JP5540043B2 - 最小侵襲ロボット手術システムのための応力推定方法 - Google Patents
最小侵襲ロボット手術システムのための応力推定方法 Download PDFInfo
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Description
器具の支点に対する位置を決定する(ここでは特に、器具の挿入深度あるいはセンサ(の基準フレーム)と支点との間の間隔を連続的に更新することを意味している)工程、
6DOF応力/トルクセンサを用いて、器具の第一端部によってエフェクタ装置へ加えられる応力及びトルクを測定する工程、及び
重ね合わせの原理を用いて、決定された位置、測定された応力及び測定されたトルクに基づいて器具の第二端部へ加えられる応力の推定値を算出する工程から構成される。
6−DOF加速度計を用いて6−DOF応力/トルクセンサに対して加わる重力負荷及び動的負荷を測定する操作、及び
測定応力及び測定トルクにおいて前記重力負荷及び動的負荷を補正する操作が含められる。
このような補正を行うことにより、器具先端部及び又は支点面において所望される応力推定値の精度を高めることが可能となる。
エフェクタ装置をマニピュレーターの作動空間、特に方向作動空間に亘って分布される一連のポーズ(pose)を経て通過させる工程、
各ポーズについて、測定された応力及び測定されたトルクを記録する工程、及び
記録された応力及びトルク測定値に基づいて応力及びトルク測定値の片寄りを判定する工程を含む較正操作がさらに含まれる。
さらに好ましい実施態様において、6−DOF加速度計が与えられる場合、前記較正操作にはさらに、
各ポーズについて、測定された線形加速度及び測定された角加速度を記録する操作、及び
記録された線形及び角加速度測定値に基づいて線形及び角加速度の片寄りを判定する操作が含まれる。
かかる較正操作を行うことにより、センサによって与えられる測定信号中の片寄り、及び所望される応力推定値の精度をさらに高めることを可能とするさらに有益なシステムパラメータを決定することが可能となる。
6−DOF応力/トルクセンサによって測定された応力データ及びトルクデータ及び、6−DOF加速度計によって測定された線形加速度データ及び角加速度データへ第一線形カルマンフィルターを適用する操作、
第一線形カルマンフィルターの適用後に重力負荷及び動的負荷による障害を補正する操作、及び
補正された応力データ及びトルクデータへ第二線形カルマンフィルターを適用する操作を含めることも可能である。
応力/トルク成分及び加速度成分用のすべてのカルマンフィルターは同様なフィルター由来の反応遅延を生ずる筈である。(加速度信号のノイズが応力/トルク測定のノイズよりもさらに大きいことによって)補正後に応力成分推定値中に過剰なノイズがある場合は、障害の補正後に第二フィルターを適用することが好ましい。第一フィルターによって補正中にノイズによって誘発される歪曲が減じられ、他方第二フィルターによって補正結果の平滑化が可能とされる。
本発明のさらなる詳細及び利点は、添付図面を参照する限定を意図しない以下に示した詳細な説明から明らかである。
図1は本発明に従った最小侵襲医療システムの主要な機械的要素を示した図である。本システムにはロボットマニピュレーターが含まれ、このマニピュレーターは全体を通して符号10で示されている。マニピュレーター10のフランジにはエフェクタ装置12が連結されている。図1に示すように、最小侵襲器具14は、第一端部16を用いてエフェクタ装置へ取り付けられる。器具14はその第二端部となる先端部20をもつ細長いシャフト18として成っている。その先端部において、器具14には通常特別なツール、例えばグラスパ、ハサミ、フック、凝固薬等が装着される。ロボットマニピュレーター10には、エフェクタ装置12の位置決めと方向決めを行うPRP−RRR連結配列によって6自由度(DOF)が与えられている。エフェクタ装置12は、器具14の縦シャフト軸と同一空間を占める6番目のDOFにあるマニピュレーター10を中心として最小侵襲器具14を回転させる一番先の回転ジョイントへ取り付けられる。理解されるように、ロボットマニピュレーター10によってエフェクタ装置12を動かすことにより、外科医の手の動きに対応可能な6軸位置定位・定方向装置が提供されることが理解されよう。
本項においては、図1〜3に示したシステムを用いた場合において、器具先端部20において所望される応力推定値に影響を与える主要障害源について概略的に述べる。
