can be easily separated from other error factors, it repeatedly obtains an error correction function for correcting other error factors. Use the method. Specifically, the calculator 9 calculates a hysteresis error correction function that is a function related to the angular position change of the arms 2 and 3 for canceling the hysteresis error, and then calculates a geometric error that is a function for canceling the geometric error. Determining a scientific error correction function, further determining a non-modeling error correction function (residual error correction function) that is a function of each position of each arm to reduce the non-modeling error (first residual error); Finally, an angle transmission error correction function that is a function of each position of each arm for canceling the angle transmission error is determined.
[0018]
Next, the robot positioning error correction method executed in the first embodiment will be described with reference to the flowchart of FIG. For simplification, only the horizontal position of the hand axis 4 of the horizontal articulated robot shown in FIG. 1 will be described.
First, the calculator 9 measures the position of the hand axis 4 for calculating a hysteresis error (step ST1), calculates a hysteresis error (step ST2), determines a hysteresis error correction function, and notifies the controller 8 ( Step ST3).
[0019]
The hysteresis error usually appears as a phenomenon in which the movement distance is insufficient with respect to the target position due to backlash of the transmission mechanism. For this reason, by correcting the command value of the controller 8 by the shortage of the moving distance, the hysteresis error, that is, the fluctuation amount of the stop position is improved. Specifically, hysteresis error correction will be described with reference to FIGS. 5 (a) to 5 (d). FIGS. 5A to 5D are plan views showing simplified elements of the horizontal articulated robot shown in FIG. It is assumed that the hand shaft 4 is moved from the movement start position P1 (X1, Y1) shown in FIG. 5A to the target position P2 (X2, Y2) shown in FIG. The angular positions of the arms 2 and 3 corresponding to the movement start position P1 and the target position P2 are obtained as shown in Expression (1) and Expression (2) by coordinate system conversion calculation.
[0020]
(Θ11, θ12) = f (X1, Y1) (1)
(Θ21, θ22) = f (X2, Y2) (2)
As shown in the figure, θ11 is the angle of the first arm 2 at the start of movement around the rotary joint axis 2a relative to the base 1, and θ12 is the second arm at the start of movement around the rotary joint axis 3a relative to the first arm 2. 3, θ 21 is the angle of the target first arm 2 around the rotary joint axis 2 a relative to the base 1, and θ 22 is the angle of the target second arm 3 around the rotary joint axis 3 a relative to the first arm 2. . f is a function for performing coordinate conversion from an orthogonal coordinate system representing the horizontal position of the hand axis 4 to a joint coordinate system expressed as an angular position of the arms 2 and 3.
[0021]
The ideal position changes of the arms 2 and 3, that is, the movement angles Δθ1 and Δθ2 are expressed by equations (3) and (4).
Δθ1 = θ21−θ11 (3)
Δθ2 = θ22−θ12 (4)
[0022]
Actually, however, because of the hysteresis error, the hand shaft 4 moves from the movement start position P1 (X1, Y1) shown in FIG. 5A to the position P3 (X3, Y3) after the actual movement shown in FIG. 5C. ). The angular positions of the arms 2 and 3 after the movement are θ31 and θ32, respectively. As shown in FIG. 5D, even when the hand shaft 4 is moved from the other movement start position P1 ′ to the same target position P2, the actual position P3 ′ (X3 ′, Y3 ′) after the movement is obtained. It is different from the target position P2. The angular positions of the arms 2 and 3 after movement are θ31 ′ and θ32 ′, respectively.
[0023]
In step ST1 of FIG. 4, the computer 9 commands the controller 8 to move the hand axis 4 from different random directions (that is, from different movement start positions P1, P1 ′...) To the same target position P2. To do. The computer 9 calculates the movement start positions P1, P1 ′. . . While calculating a number of movement start angle positions (θ11, θ12) of arms 2 and 3 corresponding to, and target angle positions (θ21, θ22) of arms 2 and 3 corresponding to target position P2, aiming at the same target position P2 Positions P3, P3 ′,... Of the hand shaft 4 after moving from different directions. . . , And the measured positions P3, P3 ′. . . Based on the above, a large number of actual angular positions (θ31, θ31 ′... Θ32, θ32 ′...) After the movement of the arms 2 and 3 are calculated, and each of these angular positions (θ31, θ31 ′. .theta.32, .theta.32 '...) are recorded. By repeating this with respect to a large number of random target positions P2, the target angular positions (θ21, θ22) of the arms 2 and 3 and the measured angular positions (θ31, θ31 ′. (.Theta.32, .theta.32 '...) are recorded.
[0024]
Each position P3, P3 ′. . . Includes not only a hysteresis error component but also other error components. However, the hysteresis error changes depending not only on the stop position but also on the movement start position, while the geometric error, angle transmission error, and non-modeling error change only on the stop position after the movement. Target position P2 and stop positions P3, P3 ′. . . Is actually very small, components other than the hysteresis error are stopped positions P3, P3 ′,. . . It can be considered that it is the same anywhere and can be ignored.
[0025]
In step ST2 of FIG. 4, the calculator 9 calculates a hysteresis error based on each measured angular position and the target angular position after the movement of the arms 2 and 3 recorded for a large number of target positions. Specifically, the angular positions P3, P3,... After movement recorded for the same target position P2. . . A hysteresis error is calculated as the difference between each angular position (θ31, θ32) corresponding to the target angle position (θ21, θ22). That is, the hysteresis error for a certain target position P2 is obtained as shown in equations (5) to (8).
[0026]
Δθh1 = θ31−θ21 (5)
Δθh2 = θ32−θ22 (6)
Δθh1 ′ = θ31′−θ21 (7)
Δθh2 ′ = θ32′−θ22 (8)
Here, Δθh1 is a hysteresis error of the first arm 2 when the hand shaft 4 is moved from the movement start position P1 to the target position P2, and Δθh2 is a position where the hand shaft 4 moves from the movement start position P1 to the target position. The hysteresis error of the second arm 3 when moved to P2, and Δθh1 ′ is the hysteresis of the first arm 2 when the hand shaft 4 is moved from the movement start position P1 ′ to the target position P2. Δθh2 ′ is a hysteresis error of the second arm 3 when the hand shaft 4 is moved from the movement start position P1 ′ to the target position P2. A number of movement start positions P1, P1 ′. . . Is set, more hysteresis errors are calculated for one target position P2. Such a hysteresis error is calculated in the same manner for other target positions.
