JPH1139021A - Route interpolation method for robot - Google Patents
Route interpolation method for robotInfo
- Publication number
- JPH1139021A JPH1139021A JP19878997A JP19878997A JPH1139021A JP H1139021 A JPH1139021 A JP H1139021A JP 19878997 A JP19878997 A JP 19878997A JP 19878997 A JP19878997 A JP 19878997A JP H1139021 A JPH1139021 A JP H1139021A
- Authority
- JP
- Japan
- Prior art keywords
- point
- teaching
- intersection
- flange
- control point
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
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Links
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- Numerical Control (AREA)
- Manipulator (AREA)
Abstract
Description
【０００１】[0001]
【発明の属する技術分野】本発明は、ロボットの手首フ
ランジに装着された工具の先端部の制御点の移動経路
（軌道）として入力された教示点から、前記制御部の目
標経路を生成するロボットの経路補間方法に関するもの
で、詳しくは、移動経路に屈曲したコーナー部分が存在
する場合に、コーナー部分を加減速なしで高速に通過可
能にするための改良に関するものである。BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a robot for generating a target path of a control unit from a teaching point input as a movement path (trajectory) of a control point at a tip of a tool mounted on a wrist flange of the robot. More specifically, the present invention relates to an improvement for enabling high-speed passage through a corner portion without acceleration or deceleration when a curved corner portion exists in a moving route.
【０００２】[0002]
【従来の技術】近年、ロボットがいろいろな作業現場で
活用されている。このようなロボットは、例えば、多関
節のアームの先端部の手首フランジに作業用の工具を装
着し、工具の先端部を、作業内容に即して、所望の移動
経路（軌道）で移動させる。従って、作業の品質向上、
信頼性向上を図るためには、工具の先端部の移動動作の
精度と安定性の追求が重要課題とされている。前記工具
の先端部（制御点）の移動経路は、複数の教示点により
予め与え、一つの教示点から次の教示点までの間を単純
に直線運動させる場合には、教示点を結ぶ直線経路を教
示点間の補間演算により求める。しかし、複数の教示点
で示した移動経路の途中に屈曲したコーナー部分が存在
する場合、直線経路と同様の取り扱いでコーナー部分を
通過させようとすると、アームの各関節部分等に過大な
衝撃がかかるという問題が生じる。そこで、従来では、
複数の教示点で示した移動経路の途中に屈曲したコーナ
ー部分が存在する場合、コーナー部分に近づくと減速し
てコーナー点で一旦停止させ、進行方向を変えた後に加
速させて通常の移動速度に戻したり、あるいは、コーナ
ー部分を形成している二つの直線経路上の加減速が必要
となる範囲を滑らかな円弧等の曲線経路に置き換えるこ
とで、コーナー部分通過時における衝撃の作用を抑える
経路補間方法が提案されている。2. Description of the Related Art In recent years, robots have been used in various work sites. In such a robot, for example, a work tool is mounted on a wrist flange at the tip of an articulated arm, and the tip of the tool is moved along a desired movement path (trajectory) in accordance with the work content. . Therefore, work quality improvement,
In order to improve the reliability, it is important to pursue the accuracy and stability of the movement of the tip of the tool. A moving path of the tip (control point) of the tool is given in advance by a plurality of teaching points, and when a simple linear movement is performed from one teaching point to the next teaching point, a linear path connecting the teaching points is provided. Is obtained by interpolation calculation between teaching points. However, if there is a bent corner in the middle of the movement path indicated by a plurality of teaching points, an excessive impact will be applied to each joint of the arm when trying to pass the corner in the same way as a straight path. Such a problem arises. So, conventionally,
If there is a bent corner part of the movement path indicated by multiple teaching points, decelerate as you approach the corner part, stop at the corner point, change the direction of travel, accelerate after moving to the normal moving speed Path interpolation that suppresses the effect of impact when passing through a corner by returning or replacing the area that requires acceleration / deceleration on two straight paths that form the corner with a curved path such as a smooth arc A method has been proposed.
【０００３】[0003]
【発明が解決しようとする課題】しかし、前述した従来
の経路補間方法では、コーナー部分の通過時に加減速と
一旦停止を実行する方法の場合は、制御点の移動速度が
コーナー部分付近で大きく変化するため、例えば、ロボ
ットによる作業がシール材を塗布するシーリングの場
合、シール材の付着量がコーナー部分付近で増えるな
ど、作業品質にばらつきが生じ易いという問題が生じ
る。また、移動経路を曲線に置き換える方法の場合は、
当初に要求された角張った教示経路を忠実に再現するこ
とができず、移動精度の低下等の問題が生じる。そこ
で、本発明の目的は上記課題を解消することにあり、ロ
ボットの制御点の移動経路に屈曲したコーナー部分が存
在する場合に、ロボットの各関節軸への衝撃を抑えなが
ら、かつ、制御点の動作は直線動作のままで、コーナー
部分を加減速なしで高速に通過させることのできるロボ
ットの経路補間方法を提供することである。However, in the above-described conventional path interpolation method, when the acceleration / deceleration and the temporary stop are executed when the vehicle passes through the corner, the moving speed of the control point greatly changes near the corner. Therefore, for example, when the operation performed by the robot is sealing in which a sealant is applied, there is a problem that the work quality tends to vary, such as an increase in the amount of the sealant attached near the corner. If you want to replace the travel route with a curve,
The originally required angular teaching path cannot be faithfully reproduced, causing problems such as a decrease in movement accuracy. Therefore, an object of the present invention is to solve the above-mentioned problems, and when there is a bent corner portion in the movement path of the control point of the robot, while controlling the impact on each joint axis of the robot, Is to provide a path interpolation method for a robot that can pass through a corner portion at high speed without acceleration / deceleration while maintaining a linear operation.