・F/Tセンサに対して加えられる静的負荷及び動的負荷、静的負荷は重力(F/TAS30が取り付けられたマニピュレーターに付属する質量体の重量)に基因するものであり、動的負荷はF/Tセンサに付属するペイロードの速度及び加速度によるものである、及び
・最小侵襲医療処置に関する障害源:トロカールガスタップ及び空気弁による侵入及び取出し方向へのトロカール摩擦応力、トロカールガスタップによる旋回抵抗、腹部への吹込み圧の変化による支点(旋回点)23の変化、支点23の不正確な限定、移動中におけるマニピュレーター10の不正確性による支点23の変動が挙げられる。
本発明の提案方法によれば、器具先端部20における応力FTip及び支点23における応力FFulcrumの正確な推定値を得ることが可能である。
TS = FTip × DTool + FFulcrum × DFulcrum (10)
FS = FTip + FFulcrum (11)
支点に対する器具の初期基準位置、例えば距離DFulcrum0は、一定の器具14がトロカール22中へ初めて挿入される場合には、以下に記載する手順を経て決定可能である。初期基準距離DFulcrum0を用いる場合、DFulcrumは、マニピュレーターの動作関数であり、マニピュレーターコントローラから分かる、侵入/取り出し指令を用いて持続的に更新される(すなわち、リアルタイムで決定される)。
理解されるように、ロボットマニピュレーター10へ取り付けられた例えばF/TAS30内の応力/トルクセンサによって、接触応力FTip、FFulcrumだけでなく、センサの感知プレートへ取り付けられた部材に対して加えられる重力負荷や動的(すなわち、動作関連)負荷も測定される。
Fcomp=Fsensor−Foffsets
− LoadMass(LinAccsensor−LinAccoffsets)
+ [(AngAccsensor - AngAccoffsets) × LoadCOG] (17)
によって与えられる。
式中、Fsensorは、F/Tセンサによって測定された場合における、SRF中の応力ベクトルを表す。
LinAccsensor は、SRF中の6−DOF加速度計によって測定された重力加速度を含む線形加速度を表す。
AngAccsensorはSRF中において6-DOF加速度計によって測定される角加速度である。
LoadCOGは、以下において概説されるように推定される、SRF中の6-DOF F/Tセンサーに付属する負荷の重量中心のベクトルである。
Foffsets・LinAccoffsets及びAngAccoffsetsは、以下において概説される較正処置期間中に推定されるセンサー片寄りベクトルである。
Tsensorは、F/Tセンサーによって測定されるSRF中のモーメントベクトルである。
TOffsetは、以下において概説されるように推定されるモーメント片寄りベクトルである。
FTは、F/TAS30の感知プレートに対してトルクを加える重力の影響及び加速度関連負荷の影響によって生成される応力を表す式(17)の右辺の3番目の項に等しい。
LoadInertiaは、オフライン分析における視覚的整調によって、すなわち慣性ベクトルの種々数値の測定プロットにおける補正精度の改善を観察することによって推定可能なSRF軸X,Y及びZを中心とする負荷慣性ベクトルである。
Fcomp = FS 及び Tcomp = Tsにおいて用いられる。
測定精度及び応力推定値計算に影響を与えるシステム関連パラメータを決定するため、適当な寸法合わせ技術、例えば最小二乗法が一連の測定データへ適用される。最小二乗法を適用するための連続データを得るため、ロボットマニピュレーター10は、該ロボットマニピュレーター10の作動空間の全体に亘って分布する予め適切に定められた一連の測定ポーズを経るように連続配置される。各ポーズにおいて、6−DOF構成の異なるマニピュレーター10を通してのF/TAS30の種々位置及び定位に対応して、ロボットマニピュレーター10は、F/TAS30のセンサから測定データが読み取られる時に静止状態となる。前記一連のポーズは、好ましくは十分な範囲(定位作動空間)に亘るその後の定位角度、すなわち、SRF(ロール)のZ軸を中心とする回転や、(例えば、重力に対するセンサの定位を変えるリスト関節/ジョイントを用いる)縦揺れ及び偏揺れ旋回軸を中心とした回転が含まれるように選定される。
Fsensor = Foffsets + LoadMass*(LinAccsensor - LinAccoffset) (21)