[0027]
In step ST3 of FIG. 4, the calculator 9 calculates hysteresis errors Δθh1, Δθh2, Δθh1 ′, Δθh2 ′. . . Based on the above, a hysteresis error correction function is determined to cancel the hysteresis error of the position of the hand shaft 4. The hysteresis error correction function is expressed as a function of the target angle position and the movement angle of the arms 2 and 3, that is, the position change, as in Expression (9) and Expression (10).
[0028]
θh1 = h1 (θ1, θ2, Δθ1, Δθ2) (9)
θh2 = h2 (θ1, θ2, Δθ1, Δθ2) (10)
Here, θh1 is a hysteresis error correction amount to be applied to the first arm 2 in order to cancel out the hysteresis error in the position of the hand shaft 4, and θh2 is second in order to cancel out the hysteresis error in the position of the hand shaft 4. This is a hysteresis error correction amount to be given to the arm 3. h1 is a hysteresis error correction function for arm 2, h2 is a hysteresis error correction function for arm 3, θ1 is a target angle position of arm 2, θ2 is a target angle position of arm 3, Δθ1 is a movement angle of arm 2, and Δθ2 is This is the movement angle of the arm 3.
[0029]
Individual hysteresis errors Δθh1, Δθh1 ′. . . So that the reciprocal numbers (−Δθh1, −Δθh1 ′...) Substantially coincide with the hysteresis error correction amount θh1, the computer 9 has a large number of target angular positions (θ21,. The hysteresis error correction function h1 is determined based on a large number of target angular positions (θ22,...) And the movement angles Δθ1 and Δθ2 of the arms 2 and 3. The type of the hysteresis error correction function h1 is not limited. For example, an appropriate function having θ1, θ2, Δθ1, and Δθ2 as variables may be selected in advance through experiments or analysis of a motion transmission mechanism. The algorithm for determining the hysteresis error correction function h1 is not limited, but, for example, the selected function is set to the obtained hysteresis errors Δθh1, Δθh1 ′. . . It is sufficient to determine the function using the least square method. Similarly, the hysteresis error correction function h2 can be determined.
[0030]
In a structure in which a load does not act in the horizontal direction in a stopped state, such as a horizontal articulated robot, the hysteresis error correction functions h1 and h2 do not depend on the joint angle, and the movement angle is as shown in Equation (11) and Equation (12). Can only be expressed as a function.
θh1 = h1 (Δθ1, Δθ2) (11)
θh2 = h2 (Δθ1, Δθ2) (12)
[0031]
In this case, the types of the hysteresis error correction functions h1 and h2 are not limited, but as specific examples, the equations (13) and (14) can be used.
[Expression 1]

[Expression 2]

[0032]
Here, k11 to k24 are constants. The obtained hysteresis errors Δθh1, Δθh1 ′. . . Equation (13) is connected as many as the number of .DELTA..theta.h1, .DELTA..theta.h1, .DELTA..theta.h1 '. . . The constants k11, k12, k21, and k22 are determined by substituting the reciprocal numbers of the above, substituting the command values of the controller 8 into θ1, θ2, Δθ1, and Δθ2 and solving a number of simultaneous equations by the method of least squares. Similarly, constants k13, k14, k23, and k24 are determined from simultaneous equations obtained by simultaneous expression (14).
[0033]
The computer 9 notifies the controller 8 of the hysteresis error correction functions h1 and h2 obtained as described above, and the controller 8 stores them inside (step ST3 in FIG. 4). As a result, the controller 8 can convert the target angular position of each arm 2 and 3 from an arbitrary target position of the hand shaft 4 while correcting the hysteresis error. That is, when moving the arm, the controller 8 calculates the hysteresis error correction amounts θc1 and θc2 using the hysteresis error correction functions h1 and h2, and sets the hysteresis error correction amount to the joint angles θ21 and θ22 corresponding to the target position P2. The command angle position can be corrected by adding θc1 and θc2, and the hysteresis error can be removed from the horizontal positioning error of the hand shaft 4 by driving the arms 2 and 3 according to the corrected command angle position. In this way, correction of the hysteresis error is completed.
[0034]
In this specification, “notifying the controller 8 of the error correction function” may mean notifying the controller 8 of all of the function types and coefficients or parameters, or a common type between the controller 8 and the computer 9. If the error correction function is used, only the coefficient or parameter obtained by the computer 9 may be notified to the controller 8.
[0035]
After completing the correction of the hysteresis error, the calculator 9 measures the position of the hand axis 4 for calculating the geometric error (step ST4 in FIG. 4), calculates the geometric error (step ST5), and calculates the geometric error correction function. Is notified to the controller 8 (step ST6).
[0036]
Geometric error correction will be described with reference to FIG. Even if P0 (X0, Y0) is given as the target command position of the hand axis 4, if there is a robot installation error Pb and a robot body geometric error Pe, the actual position of the hand axis 4 as seen in the reference coordinate system O-XY. The position P (X, Y) of is deviated from the target command position P0 (X0, Y0). Here, the robot installation error Pb and the robot body geometric error Pe are referred to as geometric errors.
[0037]
The robot installation error Pb is the installation error of the robot base 1, that is, the rotary joint axis 2a, that is, the actual robot coordinate system O′− with respect to the ideal reference coordinate system O-XY that the robot controller 8 uses as a reference for the position command. It means the relative displacement of X′Y ′. The origin O ′ of the robot coordinate system O′-X′Y ′ is at (Xb, Yb, θb) on the reference coordinate system O-XY, and for this reason, the robot installation error Pb causes the arms 2 and 3 to operate on the robot. Any rotational position within the range affects the positioning accuracy of the hand shaft 4 as a constant error vector. If there is a robot installation error Pb and the controller 8 tries to position the hand axis 4 at the target command position P0, the motor actually operates in the robot coordinate system O'-X'Y '. The motor is driven according to the target command position P0 in the coordinate system O′-X′Y ′.