【０００４】[0004]
【課題を解決するための手段】本発明のロボットの経路
補間方法は、工具が装着される手首フランジのフランジ
面が前記工具の先端部の制御点の移動経路を示唆する教
示点群のなす教示平面に対して平行に設定されると共
に、中心軸線が前記教示平面に直交するフランジ駆動軸
によって前記手首フランジが回転可能に支持され、ま
た、前記工具は前記制御点が前記フランジ駆動軸の中心
軸線に対してオフセット距離を持つように前記フランジ
面に装備されたロボットであって、前記フランジ駆動軸
の中心軸線と教示平面との交点がほぼ教示点を結んだ線
上に位置し、かつ、前記フランジ駆動軸の中心軸線と教
示平面との交点から制御点への方向がほぼ前記制御点の
移動方向となるように、３点以上の教示点を与え、前記
制御点が教示点で示した移動経路を直線動作により進む
ように経路補間を行うロボットの経路補間方法におい
て、３点の教示点Ｐ１，Ｐ２，Ｐ３を与え、教示点Ｐ１
から教示点Ｐ２への移動動作中に、前記フランジ駆動軸
の中心軸線と教示平面との交点が教示点Ｐ２から基準距
離Ｌ１の点よりも教示点Ｐ２に近づいた場合に、前記フ
ランジ駆動軸の中心軸線と教示平面との交点をＰ４、教
示点Ｐ２から交点Ｐ４までの距離をＬｅ、教示点Ｐ２か
ら教示点Ｐ３へ向かう直線上で教示点Ｐ２から距離Ｌｅ
の点をＰ５として、以後、制御点が教示点Ｐ２から教示
点Ｐ３へ向かう直線上の点Ｐ５を通過するまで、前記フ
ランジ駆動軸の中心軸線と教示平面との交点が前記交点
Ｐ４，教示点Ｐ２，点Ｐ５通る円弧上を移動するよう
に、前記手首フランジを回転駆動させて、制御点が教示
した経路上を直線動作するように経路補間するものであ
る。上記構成によれば、３点の教示点Ｐ１，Ｐ２，Ｐ３
で与えられたロボットの制御点の移動経路が、教示点Ｐ
２がコーナー部分となる折れ線経路の場合、教示点Ｐ１
から教示点Ｐ２への移動動作中に、前記フランジ駆動軸
の中心軸線と教示平面との交点が教示点Ｐ２から基準距
離Ｌ１の点よりも教示点Ｐ２に近づくと、以後、制御点
が教示点Ｐ２から教示点Ｐ３へ向かう直線上の点Ｐ５を
通過するまでは、前記フランジ駆動軸の中心軸線と教示
平面との交点が前記交点Ｐ４，教示点Ｐ２，点Ｐ５通る
円弧上を移動するように、前記手首フランジを回転駆動
させて、制御点は教示した経路上を直線動作させる。そ
のため、接続点自体は、教示点によって与えられた直線
経路を忠実にトレースすることができる。そして、関節
部である手首フランジは、滑らかな回転動作となるた
め、コーナー部分の通過時に、ロボットの基本軸（位置
を司るベースの３軸）に対して急峻な速度変動が発生し
ない。そのため、ロボットの各関節軸等の大きな衝撃荷
重が作用せず、衝撃荷重の作用に起因する振動の発生を
抑えて、コーナー点を直線動作で通過させることができ
る。According to the present invention, there is provided a path interpolation method for a robot, wherein a flange surface of a wrist flange on which a tool is mounted is formed by a teaching point group indicating a movement path of a control point at a tip end of the tool. The wrist flange is rotatably supported by a flange drive shaft whose center axis is set to be parallel to the plane and whose central axis is orthogonal to the teaching plane, and the tool is configured such that the control point is the center axis of the flange drive shaft. A robot provided on the flange surface so as to have an offset distance with respect to the flange surface, wherein the intersection of the center axis of the flange drive shaft and the teaching plane is located substantially on a line connecting the teaching points, and Three or more teaching points are provided so that the direction from the intersection between the center axis of the drive shaft and the teaching plane to the control point is substantially the moving direction of the control point, and the control point is indicated by the teaching point. In route interpolation method of a robot for performing route interpolated to a movement path proceeds by linear operations, given the teaching points P1, P2, P3 of the 3-point, the teaching point P1
During the movement operation from the teaching point P2 to the teaching point P2, when the intersection of the center axis of the flange drive shaft and the teaching plane is closer to the teaching point P2 than the reference distance L1 from the teaching point P2, The intersection point between the center axis and the teaching plane is P4, the distance from the teaching point P2 to the intersection point P4 is Le, and the distance Le from the teaching point P2 on the straight line from the teaching point P2 to the teaching point P3.
Is defined as P5, and thereafter, until the control point passes a point P5 on a straight line from the teaching point P2 to the teaching point P3, the intersection between the center axis of the flange drive shaft and the teaching plane is the intersection P4, the teaching point The wrist flange is rotationally driven so as to move on an arc passing through points P2 and P5, and the path interpolation is performed so that the control point linearly moves on the path taught by the control point. According to the above configuration, the three teaching points P1, P2, P3
The movement path of the control point of the robot given by
If 2 is a polygonal line path that is a corner, the teaching point P1
During the movement from the teaching point P2 to the teaching point P2, if the intersection between the center axis of the flange drive shaft and the teaching plane is closer to the teaching point P2 than the point at the reference distance L1 from the teaching point P2, then the control point is changed to the teaching point. Until passing a point P5 on a straight line from P2 to the teaching point P3, the intersection between the center axis of the flange drive shaft and the teaching plane moves on an arc passing through the intersection P4, the teaching point P2, and the point P5. Then, the wrist flange is driven to rotate, so that the control point moves linearly on the taught path. Therefore, the connection point itself can faithfully trace the straight line path given by the teaching point. Since the wrist flange, which is a joint, performs a smooth rotation operation, a steep speed fluctuation does not occur with respect to the basic axis (the three axes of the base that controls the position) of the robot when passing through the corner portion. Therefore, a large impact load such as each joint axis of the robot does not act, and the vibration caused by the effect of the impact load can be suppressed, and the corner point can be passed in a linear motion.