が用いられる。前記式において、
Fsensorは、SRFにおいてF/Tセンサーによって測定される場合における応力ベクトルである。
(LinAccsensor - LinAccoffset)によってSRFに対する重力応力の方向が与えられる。線形加速度測定には動作関連加速度(静止時は0)及び電気的片寄り(LinAccoffset)に加えて重力加速度条件が含まれるためである。
LoadMass*(LinAccsensor - LinAccoffset)は、F/TAS30に付属するペイロードの質量及びSRFに対するその方向によって与えられる重力応力ベクトルである。
Tsensor = LoadCOG×LoadMass*(LinAccsensor - LinAccoffset) + Toffsets (22) が用いられる。
MODULUS(LinAccsensor - LinAccoffset) = 1G (23)
が用いられる。式中Gは重力定数である。
理解されるように、ベクトル式(21)、(22)及び(23)によって、マニピュレータ10の一つの較正ポーズにおいて、F/TASセンサの測定ごとに7つのスカラー式と13の未知数が与えられる。
MEAN(AngAccsensor) = AngAccoffset
式中、AngAccsensorは加速度計によって特定される角加速度ベクトルであり、
AngAccoffsetは、角加速度成分についての電気的片寄りベクトルである。
F/TAS30を用いて得られた未処理の測定データに対してフィルタリング処理が行われなければならない。原則として種々の適切な方法が存在するが、線形推計学的処理においては、効率的に加速度及び応力/トルク処理変数を推定するため、及び特にF/Tセンサ及び加速度計に固有な測定ノイズを減ずるため、基礎的古典的形式及び離散カルマンフィルターの2種変形の適用が提案される。
・応力測定におけるFx、Fy及びFz
モーメント測定におけるMx、My及びMz
線形加速度測定におけるAx、Ay及びAz
・角加速度測定におけるRx、Ry及びRz
xk = A xk-1 + B uk-1 + wk-1
によって決定される処理であると仮定することが可能である。
本発明システムにおいては、全ての信号についてH=1であると仮定することができる。何故なら制御インプットがないため、測定値はその状態から直接得られ、またu=0だからである。さらに、前記状態はステップからステップへと変わってもほぼ不変であるため、すべての信号についてA=1と仮定される。しかしながら、応力及びモーメントの場合、前記状態は重力負荷および加速度負荷に従って変化し、また他のすべての信号については、前記状態はオペレータ動作指令すなわちマニピュレータ10の動作関数となる。従って、この後者の近似によって状態変化の原因が処理ノイズへ同化される。
・測定ノイズの共分散R=1.0: 最良値はセンサ較正段階において得ることができる真の測定ノイズ共分散であるが、測定値が信頼できないことを意味する厳密な正の数値(R>0)を用いることが可能である。実際、フィルター調整段階において決定されるシステム/処理ノイズ共分散パラメーターQによって初期測定ノイズ共分散値R中の誤差が補正される。
・初期状態値xk-1 = 最初の観察値
・初期カルマンゲイン値Kk=1.0
・フィルター同調によって決まる初期処理/システムノイズ共分散Q0
理解されるように、F/Tセンサ及びF/TAS30中の加速度計から得られた各成分測定値(信号)は、通常時間とともに変化し及び温度依存性である電気的バイアスまたは片寄りによって影響される。実験室での試験において、6−DOFフォイル型F/Tセンサ(温度補正装置内蔵)からの測定信号は約3時間の暖気運転後に安定化し、その後全測定範囲の約1.5%の範囲内に保持されることが見出された。しかしながら、各信号についての片寄り値は時間と共に変化し、医学的、特に外科用途の場合には、この変化によって上記応力の推定計算結果が変わってくるためこのような変化は許容できないものである。
この提案された機能は、コマンド要求に対応して点検を実施するソフトウエア実行操作として構成可能である。片寄りずれが過剰な場合には、上記操作によってマニピュレターコントローラへ警告が送られ、これにより例えば外科医に再度較正を行うように要求が行われる。さらに、この機能は、HMIに対して与えられるコマンドに基づいて、あるいはエフェクタ装置12上の手術器具存在検知装置の信号に基づいて自動的に手術器具を変える際にも遂行可能である。