[0038]
The geometric error Pe of the robot body means a positioning error that occurs in the hand shaft 4 due to a link element shape error and a positional error (an arm length error and an arm rotation angle error). The geometric error Pe of the robot body changes depending on the lengths and angular positions of the arms 2 and 3, and is expressed in the robot coordinate system O′-X′Y ′. Even if the motor is driven in accordance with the target command position P0 (X0, Y0) in the robot coordinate system O′−X′Y ′ due to the geometric error Pe of the robot body, the robot coordinate system O′−X′Y ′. Thus, the position of the hand axis 4 becomes Pr (Xr, Yr), and the position of the hand axis 4 in the reference coordinate system O-XY becomes P (X, Y) as a result of Pb and Pr.
[0039]
In the robot coordinate system O′-X′Y ′ that can actually control the arms 2 and 3, the actual position of the hand axis 4 corresponding to the target command position P0 (X0, Y0) is Pr (Xr, Yr). Can be expressed by equation (15).
[0040]
Pr = g (P0, v + e) (15)
Here, g is a function that represents the geometric relationship of the robot body and can calculate the actual position Pr (Xr, Yr) from the target command position P0 on the robot coordinate system O′-X′Y ′. is there. v represents an ideal dimension and target angle of the link element, that is, an ideal geometric parameter, and can be expressed by a sequence of parameters defining a model on the robot coordinate system O′-X′Y ′, that is, a vector. e represents an arm length error and an arm rotation angle error, that is, the geometric error parameter, and can be expressed by a vector of parameters defining a model on the robot coordinate system O′-X′Y ′. Cause a geometric error Pe.
[0041]
When Expression (15) is expressed with respect to the X ′ direction component and the Y ′ direction component, Expression (16) and Expression (17) are obtained.
Xr = gx (X0, Y0, v + e) (16)
Yr = gy (X0, Y0, v + e) (17)
[0042]
When the target command position P0 (X0, Y0) is given to an ideal robot having no geometric error, that is, no robot installation error Pb and no robot body geometric error Pe, the hand axis 4 is at the target position P0. Positioned at (X0, Y0). This relationship is a special case of equation (15) and can be expressed as equation (18).
Pr = P0 = g (P0, v) (18)
[0043]
The ideal geometric parameter v and the geometric error parameter e will be described with reference to FIG. FIG. 7 is a plan view showing simplified elements of the horizontal articulated robot shown in FIG. In the drawing, L1 is a specified design length of the first arm 2, dL1 is an error in the length of the arm 2, L2 is a specified design length of the second arm 3, and dL2 is the design length of the arm 3. The length error, θ1 is the commanded rotation angle position (joint angle) of the first arm 2, dLθ is the error of the angle position of the arm 2 (for example, due to the positional deviation of the origin O ′), and θ2 is the second The commanded rotation angle position (joint angle) of the arm 3, dLθ is an error in the angular position of the arm 2 (for example, due to a position shift of the origin O ′ and a position shift of the rotary joint shaft 3 a).
[0044]
The ideal geometric parameter v is expressed as a vector as shown in Equation (19), and the geometric error parameter e is expressed as a vector as shown in Equation (20).
v = (L1, L2, θ1, θ2) (19)
e = (dL1, dL2, dθ1, dθ2) (20)
Of the geometric error parameter e, the angular position errors dθ1 and dθ2 vary depending on the angular positions of the arms 2 and 3.
[0045]
The function g representing the geometric relationship of the robot body is uniquely expressed using the ideal geometric parameter v and the geometric error parameter e.
[0046]
Further, when there is an installation error Pb in addition to the geometric error Pe of the robot body caused by the mechanical error of the link element, the position P (X, Y) of the hand axis 4 on the reference coordinate system O-XY is expressed by the equation (21)
P = Pb · Pr (21)
[0047]
The robot installation error Pb (Xb, Yb, θb) and the actual position Pr (Xr, Yr) of the hand axis 4 on the robot coordinate system O′-X′Y ′ are in a homogeneous transformation format using a 3 × 3 matrix. Is expressed as shown in equations (22) and (23).
[Equation 3]

[Expression 4]

[0048]
The matrix components of the first column and the second column of the first row and the second row of Equation (22) indicate the rotation error components of the robot installation error Pb, and the third column of the first row and the second row is The translation error component of the robot installation error Pb is shown. In equation (23), since the rotation of the coordinate system is not considered, the rotation error component is a 2 × 2 unit matrix. The third column of the first row and the second row of Equation (23) shows the translation error component (Xr, Yr) of the actual position Pr of the hand axis 4 on the robot coordinate system O′-X′Y ′.
[0049]
According to the equations (21) to (23), the position P (X, Y) of the hand axis 4 on the reference coordinate system O-XY is expressed as the equation (24) in the homogeneous conversion format.
[Equation 5]

[0050]
Since the translation error components of the position P of the hand axis 4 on the reference coordinate system O-XY are X and Y, from the third column of the first row and the second row of the equation (24), X and Y are the equations (25) and Expression (26).

[0051]
As is apparent from the equations (25) and (26), the actually measured position P (X, Y) of the hand axis 4 on the reference coordinate system O-XY is the robot installation error Pb (Xb, Yb, θb). The target command position P0 and the geometric error parameter e, that is, dL1, dL2, dθ1, dθ2, have a corresponding relationship.
[0052]
In step ST4 of FIG. 4, the computer 9 instructs the controller 8 on a large number of random target positions P0 (X0, Y0) of the hand axis 4 and the controller 8 corrects many of the hand axes 4 while correcting with the hysteresis error correction function. To move to a random target position P0 (X0, Y0). On the other hand, the computer 9 measures the measured position P (X, Y) of the hand shaft 4 after movement for each target position. In this way, for each of a large number of target positions P0, each target position P0 (X0, Y0) of the hand shaft 4 and the measured position P (X, Y) are recorded.