【０００５】[0005]
【発明の実施の形態】以下、図面を参照して本発明の実
施の形態について説明する。図１乃至図７は本発明に係
るロボットの経路補間方法の一実施形態を示したもの
で、図１は本発明に係る経路補間方法の一実施形態によ
り作業するロボットの全体概略図、図２は図１に示した
ロボットの手首フランジの上面図、図３は図１に示した
ロボットの手首フランジの側面図、図４は本発明に係る
経路補間方法の一実施形態における補間演算処理の手順
を示すフローチャート、図５は図４に示した処理におい
て、制御点がコーナー点に到達するまでのフランジ駆動
軸の中心軸線と教示平面との交点と、制御点との移動動
作説明図、図６は図４に示した処理において、制御点が
コーナー点通過後のフランジ駆動軸の中心軸線と教示平
面との交点と、制御点との移動動作説明図、図７は図４
に示した処理によって制御点が教示点Ｐ１から教示点Ｐ
２を経て教示点Ｐ３に到達するまでのフランジ駆動軸の
中心軸線と教示平面との交点と、制御点との移動動作説
明図である。まず、本発明の一実施形態の経路補間方法
により動作するロボット１について、図１乃至図３に基
づいて説明する。前記ロボット１は、いわゆる多関節ロ
ボットで、工具３が装着される手首フランジ５のフラン
ジ面６が、前記工具３の先端部の制御点８の移動経路９
を示唆する教示点群のなす教示平面１１に対して平行に
設定されている。また、このロボット１では、前記手首
フランジ５がフランジ駆動軸１３によって回転可能に支
持されており、前記フランジ駆動軸１３の中心軸線Ｃ１
が前記教示平面１１に直交している。また、前記工具３
は、図３に示すように、前記制御点８が前記フランジ駆
動軸１３の中心軸線Ｃ１に対してオフセット距離Ｒ１を
持つように前記フランジ面６に装備されている。そし
て、ロボット１には、前記制御点８の移動経路の補間演
算処理や、補間演算処理結果に基づいて各関節部に動作
信号を出力する制御装置（図示略）が備えられている。
前記制御装置は、前記制御点８を教示平面１１上へ投影
した点を制御点Ｐｃ、前記フランジ駆動軸１３の中心軸
線Ｃ１と教示平面１１との交点（即ち、手首フランジ５
の回転中心Ｐｆを教示平面１１上に投影した点）をＰｆ
0とするとき、交点Ｐｆ0がほぼ教示点を結んだ線上に位
置し、かつ、前記交点Ｐｆ0から制御点Ｐｃへの方向が
ほぼ前記制御点Ｐｃの移動方向となるように、予め３点
の教示点Ｐ１，Ｐ２，Ｐ３を与え、前記制御点Ｐｃが教
示点Ｐ１，Ｐ２，Ｐ３で示した移動経路９を直線動作に
より進むように経路補間を行う。３点の教示点Ｐ１，Ｐ
２，Ｐ３の示す移動経路９が、図１に示すように、教示
点Ｐ１を出発点として直線動作で教示点Ｐ３まで進む
時、教示点Ｐ２をコーナー点とする直交２直線の軌道と
なる場合、前記制御装置は、図４に示す手順で、コーナ
ー部分に対する経路補間処理を行う。なお、図４に示し
た処理は、基本制御クロック毎に実施される。まず、制
御点Ｐｃが教示点Ｐ１から教示点Ｐ２に向かっている途
中なのか、あるいは既に教示点Ｐ２を通過して教示点Ｐ
３に向かっている途中なのかを判別する（Ｓ１０１）。
そして、前記Ｓ１０１で、制御点Ｐｃが教示点Ｐ１から
教示点Ｐ２に向かっている途中と判別された場合には、
まず、通常の逆変換（＝逆運動学の解を求めて直交座標
をロボットの各軸座標に変換すること）処理を行う直前
まで、直線補間処理を行う（Ｓ２０１）。次いで、次の
（１）式に基づいて制御点Ｐｃから手首フランジ５の回
転中心Ｐｆを求めると共に、求めた手首フランジ５の回
転中心Ｐｆから直線Ｐ１Ｐ２へ下した垂線の交点Ｐｆ0
を求める（Ｓ２０２）。 Ｐｆ＝Ｐｃ＊Ｅ-1 …（１） 前記（１）式において、Ｅはエンドエフェクタである。
次いで、既にコーナー部の補間処理中か否かを、制御フ
ラグに基づいて判別する（Ｓ２０３）。前記Ｓ２０３
で、コーナー部の補間処理中でないと判断された場合
は、前記交点Ｐｆ0から教示点Ｐ２までの距離が基準距
離Ｌ１よりも小さいか否かを判別し（Ｓ２１１）、交点
Ｐｆ0から教示点Ｐ２までの距離が基準距離Ｌ１よりも
大きい場合には、先にＳ２０１で算出した制御点Ｐｃを
補間した制御点位置Ｐｃ0として所定の逆変換処理を行
い（Ｓ４０１）、さらに算出したロボットの各軸角度を
モータ現在パルスに変換してサーボ部に払い出して処理
を終了する（Ｓ４０２）。前述のＳ２１１で、交点Ｐｆ
0から教示点Ｐ２までの距離が基準距離Ｌ１よりも小さ
いと判断された場合は、図５に示すように、交点Ｐｆ0
を交点Ｐ４、そして該交点Ｐ４から教示点Ｐ２までの距
離をＬｅ、直線Ｐ２Ｐ３上で教示点Ｐ２から距離Ｌｅの
点を点Ｐ５とし、交点Ｐ４，教示点Ｐ２，点Ｐ５通る円
Ｃ２の中心点Ｏｐと半径Ｒ２とを求め、コーナー部の補
間処理中の制御フラグをセットして、前述したＳ４０１
に移行する（Ｓ２１２）。前述のＳ２０３で、コーナー
部の補間処理中と判断された場合は、次の（Ａ）〜
（Ｄ）の処理を順に行う（Ｓ２２１）。 （Ａ） まず、図５に示すように、制御点Ｐｃを中心と
した半径Ｒ１の円Ｃ１を求める。図５では、制御点Ｐｃ
が教示点Ｐ２に重なった状態を示している。 （Ｂ） そして、円Ｃ１と前記円Ｃ２との交点が、手首
フランジ５の回転中心Ｐｆの位置となるように、以下の
演算を実行する。まず、図５に示すように、制御点Ｐｃ
と教示点Ｐ１とを結んだ線分ＰｃＰ１と、制御点Ｐｃと
円Ｃ２の中心点Ｏｐとを結んだ線分ＰｃＯｐのなす角度
αを、次の（２）〜（４）式に基づいて求める（内
積）。 ｌ＝Ｐ１−Ｐｃ／｜Ｐ１Ｐｃ｜ …（２） ｍ＝Ｏｐ−Ｐｃ／｜ＯｐＰｃ｜ …（３） α＝ｃｏｓ-1（ｌxｍx＋ｌyｍy＋ｌzｍz） …（４） さらに、制御点Ｐｃと中心点Ｏｐとの距離をＬ２とし
て、それぞれの円Ｃ１，Ｃ２の半径Ｒ１，Ｒ２と前記距
離Ｌ２とを次の（５）式に代入して、円Ｃ１，Ｃ２相互
の交点Ｑと制御点Ｐｃとを結んだ線分ＱＰｃと、制御点
Ｐｃと中心点Ｏｐとを結んだ線分ＯｐＰｃとの成す角度
βを求める。 β＝ｃｏｓ-1（Ｒ１2＋Ｌ２2−Ｒ２2／２＊Ｒ１＊Ｌ２） …（５） （Ｃ） 次いで、線分ＱＰｃと線分Ｐ１Ｐ２との成す角
度γを次の（６）式により求める。 γ＝β−α …（６） （Ｄ）次いで、前記（６）式で求めた角度γを次の
（７）式に代入して、補間した制御点位置Ｐｃ0を算出
する。 Ｐｃ0＝Ｐｃ＊ｒｏｔ（ｚ，γ） …（７） 上記の（７）式は、制御点ＰｃをＴｚ回りに角度γ（又
は−γ）だけ回転させている。以上のＳ２２１の処理が
済んだら、前述したＳ４０１及びＳ４０２を順に実行し
て処理を終了する。以上のＳ２０１以降の処理は、制御
点Ｐｃが教示点Ｐ２に到達するまで繰り返される。ま
た、Ｓ２２１以降の処理は、最初にＳ２１２によってコ
ーナー部処理中の制御フラグがセットされたら、それ以
後、制御点Ｐｃが教示点Ｐ２に到達するまで繰り返され
る。また、前記Ｓ１０１で、制御点Ｐｃが教示点Ｐ２か
ら教示点Ｐ３に向かっている途中と判別された場合に
は、まず、通常の逆変換（＝逆運動学の解を求めて直交
座標をロボットの各軸座標に変換すること）処理を行う
直前まで、直線補間処理を行う（Ｓ３０１）。次いで、
前述の（１）式に基づいて制御点Ｐｃから手首フランジ
５の回転中心Ｐｆを求めると共に、求めた手首フランジ
５の回転中心Ｐｆから直線Ｐ２Ｐ３へ下した垂線の交点
Ｐｆ0を求める（Ｓ３０２）。次いで、既にコーナー部
の補間処理中か否かを、制御フラグに基づいて判別する
（Ｓ３０３）。前記Ｓ３０３で、コーナー部の補間処理
中でないと判断された場合は、前述のＳ４０１に移行し
て、先にＳ３０１で算出した制御点Ｐｃを補間した制御
点位置Ｐｃ0として所定の逆変換処理を行い、さらに算
出したロボットの各軸角度をモータ現在パルスに変換し
てサーボ部に払い出して処理を終了する（Ｓ４０２）。
前述のＳ３０３で、コーナー部の補間処理中と判断され
た場合は、次の（Ａ）〜（Ｄ）の処理を順に行う（Ｓ３
２１）。 （Ａ） まず、図６に示すように、制御点Ｐｃを中心と
した半径Ｒ１の円Ｃ１を求める。 （Ｂ） そして、円Ｃ１と前記円Ｃ２との交点Ｑが、手
首フランジ５の回転中心Ｐｆの位置となるように、以下
の演算を行う。まず、図６に示すように、制御点Ｐｃと
教示点Ｐ３とを結んだ線分ＰｃＰ３と、制御点Ｐｃと円
Ｃ２の中心点Ｏｐとを結んだ線分ＰｃＯｐのなす角度α
を、次の（８）〜（１０）式に基づいて求める（内
積）。 ｌ＝Ｐ３−Ｐｃ／｜Ｐ３Ｐｃ｜ …（８） ｍ＝Ｏｐ−Ｐｃ／｜ＯｐＰｃ｜ …（９） α＝π−ｃｏｓ-1（ｌxｍx＋ｌyｍy＋ｌzｍz） …（１０） さらに、制御点Ｐｃと中心点Ｏｐとの距離をＬ２とし
て、それぞれの円Ｃ１，Ｃ２の半径Ｒ１，Ｒ２と前記距
離Ｌ２とを次の（１１）式に代入して、円Ｃ１，Ｃ２相
互の交点Ｑと制御点Ｐｃとを結んだ線分ＱＰｃと、制御
点Ｐｃと中心点Ｏｐとを結んだ線分ＯｐＰｃとの成す角