最初に、以下において述べるソフトウェアアーキテクチャーは、器具先端部20及び支点23のレベルにおける接触応力推定値についてのデータ処理及び計算に目的が限定されているソフトウェアモジュールに関するものであることに注意が必要である。このアーキテクチャーにおいては、マニピュレーター10、エフェクタ装置12、あるいは他のシステム構成部分の制御に関する機能及び構造については考慮されていない。しかしながら、このモジュールは、当業者によればマニピュレーターコントローラのソフトウェアプログラム中へ一体化させることが可能である。
・クロックサイクルごとに読み取られるメッセージ待ち行列、
・フィルタリングされていない応力、トルク、及び加速度データが読み取られるハードウェアボードへのインタフェース、
・モジュールの機能によって要求される情報を読み取り及び結果を書き込むリアルタイムデータベースへのインタフェース、
・外部モジュールへのコマンドおよび事象メッセージ用のインタフェース。
図6は、有限状態機械として実施される応力感知システム(FSS)タスク(図5参照)の主要な5つの状態を示した図である。以下において、図5に示されている状態について簡潔に説明する。
・例えば離散カルマンフィルターカスケードを用いた線形推計学的処理のためのデータフィルタリング(「センサデータフィルタリング」の項参照)。
・F/Tセンサデータにおける重力負荷及び動的負荷の影響の補正(「片寄り及び、重力及び動的負荷の補正」の項参照)。
・マニピュレーター10の動作に基づく器具14の支点23に対する位置の決定、すなわち継続的更新(「支点に対する器具位置の決定」)。
・器具先端部20および支点のそれぞれにおける応力推定値の計算(「器具先端部及び支点レベルにおける応力の計算」の項参照)。
任意であるが、以下の操作も周期的処理として実施される。
・例えばリアルタイムデタベース中に記憶される所定の最大閾値に対する補正負荷のモニタリング。数値が過剰な場合には、警告メッセージあるいは動作停止コマンドが発せられ、この状態がリアルタイムデータベース中に書き込まれる。このような処理は、F/TAS30の安全でない状態あるいは障害を検出するために、器具先端部20及び支点レベル(トロカール22)における応力推定値にも適用される。
・センサの片寄りによるずれの点検(「片寄りずれの点検」の項参照)。
・腹空内吹込み圧のモニタリング。減圧となった場合における、この機能は適切な行動を取るための特に支点23の位置の見直し等の警告メッセージを発出する。
本発明による方法/システムは、正確かつコスト効率的方法で器具先端部における、また任意であるがトロカールレベルにおける接触応力の推定を可能とすることによって、ロボット及び又はコンピュータ補助型最小侵襲手術に貢献するものである。
Claims (15)
- 次の要件からなるマニプュレーター(10)を有する最小侵襲システムの操作方法、
互いに対して垂直な3軸をもつセンサ基準フレーム(X,Y,Z)を有する、6自由度(6−DOF)応力/トルクセンサ(30)が取り付けられたエフェクタ装置(12)、及び
最小侵襲器具(14)であって、前記エフェクタ装置(12)へ取り付けられる第一端部(16)、最小侵襲器具(14)の動作を制限する外部支点(23)を超えて定位される第二端部(20)、及び前記センサ基準フレーム(X,Y,Z)の器具軸(Z)に対して同一線上となる長手方向軸を有する器具シャフト(18)を有する最小侵襲器具(14)、
前記方法は、前記センサ基準フレーム(X,Y,Z)の原点から外部支点(23)までの初期基準距離ベクトル(DFulcrum 0)の決定を含む外部支点(23)に対する前記器具の位置の決定から構成され、
初期基準距離ベクトル(DFulcrum 0)の決定は、
前記最小侵襲器具(14)を、前記センサ基準フレーム(X,Y,Z)の前記器具軸(Z)に対して垂直となる両軸(X,Y)に沿って、両軸(X,Y)に沿った反作用力が一定閾値以下になるまで移動させる操作と、及び
前記器具軸(Z)に沿った外部支点(23)の位置を、次の(1)〜(3)のような「てこの原理」(lever principle)に基づく操作、
(1)最小侵襲器具(14)を十分な接触応力に達するまで旋回させ、
(2)前記接触応力に対応するモーメントベクトルモジュール及び応力ベクトルモジュールを測定し、及び
(3)前記モーメントベクトルモジュールを前記応力ベクトルモジュールで割算して前記器具軸(Z)に沿った外部支点(23)の位置を算出すること、