[0053]
Next, the computer 9 calculates a geometric error based on each measured position of the hand axis 4 and each target position of the hand axis 4 (step ST5 in FIG. 4). Specifically, these many target positions P0 (X0, Y0), many actual measurement positions P (X, Y) on the reference coordinate system O-XY, and ideal geometric parameters v (= L1, L2, θ1, By substituting θ2) into the equations (23) and (24) and using the least square method, the robot installation error Pb (Xb, Yb, θb) and the geometric error parameter e (= dL1, dL2, dθ1) , Dθ2).
[0054]
If the robot installation error Pb and the geometric error parameter e are known in this way, a method for correcting the target position command to cancel the geometric error can be determined. As described above, even if the motor is driven according to the target command position P0 (X0, Y0) in the robot coordinate system O′-X′Y ′, the position of the hand axis 4 in the robot coordinate system O′-X′Y ′ is Pr. (Xr, Yr), and as a result of Pb and Pr, the position of the hand axis 4 in the reference coordinate system O-XY is P (X, Y). From another viewpoint, if the position of the hand axis 4 is Prc in FIG. 6 in the robot coordinate system O′-X′Y ′, the hand axis in the reference coordinate system O-XY is obtained as a result of Pb and Prc. The position 4 becomes the target position P0 (X0, Y0). That is, when the hand axis 4 is to be moved to the target position P0 in the reference coordinate system O-XY, the hand axis 4 may be actually moved to the position Prc in the robot coordinate system O′-X′Y ′. It can be expressed by the general formula (15) that the actual position of the hand axis 4 corresponding to the target command position P0 (X0, Y0) in the robot coordinate system O′-X′Y ′ is Pr (Xr, Yr). Therefore, when the position Pr of the actual hand axis 4 on the robot coordinate system O′-X′Y ′ in the general formula (15) is replaced with Prc, and the target command position P0 for commanding the motor is replaced with Pc, the formula ( 27) is obtained.
Prc = g (Pc, v + e) (27)
[0055]
Further, the position P (X, Y) of the hand axis 4 on the reference coordinate system O-XY in the equation (21) is replaced with the true target position P0, and the actual hand on the robot coordinate system O′-X′Y ′. When the position Pr of the shaft 4 is replaced with Prc, the equation (28) is obtained.
P0 = Pb · Prc (28)
[0056]
Therefore, if the robot installation error Pb can be identified, the target position Prc in the robot coordinate system O′-X′Y ′ can be obtained from the true target command position P0 of the hand axis 4 in the reference coordinate system O-XY. . Furthermore, if the geometric error parameter e can be identified, the target command position Pc for realizing the target position Prc in the robot coordinate system O′-X′Y ′ can be obtained. In this way, a function for obtaining the effective target command position Pc on the robot coordinate system O′-X′Y ′ from the true target command position P0 of the hand axis 4 in the reference coordinate system O-XY is represented by a geometric error here. This is called a correction function. Based on the geometric error correction function, the controller 8 resets the true target command position P0 to an effective target command position Pc on the robot coordinate system O′-X′Y ′, and controls the motor. Geometric errors can be canceled out.
[0057]
In step ST6 of FIG. 4, the computer 9 determines a geometric error correction function for canceling the geometric error based on the robot installation error Pb and the geometric error parameter e, and notifies the controller 8 of the geometric error correction function. 8 stores this internally. As a result, the controller 8 can convert the target angular position of each arm 2 and 3 from an arbitrary target position of the hand axis 4 while correcting the geometric error in addition to the hysteresis error. That is, when moving the arm, the controller 8 can calculate the true target command position of the hand axis 4 from which the geometric error is eliminated using the geometric error correction function, and the command angle corresponding to the true target command position. By driving the arms 2 and 3 according to the position, the geometric error can be removed from the horizontal positioning error of the hand axis 4. In this way, the correction of the geometric error is completed in addition to the correction of the hysteresis error.
[0058]
After completing the correction of the geometric error, the calculator 9 measures the position of the hand axis 4 for calculating the residual error (step ST7 in FIG. 4), calculates the residual error (step ST8), and is included in the residual error. A non-modeling error correction function (residual error correction function) for canceling the non-modeling error is determined (step ST9).
[0059]
Causes of mechanical errors of link elements generated in an actual robot include not only the arm length error and arm rotation angle error used as the geometric error parameter e described above, but also the rotational joint axes 2a and 3a. All geometric factors such as torsion and eccentricity can be included. Theoretically, it is also conceivable to include the twist or eccentricity of the joint axis in the geometric error parameter e related to the aforementioned geometric error. However, in general, even if consideration is given to the torsion and eccentricity of the joint axis as the error parameter e, the calculation model becomes complicated, and the identification accuracy of the error parameter does not improve. Therefore, in this embodiment, only the arm length error and the arm rotation angle error that can be easily expressed by a model with an appropriate number of parameters are considered as the geometric error parameter e. The error due to the geometric error factor excluded from the geometric error parameter e is corrected as a non-modeling error.
[0060]
In this embodiment, the non-modeling error includes, in addition to the above-described geometric error such as torsion or eccentricity of the joint shaft, an error due to deflection due to the gravity of the arm, and a motion transmission mechanism such as a reduction gear device. Error due to a transmission error that does not exhibit a clear regular change tendency that occurs within the network. However, error factors that can be expressed by a model, such as deflection due to gravity, may be handled separately from non-modeling errors. Depending on the relationship between the structural strength of the robot and the load, it may be preferable to separate this type of error factor from the unmodeled error.
[0061]
In step ST7, the computer 9 instructs the controller 8 on a plurality of random target command positions Pc (Xc, Yc) of the hand axis 4, and the controller 8 corrects the hysteresis with the hysteresis error correction function and the geometric error correction function. The hand shaft 4 is commanded to move to a plurality of random target command positions Pc (Xc, Yc). The computer 9 records the target angular positions θ1c and θ2c of the arms 2 and 3 corresponding to the target positions Pc (Xc, Yc) of the hand shaft 4 while moving the arms 2 and 2 for the target positions Pc. 3, each angular position θ1a, θ2a is measured, and each angular position θ1a, θ2a is recorded. In this way, the target angular positions θ1c and θ2c of the arms 2 and 3 and the measured angular positions θ1a and θ2a are recorded for a large number of target positions Pc.