度βを求める。 β＝ｃｏｓ-1（Ｒ１2＋Ｌ２2−Ｒ２2／２＊Ｒ１＊Ｌ２） …（１１） （Ｃ） 次いで、線分ＱＰｃと線分Ｐ２Ｐ３との成す角
度γを次の（１２）式により求める。 γ＝α−β …（１２） （Ｄ）次いで、前記（６）式で求めた角度γを次の（１
３）式に代入して、補間した制御点位置Ｐｃ0を算出す
る。 Ｐｃ0＝Ｐｃ＊ｒｏｔ（ｚ，γ） …（１３） 上記の（１３）式は、制御点ＰｃをＴｚ回りに角度γ
（又は−γ）だけ回転させている。以上のＳ３２１の処
理が済んだら、交点Ｐｆ０から点Ｐ５までの距離が最短
か否かを判断し（Ｓ３２２）、最短でない場合は、前述
したＳ４０１及びＳ４０２を順に実行して処理を終了す
る。前記Ｓ３２２において、交点Ｐｆ０から点Ｐ５まで
の距離が最短であると判断された場合には、前述したコ
ーナー部処理中の制御フラグをリセットし（Ｓ３２
３）、その後に、前述したＳ４０１及びＳ４０２を順に
実行して処理を終了する。以上のＳ３２１以降の処理
は、交点Ｐｆ０から点Ｐ５までの距離が最短となってコ
ーナー部処理中の制御フラグがリセットされるまで繰り
返され、それ以後、教示点Ｐ３に向かう間は、再度、通
常の直線補間制御が行われる。以上の補間処理によっ
て、前記制御点Ｐｃが教示点Ｐ１から教示点Ｐ３へ到達
するまでの制御点Ｐｃの軌跡を経時的に、連続描画した
のが、図７である。以上の説明から明らかなように、本
発明の一実施形態の経路補間方法は、３点の教示点Ｐ
１，Ｐ２，Ｐ３を与え、教示点Ｐ１から教示点Ｐ２への
移動動作中に、前記フランジ駆動軸１３の中心軸線Ｃ１
と教示平面１１との交点が教示点Ｐ２から基準距離Ｌ１
の点よりも教示点Ｐ２に近づいた場合に、前記フランジ
駆動軸１３の中心軸線Ｃ１と教示平面１１との交点をＰ
４、教示点Ｐ２から交点Ｐ４までの距離をＬｅ、教示点
Ｐ２から教示点Ｐ３へ向かう直線上で教示点Ｐ２から距
離Ｌｅの点をＰ５として、以後、制御点８が教示点Ｐ２
から教示点Ｐ３へ向かう直線上の点Ｐ５を通過するま
で、前記フランジ駆動軸１３の中心軸線Ｃ１と教示平面
１１との交点が前記交点Ｐ４，教示点Ｐ２，点Ｐ５通る
円弧上を移動するように、前記手首フランジ５を回転駆
動させて、制御点８が教示した経路上を直線動作するよ
うに経路補間するもので、３点の教示点Ｐ１，Ｐ２，Ｐ
３で与えられたロボットの制御点８の移動経路９が、教
示点Ｐ２がコーナー部分となる折れ線経路の場合、教示
点Ｐ１から教示点Ｐ２への移動動作中に、前記フランジ
駆動軸１３の中心軸線Ｃ１と教示平面１１との交点が教
示点Ｐ２から基準距離Ｌ１の点よりも教示点Ｐ２に近づ
くと、以後、制御点８が教示点Ｐ２から教示点Ｐ３へ向
かう直線上の点Ｐ５を通過するまでは、前記フランジ駆
動軸１３の中心軸線Ｃ１と教示平面１１との交点が前記
交点Ｐ４，教示点Ｐ２，点Ｐ５通る円弧上を移動するよ
うに、前記手首フランジ５を回転駆動させて、制御点８
は教示した経路上を直線動作させる。そのため、接続点
自体は、教示点によって与えられた直線経路を忠実にト
レースすることができる。そして、関節部である手首フ
ランジ５は、滑らかな回転動作となるため、コーナー部
分の通過時に、ロボットの基本軸（位置を司るベースの
３軸）に対して急峻な速度変動が発生しない。そのた
め、ロボットの各関節軸等の大きな衝撃荷重が作用せ
ず、衝撃荷重の作用に起因する振動の発生を抑えて、コ
ーナー点を直線動作で通過させることができる。Embodiments of the present invention will be described below with reference to the drawings. FIGS. 1 to 7 show one embodiment of a robot path interpolation method according to the present invention. FIG. 1 is an overall schematic view of a robot working by one embodiment of the path interpolation method according to the present invention. Is a top view of the wrist flange of the robot shown in FIG. 1, FIG. 3 is a side view of the wrist flange of the robot shown in FIG. 1, and FIG. 4 is a flowchart of an interpolation calculation process in one embodiment of the path interpolation method according to the present invention. FIG. 5 is a flowchart showing the movement of the intersection between the center axis of the flange drive shaft and the teaching plane until the control point reaches the corner point and the movement of the control point in the processing shown in FIG. FIG. 7 is an explanatory diagram of a movement operation between the control point and the intersection of the center axis of the flange drive shaft and the teaching plane after the control point passes through the corner point in the processing shown in FIG.
The control point changes from the teaching point P1 to the teaching point P
FIG. 7 is an explanatory diagram of a movement operation between a control point and an intersection between the center axis of the flange drive shaft and the teaching plane until reaching a teaching point P3 via the control point 2; First, a robot 1 that operates by a path interpolation method according to an embodiment of the present invention will be described with reference to FIGS. The robot 1 is a so-called articulated robot, in which a flange surface 6 of a wrist flange 5 on which the tool 3 is mounted has a movement path 9 of a control point 8 at the tip of the tool 3.
Are set in parallel with the teaching plane 11 formed by the teaching point group indicating the above. In the robot 1, the wrist flange 5 is rotatably supported by the flange drive shaft 13, and the center axis C1 of the flange drive shaft 13 is provided.
Are perpendicular to the teaching plane 11. The tool 3
Are mounted on the flange surface 6 so that the control point 8 has an offset distance R1 with respect to the center axis C1 of the flange drive shaft 13, as shown in FIG. The robot 1 is provided with a control device (not shown) that outputs an operation signal to each joint based on an interpolation calculation process of the movement path of the control point 8 and a result of the interpolation calculation process.