によって決定することを特徴とする方法。 - 外部支点(23)の位置が前記器具軸(Z)に沿って「てこの原理」を用いて決定されることを特徴とする請求項1項記載の方法であって、
該「てこの原理」が、
最小侵襲器具(14)を、十分な第一接触応力に達するまで第一方向へ旋回させ、
前記接触応力に対応する第一モーメントベクトルモジュールと第一応力ベクトルモジュールを測定し、
該第一モーメントベクトルモジュールを該第一応力ベクトルモジュールで割算して前記器具軸(Z)に沿った外部支点(23)の第一位置を算出し、
前記第一方向の反対方向となる第二方向へ器具(14)を十分な第二接触応力に達するまで旋回させ、
前記接触応力に対応する第二モーメントベクトルモジュールと第二応力ベクトルモジュールを測定し、
該第二モーメントベクトルモジュールを該第二応力ベクトルモジュールで割算して前記器具軸(Z)に沿った外部支点(23)の第二位置を算出し、及び
前記算出された第一位置と前記算出された第二位置の平均値を用いて前記初期基準距離ベクトル(DFulcrum 0)を設定する各過程から構成されることを特徴とする前記方法。 - 前記初期基準距離ベクトル(DFulcrum 0)の決定に基いて、前記器具のすべての動作が前記外部支点(23)に対して為されることを特徴とする請求項1項または2項記載の方法。
- 前記エフェクタ装置に6自由度加速度計が備えられること、及び前記方法に、
前記6自由度加速度計を用いて前記6自由度応力/トルクセンサに対して働く重力負荷及び又は動的負荷を測定する工程と、
前記測定された応力及び前記測定されたトルク中に含まれる前記重力負荷及び又は動的負荷を補正する工程がさらに含まれることを特徴とする請求項1項または2項記載の方法。 - 外部支点(23)に対する前記器具の位置決定が、前記距離ベクトル(DFulcrum) 及びマニピュレーター動作情報を用いる連続更新に基づいて行われることを特徴とする請求項3項記載の方法。
- 前記与えられる閾値が約0.3Nであり、及び又は前記十分な接触応力が約3Nであることを特徴とする請求項1〜5のいずれかに記載の方法。
- 線形カルマンフィルターを前記6DOF応力/トルクセンサによって測定された応力及びトルクデータに適用する工程がさらに含まれることを特徴とする請求項1〜6のいずれかに記載の方法。
- 前記センサ基準フレーム(X,Y,Z)から一定基準フレームへの座標変換を経由して、一定基準フレームに対する外部支点(23)の位置を算出する工程がさらに含まれることを特徴とする請求項1〜7のいずれかに記載の方法。
- 互いに対して垂直な3軸を有し、かつ最小侵襲器具(14)を把持するように形状化されるセンサ基準フレーム(X,Y,Z)を有する、6自由度(6−DOF)応力/トルクセンサが取り付けられたエフェクタ装置(12)を備えるマニピュレーター(10)から構成される最小侵襲医療システムであって、
該最小侵襲器具(14)には、前記エフェクタ装置(12)で支えられる時に、該エフェクタ装置へ取り付けられる第一端部(16)、前記最小侵襲器具(14)の動作を制限する外部支点(23)を超えて定位される第二端部(20)、及び前記センサ基準フレーム(X,Y,Z)の器具軸(Z)と共軸となる長手方向軸をもつ器具シャフト(18)が備えられ、
前記システムには、
前記センサ基準フレーム(X,Y,Z)の原点から外部支点(23)までの初期基準距離ベクトル(DFulcrum 0)を決定することを含め、前記最小侵襲器具(14)の外部支点に対する位置を決定するようにプログラムされるプログラム可能な計算装置が含まれ、
初期基準距離ベクトル(DFulcrum 0)の決定が、
前記最小侵襲器具(14)を、前記器具軸(Z)に対してそれぞれ垂直となる前記センサ基準フレーム(X,Y,Z)の両軸(X,Y)に沿って、両軸(X,Y)に沿った反作用力が一定閾値以下となるまで移動させる操作と、
次の(1)〜(3)のようなてこの原理を用いて、
(1)最小侵襲器具(14)を十分な接触応力に達するまで旋回させ、
(2)前記接触応力に対応するモーメントベクトルモジュールと応力ベクトルモジュールを測定すること、及び
(3)前記モーメントベクトルモジュールを前記応力ベクトルモジュールで割算することによって前記器具軸(Z)に沿った外部支点(23)の位置を算出することによって、前記器具軸に沿った外部支点(23)の位置を決定すること、