[0062]
Assuming that the measured position in the horizontal direction of the hand shaft 4 when the target command position Pc (Xc, Yc) is given to the robot is Pa (Xa, Ya), the joint angle corresponding to Pc and Pa is given by equation (29) And expressed as equation (30).
(Θ1c, θ2c) = f (Xc, Yc) (29)
(Θ1a, θ2a) = f (Xa, Ya) (30)
[0063]
In step ST8, the computer 9 still remains the difference between the measured angular positions θ1a and θ2a after the movement of the arms 2 and 3 and the target angular positions θ1c and θ2c of the arms 2 and 3. Calculated as errors (first residual errors) θe1 and θe2. The residual errors θe1 and θe2 converted to the joint angles of the arms 2 and 3 can be expressed as in Expression (31) and Expression (32).
θe1 = θ1a−θ1c (31)
θe2 = θ2a−θ2c (32)
[0064]
The residual errors θe1 and θe2 calculated in step ST8 include a non-modeling error and an angle transmission error. As described above, unmodeled errors are difficult to express in the model, and depend on the individual angular positions of the arm within the robot movement range, but unlike angular transmission errors, they have a distinct regular change trend. Not present. On the other hand, the angle transmission error is a positioning error caused by the dimensional accuracy of parts of the motion transmission mechanism and the mounting accuracy of those parts, and exhibits a regular change tendency depending on the angular position of the arm.
In general, the angle transmission error is often much smaller than the non-modeling error.
[0065]
In step ST9 of FIG. 4, the computer 9 cancels the non-modeling errors θm1 and θm2 included in the residual errors θe1 and θe2 based on the set of the residual errors θe1 and θe2 calculated in step ST8. A modeling error correction function (residual error correction function) is determined. Since the non-modeling error is generally much larger than the angle transmission error and changes less with respect to the angle than the angle transmission error, it is assumed that the residual errors θe1 and θe2 are non-modeling errors θm1 and θm2 at this stage. handle. The mathematical model representing the non-modeling error is expressed by a function related to the target joint angles θ1c and θ2c of the arms 2 and 3 as shown in the equations (33) and (34).
[0066]
θe1 = θm1 = fm1 (θ1c, θ2c) (33)
θe2 = θm2 = fm2 (θ1c, θ2c) (34)
Here, fm1 and fm2 are non-modeling error correction functions that can calculate the non-modeling errors θm1 and θm2 from the target joint angles θ1c and θ2c of the arms 2 and 3, respectively. The non-modeling error correction functions fm1 and fm2 can be expressed by polynomials, and the order of the polynomials may be determined according to a desired correction effect. For example, the unmodeled error correction functions fm1 and fm2 may be expressed as 2 It can be expressed by an original cubic polynomial.
[0067]

[0068]
Here, k101 to k210 are coefficients identified based on the actual measurement results. The non-modeling error correction functions fm1 and fm2 are determined by obtaining the coefficients k101 to k210. For the coefficients k101 to k110 in the equation (35), the residual error θe1 obtained for a large number (n) of target positions. ₁ ~ Θe1 _n Equation (35) is provided for the number (n) of. This can be expressed by matrix multiplication as shown in equation (37).
[Formula 6]

[0069]
Where θ1c ₁ ~ Θ1c _n Is the target joint angle of the first arm 2 for n target positions, θ2c ₁ ~ Θ2c _n Is the target joint angle of the second arm 3 for n target positions. Residual error θe1 ₁ ~ Θe1 _n (Ie, non-modeling error θm1 ₁ ~ Θm1 _n ) And the target joint angle θ1c of the arm 2 recorded ₁ ~ Θ1c _n And the target joint angle θ2c of the arm 3 ₁ ~ Θ2c _n Is substituted into equation (35) to obtain a general linear expression. Therefore, unknown coefficients k101 to k110 can be obtained from a large number of simultaneous equations by the method of least squares.
[0070]
That is, Expression (37) can be expressed in the form of Expression (38), and the least square solution of p1 can be obtained from Expression (39).
θm1 = M1 · p1 (38)
p1 = [(M1 ^T ・ M1) ^-1 ・ M1 ^T ] ・ Θm1 (39)
Here, θm1 is an n-row vector on the left side of Equation (37), M1 is an n × 10 matrix on the right side of Equation (37), and p1 is a 10-row vector on the right side of Equation (37) representing coefficients k101 to k110. . In this way, the non-modeling error correction function fm1 is determined. Similarly, the equations (37) are solved simultaneously to obtain the coefficients k201 to k210, and the non-modeling error correction function fm2 can be determined.
[0071]
Next, the computer 9 calculates a calculation non-modeling error (each calculation residual error) (step ST10 in FIG. 4), calculates an angle transmission error (step ST11), and calculates an angle transmission error correction function. The angle transfer error correction function and the non-modeling error correction function are determined and notified to the controller 8, and the controller 8 stores them internally (step ST12).
[0072]
First, in step ST10, the computer 9 records the non-modeling error correction functions fm1 and fm2 obtained in step ST9, and then uses the non-modeling error correction functions fm1 and fm2 to each target joint of the arm 2. Angle θ1c ₁ ~ Θ1c _n And each target joint angle θ2c of the arm 3 ₁ ~ Θ1c _n Is substituted, and calculation non-modeling error (calculation residual error) θm1 ₁ '~ Θm1 _n ', Θm2 ₁ '~ Θm2 _n 'Is calculated. Subsequently, the computer 9 determines each residual error θe1 calculated in step ST8. ₁ '~ Θe1 _n ', Θe2 ₁ '~ Θe2 _n 'And each non-modeling error in calculation θm1 ₁ '~ Θm1 _n ', Θm2 ₁ '~ Θm2 _n Each angle transmission error (second residual error) θg1 that is different from ' ₁ ~ Θg1 _n , Θg2 ₁ ~ Θg2 _n Is calculated (step ST11). In general, when the angle transmission errors θg1 and θg2 are expressed, the equations (40) and (41) are obtained.