The control device controls the control point Pc by projecting the control point 8 onto the teaching plane 11 and the intersection (i.e., the wrist flange 5) of the center axis C <b> 1 of the flange drive shaft 13 with the teaching plane 11.
(The point where the rotation center Pf is projected on the teaching plane 11)
When set to 0 , three points are set in advance so that the intersection Pf 0 is substantially on the line connecting the teaching points, and the direction from the intersection Pf 0 to the control point Pc is substantially the moving direction of the control point Pc. Of the teaching points P1, P2, and P3, and the path interpolation is performed so that the control point Pc advances on the moving path 9 indicated by the teaching points P1, P2, and P3 by a linear operation. 3 teaching points P1, P
As shown in FIG. 1, when the traveling route 9 indicated by P2 and P3 moves to the teaching point P3 in a linear motion with the teaching point P1 as a starting point, the trajectory is an orthogonal two straight lines with the teaching point P2 as a corner point. The control device performs a path interpolation process on a corner portion according to the procedure shown in FIG. The processing shown in FIG. 4 is performed for each basic control clock. First, whether the control point Pc is on the way from the teaching point P1 to the teaching point P2, or has already passed the teaching point P2 and
It is determined whether the vehicle is in the middle of moving toward 3 (S101).
If it is determined in S101 that the control point Pc is on the way from the teaching point P1 to the teaching point P2,
First, linear interpolation processing is performed until immediately before normal inverse conversion (= conversion of orthogonal coordinates to a coordinate of each axis of a robot by obtaining a solution of inverse kinematics) (S201). Next, based on the following equation (1), the rotation center Pf of the wrist flange 5 is obtained from the control point Pc, and the intersection Pf 0 of a perpendicular drawn from the obtained rotation center Pf of the wrist flange 5 to the straight line P1P2.
Is obtained (S202). Pf = Pc * E -1 (1) In the above equation (1), E is an end effector.
Next, it is determined whether or not the interpolation process of the corner portion is already being performed based on the control flag (S203). S203
In, if it is determined that not being the interpolation processing of the corner section, the distance from the intersection point Pf 0 to the teaching point P2 is to determine less or not than the reference distance L1 (S211), the teaching point from the intersection point Pf 0 If the distance to P2 is greater than the reference distance L1 is as the control point position Pc 0 interpolated control points Pc calculated at S201 above performs predetermined inverse transform process (S401), the further the calculated robot The shaft angle is converted into the current pulse of the motor and paid out to the servo unit, and the process is terminated (S402). In the aforementioned S211, the intersection Pf
If the distance from 0 to the teaching point P2 is determined to be smaller than the reference distance L1, as shown in FIG. 5, the intersection point Pf 0
Is the intersection point P4, the distance from the intersection point P4 to the teaching point P2 is Le, the point Le from the teaching point P2 on the straight line P2P3 is the point P5, and the center point of the circle C2 passing through the intersection point P4, the teaching point P2, and the point P5 Op and the radius R2 are obtained, and a control flag during the interpolation process of the corner portion is set, and the above-mentioned S401 is set.