から構成されることを特徴とするシステム。 - てこの原理を用いて前記器具軸(Z)に沿った外部支点(23)の位置を決定する工程が、
最小侵襲器具(14)を第一方向へ十分な接触応力に達するまで旋回させ、
前記接触応力に対応する第一モーメントベクトルモジュールと第一応力ベクトルモジュールを測定し、
前記第一モーメントベクトルモジュールを前記第一応力ベクトルモジュールで割算することによって前記器具軸(Z)に沿った外部支点(23)の第一位置を算出し、
最小侵襲器具(14)を前記第一方向と反対方向となる第二方向へ十分な接触応力に達するまで旋回させ、
前記接触応力に対応する第二モーメントベクトルモジュールと第二応力ベクトルモジュールを測定し、
前記第二モーメントベクトルモジュールを前記第二応力ベクトルモジュールで割算することによって前記器具軸(Z)に沿った外部支点(23)の第二位置を算出し、及び
前記算出された第一位置と前記算出された第二位置の平均値を用いて前記初期基準距離ベクトル(DFulcrum 0)を設定する各操作から構成されることを特徴とする請求項9項記載のシステム。 - 前記プログラム可能な計算装置が、前記初期基準距離ベクトル(DFulcrum 0)の決定に際して、前記外部支点(23)に対して前記最小侵襲器具があらゆる動作を行えるようにさらにプログラムされることを特徴とする請求項9項または10項記載のシステム。
- 前記エフェクタ装置に6−DOF加速度計が備えられ、及び前記プログラム可能な計算装置が、前記6−DOF加速度計を用いて行われる前記6−DOF応力/トルクセンサに対して課される重力負荷及び又は動的負荷の測定を処理し、及び前記測定された応力及び前記測定されたトルク中の重力負荷及び又は動的負荷を補正するようにさらにプログラムされることを特徴とする請求項9項、10項または11項記載のシステム。
- 前記プログラム可能な計算装置がさらに、前記最小侵襲器具の支点(23)に対する位置の決定が前記距離ベクトル(DFulcrum)及びマニピュレーター動作情報を用いての連続更新に基づいて行われるようにプログラムされることを特徴とする請求項10項記載のシステム。
- 前記プログラム可能な計算装置がさらに、前記センサ基準フレーム(X,Y,Z)から一定基準フレームまでの座標変換を経由して外部支点(23)の一定基準フレームに対する位置が算出されるようにプログラムされることを特徴とする請求項11〜13のいずれかに記載のシステム。
- プログラム可能な計算装置及び、互いに対して垂直な3軸をもつセンサ基準フレーム(X,Y,Z)を有し、かつ最小侵襲器具(14)を把持するように形状化される6自由度(6−DOF)応力/トルクセンサ(30)が取り付けられる、エフェクタ装置(12)を有するマニピュレーター(10)から構成される最小侵襲医療システムに用いられるソフトウェアプログラムであって、
前記最小侵襲器具(14)には、前記エフェクタ装置(12)によって把持される時に、前記エフェクタ装置へ取り付けられる第一端部(16)、前記器具の動作を制限する外部支点(23)を超えて定位される第二端部(20)、及び前記センサ基準フレーム(X,Y,Z)の器具軸と同一線上にある長手方向軸をもつ器具シャフト(18)が備えられ、
前記ソフトウェアプログラムには、前記プログラム可能計算装置を作動させた時に、前記センサ基準フレーム(X,Y,Z)の原点から外部支点への初期基準距離ベクトル(DFulcrum 0)を決定することを含め、前記器具の外部支点(23)に対する位置を決定する方法を前記システムに遂行させるプログラムコードが含まれ、
該初期基準距離ベクトル(DFulcrum 0)の決定は、
それぞれ前記器具軸(Z)に対して垂直となる前記センサ基準フレーム(X,Y,Z)の両軸(X,Y)に沿って、両軸(X,Y)に沿った反作用力が一定閾値以下となるまで前記最小侵襲器具(14)を動作させ、及び
次の(1)〜(3)のようなてこの原理を用いて、
(1)最小侵襲器具(14)を十分な接触応力に達するまで旋回させ、
(2)前記接触応力に対応するモーメントベクトルモジュール及び応力ベクトルモジュールを測定し、及び
(3)前記モーメントベクトルモジュールを前記応力ベクトルモジュールで割算することによって前記器具軸(Z)に沿った外部支点(23)の位置を算出することによって、前記器具軸(Z)に沿った外部支点(14)の位置を決定すること、
によって為されることを特徴とするソフトウェアプログラム。
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