θg1 = θe1−θm1 ′ (40)
θg2 = θe2−θm2 ′ (41)
[0073]
As described above, when the non-modeling error correction functions fm1 and fm2 are determined, the residual errors θe1 and θe2 obtained in step ST8 are determined as the non-modeling errors θm1 and θm2 as in Expression (33) to Expression (36). Although it is assumed that they are equal, the non-modeling error correction functions fm1 and fm2 are averaged with regular changes in angular transmission error by a polynomial representation and a method of least squares. Therefore, it is considered that the computational non-modeling errors θm1 ′ and θm2 ′ calculated from the non-modeling error correction functions fm1 and fm2 also do not include regularly changing angle transmission error components. Actually, the non-modeling errors θm1 ′ and θm2 ′ do not coincide with the residual errors θe1 and θe2 obtained in step ST8, and the angle transmission error θg1 obtained by the equations (40) and (41). ₁ ~ Θg1 _n , Θg2 ₁ ~ Θg2 _n Has regularity.
[0074]
In step ST12 of FIG. 4, the computer 9 determines an angle transmission error correction function based on each angle transmission error. As described above, the angle transmission error is caused by an error in the accuracy of the motion transmission mechanism (part dimensional accuracy and component mounting accuracy), and the positioning error is highly regular and varies depending on the positions of the arms 2 and 3. It is. The highly regular angle transmission errors θg1 and θg2 depend on the accuracy error of the motion transmission mechanism, and therefore can be expressed by the equations (42) and (43) as a function of the rotation angle of the rotation element of the motion transmission mechanism.
[0075]
θg1 = A1 · sin (ω · θ10 + φ1) (42)
θg2 = A2 · sin (ω · θ20 + φ2) (43)
Here, A1, A2, φ1, and φ2 are coefficients, and ω is a ratio of an input shaft rotation period of a motion transmission mechanism (for example, a reduction gear device) to an angle transmission error generation period. The ratio ω is obtained by Expression (44).
[0076]
ω = n · Ng (44)
Here, n is an integer determined corresponding to the generation cycle of the angle transmission error, and Ng is a reduction ratio of the motion transmission mechanism. For example, if the angle transmission error occurs in the same cycle as the input shaft rotation of the reduction gear device, n = 1 and ω = Ng, and if the angle transmission error occurs in half the input rotation cycle, n = 2. And ω = 2Ng.
[0077]
The angle transmission error correction function is determined by obtaining the coefficients A1, A2, φ1, and φ2. Regarding the coefficients A1 and φ1 in the equation (42), the angle transmission error θg1 obtained for a large number (n) of target positions. ₁ ~ Θg1 _n Equation (42) is simultaneously provided by the number (n) of. Since Equation (42) is a nonlinear expression, the least squares solution of the coefficients A1 and φ1 can be obtained by, for example, the Gauss-Newton method. Similarly, the least squares solution of the coefficients A2 and φ2 of Equation (43) can be obtained. In this way, the angle transmission error correction function is determined.
[0078]
After the determination of the angle transmission error correction function, the computer 9 notifies the controller 8 of the non-modeling error correction functions fm1 and fm2 and the angle transmission error correction function, and the controller 8 stores them inside. Thus, the controller 8 can convert the target angular position of each arm 2 and 3 from the target position of the hand axis 4 while correcting the non-modeling error and the angle transmission error in addition to the hysteresis error and the geometric error. become. That is, when moving the arm, the controller 8 calculates the non-modeling errors θm1 and θm2 using the non-modeling error correction functions fm1 and fm2, and uses the angle transmission error correction function to calculate the angle transmission errors θg1 and θg2. The command angle position can be corrected by subtracting the non-modeling errors θm1 and θm2 and the angle transmission errors θg1 and θg2 from the joint angles of the arms 2 and 3 corresponding to the target command position. By driving the arms 2 and 3 according to the angular position, the non-modeling error and the angle transmission error can be removed from the horizontal positioning error of the hand shaft 4. In this way, correction of non-modeling error and angle transmission error is completed in addition to correction of hysteresis error and geometric error.
[0079]
As described above, in the first embodiment, in order to avoid the influence of other error factors as much as possible when identifying the error factors, a hysteresis error having regularity with respect to the direction of movement and the movement amount is first introduced. Next, geometric errors that have a large absolute value of error and are easy to model as a planar geometric relationship are corrected. Finally, non-modeling errors and angular transmission errors that are small and difficult to model are corrected. The procedure to correct is taken. By correcting the four types of error factors in this order, it is possible to reduce the influence that other error factors are included in the error factor to be identified even in a configuration including a motion transmission mechanism such as a reduction gear device. Thus, a desired error can be corrected with high accuracy, and as a result, a robot with high positioning accuracy can be realized.
[0080]
In the first embodiment, two different errors, that is, a non-modeling error and an angle transmission error of the motion transmission mechanism, are identified using the same data (residual errors θe1, θe2). The effect is negligible. In other words, the non-modeling error has a slower error fluctuation with respect to the joint angle than the angle transmission error, and even if the non-modeling error is identified from the data including the angle transmission error, the periodic error of the angle transmission error Is averaged with non-modeling errors, and the identification results are hardly affected.
[0081]
In this embodiment, measurement data with extremely high accuracy can be obtained by using an optical planar grid encoder for position measurement. By combining with the error identification procedure, accurate identification results can be obtained with a simple configuration. Can be obtained. In particular, even minute error factors can be accurately measured and identified. In addition, since all error factors are implemented by a single measuring means, the measuring device can be configured at low cost, and error correction can be easily automated.
[0082]
Embodiment 2. FIG.
In the first embodiment, the non-modeling error correction functions fm1 and fm2 are obtained from the residual errors θe1 and θe2, and then calculated non-modeling errors θm1 ′ calculated using the non-modeling error correction functions fm1 and fm2. , Θm2 ′ is subtracted from the residual errors θe1 and θe2 to calculate the angle transmission errors θg1 and θg2 (Equation (40) and Equation (41)). However, the following procedure may be adopted as the second embodiment of the present invention.
[0083]
The robot positioning error correction method executed in the second embodiment will be described with reference to the flowchart of FIG. Here, for simplification, only the horizontal position of the hand axis 4 of the horizontal articulated robot shown in FIG. 1 will be described. First, as in the first embodiment, the calculator 9 determines a hysteresis error correction function, a geometric error correction function, and a non-modeling error correction function (step ST1 to step ST9).