(S212). If it is determined in step S203 that the interpolation process of the corner is being performed, the following (A) to
The processing of (D) is performed sequentially (S221). (A) First, as shown in FIG. 5, a circle C1 having a radius R1 around the control point Pc is obtained. In FIG. 5, the control point Pc
Indicates a state in which it overlaps the teaching point P2. (B) Then, the following calculation is performed so that the intersection of the circle C1 and the circle C2 is located at the position of the rotation center Pf of the wrist flange 5. First, as shown in FIG.
An angle α formed by a line segment PcP1 connecting the control point Pc and the center point Op of the circle C2 with the line segment PcP1 connecting the control point P1 and the teaching point P1 is obtained based on the following equations (2) to (4). (inner product). l = P1Pc / | P1Pc | ... (2) m = OpPc / | OpPc | ... (3) α = cos -1 (l x m x + l y m y + l z m z) ... (4) further , The distance between the control point Pc and the center point Op is L2, and the radii R1, R2 of the circles C1, C2 and the distance L2 are substituted into the following equation (5) to obtain the intersection of the circles C1, C2. An angle β formed between a line segment QPc connecting Q and the control point Pc and a line segment OpPc connecting the control point Pc and the center point Op is determined. β = cos -1 (R1 2 + L2 2 -R2 2/2 * R1 * L2) ... (5) (C) Then, determine the angle formed between the line segment QPc and a line segment P1P2 gamma by the following formula (6) . γ = β−α (6) (D) Next, the angle γ obtained by the above equation (6) is substituted into the following equation (7) to calculate the interpolated control point position Pc 0 . Pc 0 = Pc * rot (z, γ) (7) In the above equation (7), the control point Pc is rotated around Tz by an angle γ (or −γ). After the above-described processing of S221 is completed, the above-described S401 and S402 are sequentially executed, and the processing is terminated. The processing from S201 onward is repeated until the control point Pc reaches the teaching point P2. After the control flag during corner processing is set in S212 at first, the processing from S221 is repeated until the control point Pc reaches the teaching point P2. If it is determined in step S101 that the control point Pc is on the way from the teaching point P2 to the teaching point P3, first, a normal inverse transformation (= a solution of inverse kinematics is obtained and the orthogonal coordinates are obtained by the robot) Linear interpolation processing is performed until immediately before the processing is performed (S301). Then
The rotation center Pf of the wrist flange 5 is obtained from the control point Pc based on the above equation (1), and the intersection Pf 0 of a perpendicular drawn from the obtained rotation center Pf of the wrist flange 5 to the straight line P2P3 is obtained (S302). Next, it is determined whether or not the interpolation processing of the corner portion is already being performed based on the control flag (S303). If it is determined in step S303 that the interpolation process for the corner portion is not being performed, the process proceeds to step S401, in which a predetermined inverse conversion process is performed as the control point position Pc 0 obtained by interpolating the control point Pc previously calculated in step S301. Then, the calculated respective axis angles of the robot are converted into current pulses of the motor and paid out to the servo unit, and the process is terminated (S402).
If it is determined in step S303 that the interpolation process of the corner is being performed, the following processes (A) to (D) are sequentially performed (S3).
21). (A) First, as shown in FIG. 6, a circle C1 having a radius R1 around the control point Pc is obtained. (B) Then, the following calculation is performed such that the intersection Q between the circle C1 and the circle C2 is located at the position of the rotation center Pf of the wrist flange 5. First, as shown in FIG. 6, an angle α formed by a line segment PcP3 connecting the control point Pc and the teaching point P3 and a line segment PcOp connecting the control point Pc and the center point Op of the circle C2.
Is calculated based on the following equations (8) to (10) (inner product). l = P3Pc / | P3Pc | ... (8) m = OpPc / | OpPc | ... (9) α = π-cos -1 (l x m x + l y m y + l z m z) ... (10 Further, assuming that the distance between the control point Pc and the center point Op is L2, the radii R1 and R2 of the circles C1 and C2 and the distance L2 are substituted into the following equation (11), and the distance between the circles C1 and C2 is An angle β formed by a line segment QPc connecting the intersection Q of the control point Pc and the control point Pc and a line segment OpPc connecting the control point Pc and the center point Op is determined. β = cos -1 (R1 2 + L2 2 -R2 2/2 * R1 * L2) ... (11) (C) Then, determine the angle formed between the line segment QPc and a line segment P2P3 gamma by the following equation (12) . γ = α−β (12) (D) Next, the angle γ obtained by the above equation (6) is calculated by the following equation (1).
Substituting in the equation 3), the interpolated control point position Pc 0 is calculated. Pc 0 = Pc * rot (z, γ) (13) In the above equation (13), the control point Pc is set at an angle γ about Tz.
(Or -γ). After the above processing of S321, it is determined whether or not the distance from the intersection Pf0 to the point P5 is the shortest (S322). If the distance is not the shortest, the above-described S401 and S402 are sequentially executed and the processing is terminated. In S322, when it is determined that the distance from the intersection Pf0 to the point P5 is the shortest, the control flag during the corner processing described above is reset (S32).
3) After that, the above-described steps S401 and S402 are sequentially executed, and the process ends. The processing from S321 onward is repeated until the distance from the intersection point Pf0 to the point P5 becomes the shortest and the control flag during the corner part processing is reset. Thereafter, while heading to the teaching point P3, the normal processing is repeated again. Is performed. FIG. 7 shows the trajectory of the control point Pc from when the control point Pc reaches the teaching point P3 until the control point Pc reaches the teaching point P3. As is clear from the above description, the path interpolation method according to the embodiment of the present invention employs three teaching points P
1, P2, and P3, and during the movement operation from the teaching point P1 to the teaching point P2, the center axis C1 of the flange drive shaft 13
Is the reference distance L1 from the teaching point P2
Is closer to the teaching point P2 than the point, the intersection point between the center axis C1 of the flange drive shaft 13 and the teaching plane 11 is defined as P.
4. The distance from the teaching point P2 to the intersection point P4 is Le, and the point from the teaching point P2 to the distance Le on the straight line from the teaching point P2 to the teaching point P3 is P5.