[0084]
However, unlike the first embodiment, after the determination of the correction function after step ST9, the computer 9 notifies the controller 8 of the non-modeling error correction functions fm1 and fm2, and the controller 8 stores these in the inside. Thereby, the controller 8 can convert the target angular position of each arm 2 and 3 from the target position of the hand shaft 4 while correcting the non-modeling error in addition to the hysteresis error and the geometric error. That is, when moving the arm, the controller 8 calculates the non-modeling errors θm1 and θm2 using the non-modeling error correction functions fm1 and fm2, and determines the joint angle of the arms 2 and 3 corresponding to the target command position. The command angle position can be corrected by subtracting the non-modeling errors θm1 and θm2 from each, and the arm 2 and 3 are driven according to the corrected command angle position, thereby non-modeling from the horizontal positioning error of the hand shaft 4 Errors can be removed. In this way, correction of non-modeling errors is completed in addition to correction of hysteresis errors and geometric errors.
[0085]
After completing the correction of the non-modeling error, the calculator 9 measures the position of the hand shaft 4 for calculating the angle transmission error (step ST13) and calculates the angle transmission error (second residual error) (step ST14). Then, an angle transmission error correction function (residual error correction function) for canceling the angle transmission error is determined (step ST15).
[0086]
In step ST13, as in step ST7, the computer 9 instructs the controller 8 on a plurality of random target command positions Pc (Xc, Yc) of the hand axis 4, and the controller 8 sets the hand axis 4 on a plurality of random targets. Command to move to target command position Pc (Xc, Yc). However, the controller corrects the target command position Pc (Xc, Yc) with a hysteresis error correction function, a geometric error correction function, and a non-modeling error correction function. The calculator 9 calculates the target angular positions θ1c and θ2c of the arms 2 and 3 corresponding to the target positions Pc (Xc and Yc) of the hand shaft 4 while moving the arms 2 and 2 for the target positions Pc. 3, each angular position θ1a, θ2a is measured, and each angular position θ1a, θ2a is recorded. In this way, the target angular positions θ1c and θ2c of the arms 2 and 3 and the measured angular positions θ1a and θ2a are recorded for a large number of target positions Pc.
[0087]
In step ST14, the computer 9 still has a difference between the measured angular positions θ1a and θ2a after the movement of the arms 2 and 3 and the target angular positions θ1c and θ2c of the arms 2 and 3. Calculated as a residual error of 2. The second residual error calculated in step ST14 is the angle transmission errors θg1 and θg2. The angle transmission errors θg1 and θg2 converted into the joint angles of the arms 2 and 3 can be expressed as Expression (45) and Expression (46).
θg1 = θ1a−θ1c (45)
θg2 = θ2a−θ2c (46)
[0088]
In step ST15, as in step ST12 of the first embodiment, the calculator 9 determines an angle transmission error correction function based on the angle transmission errors θg1 and θg2 obtained for a large number of target positions. After the determination of the angle transmission error correction function, the computer 9 notifies the controller 8 of the angle transmission error correction function, and the controller 8 stores this inside. In this way, correction of angle transmission error is completed in addition to correction of hysteresis error, geometric error, and non-modeling error.
[0089]
According to the procedure of the second embodiment, the angle transmission error to be corrected last is not obtained by subtracting the computational non-modeling error from the residual error, but is determined solely based on the new position measurement. The effect of improving the accuracy of correcting the angle transmission error can be expected.
[0090]
Embodiment 3 FIG.
Further, in the position measurement by the planar grid encoder, it is possible to measure the position by moving the hand shaft 4 over a wide range exceeding the area of the grid plate 6, and perform error correction based on the result. In this case, the position of the hand shaft 4 may be measured at the position where the grid plate 6 is moved and stopped.
[0091]
Specifically, the position of the grid plate 6 with respect to the robot base 1, that is, the installation error Pb is individually identified at each stop position of the grid plate 6, and parameters for other errors, that is, the geometric error e of the robot body, As the coefficient of the hysteresis error correction function, the coefficient of the non-modeling error correction function, and the coefficient of the angle transmission error correction function, the average value of the coefficients identified from the measurement results at the plurality of stop positions of the grid plate 6 may be used. Good. Assuming that the hysteresis error correction function can be expressed as a function of only the movement angle as shown in the equations (11) and (12) without depending on the joint angle, the hysteresis error correction function is identified at one stop position of the grid plate 6. do it.
[0092]
According to the method according to the third embodiment, it is possible to perform highly accurate robot positioning error correction over a wide operation range exceeding the finite position measurement range of the planar grid encoder.
[0093]
In the above-described embodiment, the error correction of the horizontal position of the hand axis 4 of the four-degree-of-freedom horizontal articulated robot is performed. However, the above-described embodiment is illustrated to facilitate understanding of the present invention. Not too much. By using a method in which the above-described embodiment is modified and modified, the positioning error of the end effector of a vertical-type robot or other multi-joint robot, or a direct-acting robot using a ball screw feed mechanism is not limited to a rotary joint type. It can be corrected.
[0094]
In the above-described embodiment, the optical planar grid encoder is used as an example of a preferable measuring unit. However, other high-precision measuring unit, such as a three-dimensional position measuring device, may be used.
[0095]
In the above embodiment, the correction function is determined in the order from the hysteresis error correction function to the geometric error correction function, the non-modeling error correction function, and the angle transfer error correction function. However, the hysteresis error can be ignored. In the case of a robot, the correction function may be determined in the order from the geometric error correction function through the non-modeling error correction function to the angle transfer error correction function.
[0096]
【The invention's effect】
As described above, according to the present invention, various types of positioning errors due to various factors can be reduced.
[Brief description of the drawings]
FIG. 1 is a perspective view showing an example of a robot in which a robot positioning error correction apparatus according to Embodiment 1 of the present invention is used.
FIG. 2 is a graph showing a movement characteristic curve that is a set of results obtained by measuring the angular position of a robot arm while continuously rotating and moving the arm.