, The intersection of the center axis C1 of the flange drive shaft 13 and the teaching plane 11 moves on an arc passing through the intersection P4, the teaching point P2, and the point P5 until passing through a point P5 on a straight line from the to the teaching point P3. Then, the wrist flange 5 is rotationally driven to interpolate the path so that the control point 8 linearly moves on the path taught. The three teaching points P1, P2, P
If the movement path 9 of the control point 8 of the robot given in 3 is a polygonal line path in which the teaching point P2 is a corner, the center of the flange drive shaft 13 during the movement operation from the teaching point P1 to the teaching point P2. When the intersection of the axis C1 and the teaching plane 11 approaches the teaching point P2 from the teaching point P2 more than the reference distance L1, the control point 8 passes through a point P5 on a straight line from the teaching point P2 to the teaching point P3. Until the wrist flange 5 is rotated so that the intersection of the center axis C1 of the flange drive shaft 13 and the teaching plane 11 moves on an arc passing through the intersection P4, the teaching point P2, and the point P5, Control point 8
Makes a linear motion on the taught path. Therefore, the connection point itself can faithfully trace the straight line path given by the teaching point. Since the wrist flange 5, which is a joint, performs a smooth rotation operation, when passing through a corner portion, a steep speed fluctuation does not occur with respect to the basic axis (the three axes of the base that controls the position) of the robot. Therefore, a large impact load such as each joint axis of the robot does not act, and the generation of vibration due to the impact load can be suppressed, and the corner point can be passed in a linear motion.
【０００６】[0006]
【発明の効果】本発明のロボットの経路補間方法によれ
ば、上記構成によれば、３点の教示点Ｐ１，Ｐ２，Ｐ３
で与えられたロボットの制御点の移動経路が、教示点Ｐ
２がコーナー部分となる折れ線経路の場合、教示点Ｐ１
から教示点Ｐ２への移動動作中に、前記フランジ駆動軸
の中心軸線と教示平面との交点が教示点Ｐ２から基準距
離Ｌ１の点よりも教示点Ｐ２に近づくと、以後、制御点
が教示点Ｐ２から教示点Ｐ３へ向かう直線上の点Ｐ５を
通過するまでは、前記フランジ駆動軸の中心軸線と教示
平面との交点が前記交点Ｐ４，教示点Ｐ２，点Ｐ５通る
円弧上を移動するように、前記手首フランジを回転駆動
させて、制御点は教示した経路上を直線動作させる。そ
のため、接続点自体は、教示点によって与えられた直線
経路を忠実にトレースすることができる。そして、関節
部である手首フランジは、滑らかな回転動作となるた
め、コーナー部分の通過時に、ロボットの基本軸（位置
を司るベースの３軸）に対して急峻な速度変動が発生し
ない。そのため、ロボットの各関節軸等の大きな衝撃荷
重が作用せず、衝撃荷重の作用に起因する振動の発生を
抑えて、コーナー点を直線動作で通過させることができ
る。従って、ロボットの各関節軸への衝撃を抑えなが
ら、かつ、制御点の動作は直線動作のままで、コーナー
部分を加減速なしで高速に通過させることができる。According to the robot path interpolation method of the present invention, according to the above configuration, three teaching points P1, P2, P3 are provided.
The movement path of the control point of the robot given by
If 2 is a polygonal line path that is a corner, the teaching point P1
During the movement from the teaching point P2 to the teaching point P2, if the intersection between the center axis of the flange drive shaft and the teaching plane is closer to the teaching point P2 than the point at the reference distance L1 from the teaching point P2, then the control point is changed to the teaching point. Until passing through a point P5 on a straight line from P2 to the teaching point P3, the intersection between the center axis of the flange drive shaft and the teaching plane moves on an arc passing through the intersection P4, the teaching point P2, and the point P5. Then, the wrist flange is driven to rotate, so that the control point moves linearly on the taught path. Therefore, the connection point itself can faithfully trace the straight line path given by the teaching point. Since the wrist flange, which is a joint, performs a smooth rotation operation, a steep speed fluctuation does not occur with respect to the basic axis (the three axes of the base that controls the position) of the robot when passing through the corner portion. Therefore, a large impact load such as each joint axis of the robot does not act, and the vibration caused by the effect of the impact load can be suppressed, and the corner point can be passed in a linear motion. Therefore, it is possible to pass the corner portion at high speed without acceleration / deceleration while suppressing the impact on each joint axis of the robot and keeping the operation of the control point in a linear operation.
【図１】本発明に係る経路補間方法の一実施形態により
作業するロボットの全体概略図である。FIG. 1 is an overall schematic view of a robot working by a path interpolation method according to an embodiment of the present invention.
【図２】図１に示したロボットの手首フランジの上面図
である。FIG. 2 is a top view of a wrist flange of the robot shown in FIG. 1;
【図３】図１に示したロボットの手首フランジの側面図
である。FIG. 3 is a side view of a wrist flange of the robot shown in FIG. 1;
【図４】本発明に係る経路補間方法の一実施形態におけ
る補間演算処理の手順を示すフローチャートである。FIG. 4 is a flowchart illustrating a procedure of an interpolation calculation process in an embodiment of a path interpolation method according to the present invention.
【図５】図４に示した処理において、制御点がコーナー
点に到達するまでのフランジ駆動軸の中心軸線と教示平
面との交点と、制御点との移動動作説明図である。FIG. 5 is an explanatory diagram of a movement operation between an intersection of a center axis of a flange drive shaft and a teaching plane and a control point until the control point reaches a corner point in the processing shown in FIG. 4;
【図６】図４に示した処理において、制御点がコーナー
点通過後のフランジ駆動軸の中心軸線と教示平面との交
点と、制御点との移動動作説明図である。FIG. 6 is an explanatory diagram of a movement operation of an intersection between a center axis of a flange drive shaft and a teaching plane after a control point passes through a corner point in the processing shown in FIG. 4 and a control point.
【図７】図４に示した処理によって制御点が教示点Ｐ１
から教示点Ｐ２を経て教示点Ｐ３に到達するまでのフラ
ンジ駆動軸の中心軸線と教示平面との交点と、制御点と
の移動動作説明図である。FIG. 7 is a diagram showing a control point set to a teaching point P1 by the processing shown in FIG.
FIG. 9 is an explanatory diagram of a movement operation between a control point and an intersection point between the center plane of the flange drive shaft and the teaching plane until reaching the teaching point P3 from the teaching point P2 through the teaching point P2.
１ ロボット ３ 工具 ５ 手首フランジ ６ フランジ面 ８，Ｐｃ 制御点 ９ 移動経路 １１ 教示平面 １３ フランジ駆動軸 DESCRIPTION OF SYMBOLS 1 Robot 3 Tool 5 Wrist flange 6 Flange surface 8, Pc Control point 9 Movement path 11 Teaching plane 13 Flange drive shaft
Claims (1)
ジ面が前記工具の先端部の制御点の移動経路を示唆する
教示点群のなす教示平面に対して平行に設定されると共
に、中心軸線が前記教示平面に直交するフランジ駆動軸
によって前記手首フランジが回転可能に支持され、ま
た、前記工具は前記制御点が前記フランジ駆動軸の中心
軸線に対してオフセット距離を持つように前記フランジ
面に装備されたロボットであって、前記フランジ駆動軸
の中心軸線と教示平面との交点がほぼ教示点を結んだ線
上に位置し、かつ、前記フランジ駆動軸の中心軸線と教
示平面との交点から制御点への方向がほぼ前記制御点の
移動方向となるように、３点以上の教示点を与え、前記
制御点が教示点で示した移動経路を直線動作により進む
ように経路補間するロボットの経路補間方法において、 ３点の教示点Ｐ１，Ｐ２，Ｐ３を与え、教示点Ｐ１から
教示点Ｐ２への移動動作中に、前記フランジ駆動軸の中
心軸線と教示平面との交点が教示点Ｐ２から基準距離Ｌ
１の点よりも教示点Ｐ２に近づいた場合に、前記フラン
ジ駆動軸の中心軸線と教示平面との交点をＰ４、教示点
Ｐ２から交点Ｐ４までの距離をＬｅ、教示点Ｐ２から教
示点Ｐ３へ向かう直線上で教示点Ｐ２から距離Ｌｅの点
をＰ５として、 以後、制御点が教示点Ｐ２から教示点Ｐ３へ向かう直線
上の点Ｐ５を通過するまで、前記フランジ駆動軸の中心
軸線と教示平面との交点が前記交点Ｐ４，教示点Ｐ２，
点Ｐ５通る円弧上を移動するように、前記手首フランジ
を回転駆動させて、制御点が教示した経路上を直線動作
するように経路補間することを特徴としたロボットの経
路補間方法。A flange surface of a wrist flange on which a tool is mounted is set in parallel with a teaching plane formed by a teaching point group indicating a movement path of a control point at a tip of the tool, and a center axis is set. The wrist flange is rotatably supported by a flange drive shaft orthogonal to the teaching plane, and the tool is mounted on the flange surface such that the control point has an offset distance with respect to a center axis of the flange drive shaft. Robot, wherein the intersection of the center axis of the flange drive shaft and the teaching plane is located substantially on a line connecting the teaching points, and the control point is determined from the intersection of the center axis of the flange drive shaft and the teaching plane. The teaching point is provided with three or more points so that the direction of the control point is substantially the moving direction of the control point, and the control point interpolates the movement path indicated by the teaching point by linear motion. In the bot path interpolation method, three teaching points P1, P2, and P3 are given, and during the movement operation from the teaching point P1 to the teaching point P2, the intersection between the center axis of the flange drive shaft and the teaching plane is the teaching point. Reference distance L from P2
When the point is closer to the teaching point P2 than point 1, the intersection between the center axis of the flange drive shaft and the teaching plane is P4, the distance from the teaching point P2 to the intersection P4 is Le, and the teaching point P2 is the teaching point P3. A point Le at a distance Le from the teaching point P2 on the straight line toward the teaching point P5, and thereafter, the center axis of the flange drive shaft and the teaching plane until the control point passes a point P5 on the straight line from the teaching point P2 to the teaching point P3. Is the intersection point P4, the teaching point P2,
A path interpolation method for a robot, characterized in that the wrist flange is rotationally driven so as to move on an arc passing through a point P5, and path interpolation is performed so that the control point linearly moves on the path taught by the control point.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| JP19878997A JP4085208B2 (en) | 1997-07-24 | 1997-07-24 | Robot control method |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| JP19878997A JP4085208B2 (en) | 1997-07-24 | 1997-07-24 | Robot control method |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| JPH1139021A true JPH1139021A (en) | 1999-02-12 |
| JP4085208B2 JP4085208B2 (en) | 2008-05-14 |
Family
ID=16396943
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| JP19878997A Expired - Fee Related JP4085208B2 (en) | 1997-07-24 | 1997-07-24 | Robot control method |
Country Status (1)
| Country | Link |
|---|---|
| JP (1) | JP4085208B2 (en) |
Cited By (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| WO2001030545A1 (en) * | 1999-10-29 | 2001-05-03 | Abb Flexible Automation A/S | A device and a method for determining coordinates and orientation |
| DE102015014236A1 (en) | 2014-11-06 | 2016-05-12 | Fanuc Corporation | Program correction device and program correction method of an industrial robot |
| WO2019077800A1 (en) * | 2017-10-20 | 2019-04-25 | 株式会社キーレックス | Teaching data generation system for vertical multi-joint robot |
| CN114234968A (en) * | 2021-12-17 | 2022-03-25 | 江西洪都航空工业集团有限责任公司 | Autonomous navigation method of mobile robot based on A star algorithm |
-
1997
- 1997-07-24 JP JP19878997A patent/JP4085208B2/en not_active Expired - Fee Related
Cited By (11)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| WO2001030545A1 (en) * | 1999-10-29 | 2001-05-03 | Abb Flexible Automation A/S | A device and a method for determining coordinates and orientation |
| DE102015014236A1 (en) | 2014-11-06 | 2016-05-12 | Fanuc Corporation | Program correction device and program correction method of an industrial robot |
| US9891618B2 (en) | 2014-11-06 | 2018-02-13 | Fanuc Corporation | Program correcting device and program correcting method of industrial robot |
| DE102015014236B4 (en) * | 2014-11-06 | 2020-09-03 | Fanuc Corporation | Program correction device and program correction method of an industrial robot |
| WO2019077800A1 (en) * | 2017-10-20 | 2019-04-25 | 株式会社キーレックス | Teaching data generation system for vertical multi-joint robot |
| JP2019076963A (en) * | 2017-10-20 | 2019-05-23 | 株式会社キーレックス | Teaching data production system for vertical multi-joint robot |
| CN111225772A (en) * | 2017-10-20 | 2020-06-02 | 希利股份有限公司 | Teaching data creation system for vertical articulated robot |
| US11203117B2 (en) | 2017-10-20 | 2021-12-21 | Keylex Corporation | Teaching data generation system for vertical multi-joint robot |
| CN111225772B (en) * | 2017-10-20 | 2022-10-14 | 希利股份有限公司 | Teaching data creation system for vertical articulated robot |
| CN114234968A (en) * | 2021-12-17 | 2022-03-25 | 江西洪都航空工业集团有限责任公司 | Autonomous navigation method of mobile robot based on A star algorithm |
| CN114234968B (en) * | 2021-12-17 | 2023-12-05 | 江西洪都航空工业集团有限责任公司 | Mobile robot autonomous navigation method based on A star algorithm |
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| Publication number | Publication date |
|---|---|
| JP4085208B2 (en) | 2008-05-14 |
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