FIG. 3 is a graph showing a change in angle transmission error extracted from the movement characteristic curve of FIG. 2;
FIG. 4 is a flowchart showing a robot positioning error correction method executed in the first embodiment.
5 is a plan view schematically showing elements of the horizontal articulated robot shown in FIG. 1. (a) is a movement start position, (b) is a target position, (c) is a position after actual movement, (D) is a figure which shows the position after the actual movement at the time of making another movement start position move to the same target position as (b).
FIG. 6 is a diagram showing hand positions of the horizontal articulated robot shown in FIG. 1 in order to explain geometric error correction performed in the embodiment of the present invention.
FIG. 7 is a plan view showing simplified elements of the horizontal articulated robot shown in FIG. 1 in order to explain ideal geometric parameters and geometric error parameters used in the embodiment of the present invention.
FIG. 8 is a flowchart showing a robot positioning error correction method executed in the second embodiment.
[Explanation of symbols]
DESCRIPTION OF SYMBOLS 1 Robot base, 2 1st arm (link element), 2a Rotary joint axis | shaft, 3 2nd arm (link element), 3a Rotary joint axis | shaft, 3b Rotary joint axis | shaft, 4 Hand axis | shaft (link element), 5 Read head , 6 Grid plate, 6a Plate base, 7 Work table, 8 Controller, 9 Computer (robot positioning error correction device), 10 Communication line.

Claims (7)

A robot for correcting a positioning error of a robot, comprising at least two link elements connected to each other, a drive device for driving the link element, and a motion transmission mechanism for transmitting motion from the drive device to each link element In the positioning error correction device,
Based on the measured and post-movement positions of each link element recorded for multiple target positions by repeatedly moving each link element from different directions to the same target position, each link A hysteresis error correction function determination unit that determines a hysteresis error correction function that is a function related to a change in position of the link element for canceling out a hysteresis error that is a positioning error depending on a position before movement of the element;
Based on each measured position and each target position after movement of the link element recorded by moving at least one link element to a plurality of positions in a state corrected by the hysteresis error correction function, A robot positioning error correction apparatus comprising: a second error correction function determination unit that determines a second error correction function that reduces an error different from a hysteresis error. The second error correction function determination unit is measured after moving each link element recorded by moving a specific part of any link element to a plurality of positions in a state corrected by the hysteresis error correction function. Based on each position and each target position, a geometric error caused by a link element shape error, a positional error, and a robot installation error is calculated, and the geometric error is canceled based on the geometric error. 2. The robot positioning error correction device according to claim 1, wherein the geometric error correction function determination unit determines a geometric error correction function that is a function of Based on each measured position and each target position after movement of each link element recorded by moving each link element to multiple positions in a state corrected by the hysteresis error correction function and the geometric error correction function A first residual error at each position of each link element is calculated, and a function of each position of each link element to reduce the first residual error based on the first set of residual errors. 3. The robot positioning error correction apparatus according to claim 2, further comprising a residual error correction function determination unit that determines a certain residual error correction function. Each residual error in calculation at each position of each link element is calculated using a residual error correction function, and a second residual error that is a difference between each first residual error and each residual error in calculation is calculated. Then, based on each second residual error, an angle transmission error correction function that determines an angle transmission error correction function that is a function of each position of each link element for canceling the angle transmission error caused by the accuracy error of the motion transmission mechanism 4. The robot positioning error correction apparatus according to claim 3, further comprising a determination unit. Each measured position and each post-movement of each link element recorded by moving each link element to multiple positions in a state corrected by a hysteresis error correction function, a geometric error correction function and a residual error correction function A second residual error at each position of each link element is calculated based on the target position, and an angle transmission error due to an accuracy error of the motion transmission mechanism is canceled based on each second residual error 4. The robot positioning error correction device according to claim 3, further comprising an angle transmission error determination unit that determines an angle transmission error correction function that is a function of each position of each link element. A robot for correcting a positioning error of a robot, comprising at least two link elements connected to each other, a drive device for driving the link element, and a motion transmission mechanism for transmitting motion from the drive device to each link element In the positioning error correction device,
Based on each measured position and each target position after the movement of each link element recorded by moving a specific part of any one of the link elements to a plurality of positions, the shape error and positional error of the link element And a geometric error correction function determining unit that calculates a geometric error caused by a robot installation error and determines a geometric error correction function that is a function for canceling the geometric error based on the geometric error When,
Based on each measured position and each target position after movement of each link element recorded by moving each link element to a plurality of positions in a state corrected by the geometric error correction function, each link element A residual error correction that is a function of each position of each link element to reduce the first residual error based on the set of first residual errors. A residual error correction function determination unit for determining a function;
Each residual error in calculation at each position of each link element is calculated using the residual error correction function, and a second residual error that is a difference between each first residual error and each residual error in calculation is calculated. An angle transmission that calculates and determines an angle transmission error correction function that is a function of each position of each link element for canceling the angle transmission error caused by the accuracy error of the motion transmission mechanism based on each second residual error A robot positioning error correction device comprising an error determination unit. A robot for correcting a positioning error of a robot, comprising at least two link elements connected to each other, a drive device for driving the link element, and a motion transmission mechanism for transmitting motion from the drive device to each link element In the positioning error correction device,
Based on each measured position and each target position after the movement of each link element recorded by moving a specific part of any one of the link elements to a plurality of positions, the shape error and positional error of the link element And a geometric error correction function determining unit that calculates a geometric error caused by a robot installation error and determines a geometric error correction function that is a function for canceling the geometric error based on the geometric error When,
Based on each measured position and each target position after movement of each link element recorded by moving each link element to a plurality of positions in a state corrected by the geometric error correction function, each link element A residual error correction that is a function of each position of each link element to reduce the first residual error based on the set of first residual errors. A residual error correction function determination unit for determining a function;
In the state corrected by the geometric error correction function and the residual error correction function, each link element is moved to a plurality of positions, and each measured position after movement of each link element and each target position are recorded. Each link element for calculating a second residual error at each position of each link element and canceling out the angle transmission error caused by the accuracy error of the motion transmission mechanism based on each second residual error A robot positioning error correction device comprising an angle transmission error determination unit that determines an angle transmission error correction function that is a function of each position of the robot.

Images