JPS61122707A - Locus control method of robot - Google Patents

Locus control method of robot

Info

Publication number
JPS61122707A
JPS61122707A JP24518384A JP24518384A JPS61122707A JP S61122707 A JPS61122707 A JP S61122707A JP 24518384 A JP24518384 A JP 24518384A JP 24518384 A JP24518384 A JP 24518384A JP S61122707 A JPS61122707 A JP S61122707A
Authority
JP
Japan
Prior art keywords
arm
displacement
joint
theta
tip
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.)
Pending
Application number
JP24518384A
Other languages
Japanese (ja)
Inventor
Yoshiki Arakawa
荒川　佳樹
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Panasonic Holdings Corp
Original Assignee
Matsushita Electric Industrial Co Ltd
Priority date (The priority date 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 date listed.)
Filing date
Publication date
Application filed by Matsushita Electric Industrial Co Ltd filed Critical Matsushita Electric Industrial Co Ltd
Priority to JP24518384A priority Critical patent/JPS61122707A/en
Publication of JPS61122707A publication Critical patent/JPS61122707A/en
Pending legal-status Critical Current

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Classifications

    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B19/00—Programme-control systems
    • G05B19/02—Programme-control systems electric
    • G05B19/42—Recording and playback systems, i.e. in which the programme is recorded from a cycle of operations, e.g. the cycle of operations being manually controlled, after which this record is played back on the same machine

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  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Engineering & Computer Science (AREA)
  • Automation & Control Theory (AREA)
  • Numerical Control (AREA)
  • Manipulator (AREA)

Abstract

PURPOSE:To improve a processing speed by finding out the displacement of a joint at first, and then finding out the rotational angles of respective axes. CONSTITUTION:An objective point of the leading end of an arm and its posture Xe are inputted at first, and then the position (x) of the joint and the positional posture X of the leading end of the arm are found out on the basis of a current axial angle theta. Fine displacement DELTAX of the X on a given locus is calculated on the basis of the X and Xe to form X'=X+DELTAX. Then, 6-element simultaneous linear equations are solved on the basis of fx(x,X').DELTAX=-f(x,X) to find out the fine displacement DELTAx. A position x' after the displacement of the joint is found out on the basis of x'=x+DELTAx and its axial angle theta' is found from the x' to find out the axial rotational angle DELTAtheta from DELTAtheta=theta'-theta. The DELTAtheta is outputted to control the arm on the basis of PTP method to device whether the leading end of the arm reaches the objective point or not, and if the leading end does not reach the objective point, theta' is substituted for theta and the processing for calculating the (x) and X from theta is restored.

Description

【発明の詳細な説明】 産業上の利用分野 本発明はロボットの軌跡制御方法に関するものである。[Detailed description of the invention] Industrial applications The present invention relates to a robot trajectory control method.

従来例の構成とその問題点 一般に、ロボットはアームの先端を所望する軌跡に沿っ
て動作させることが必要である。このような制御を行う
ために、アーム先端の軌道を細かく分割しそれらの点列
をＦＴＰ　（ポイント・ツー・ポイント、以下ＦＴＰと
略す。）方式で制御する方法が採用されている。このよ
うな制御を行うにはアーム先端の位置姿勢から各軸の回
転角を求める（以下、「逆変換」と称する）必要がある
〇しかし、この逆変換は、軸構成によりあるいは軸数が
増えてくると載置的に解を求めることが困難な場合も生
じる。徒た、求められたとしてもかなりの演算量となり
これをマイクロコンピュータでリアルタイムで処理する
には、時間的にも精度的にも問題が多く制御に支障が生
じる場合も多い。Conventional configurations and their problems In general, it is necessary for a robot to move the tip of its arm along a desired trajectory. In order to perform such control, a method has been adopted in which the trajectory of the tip of the arm is divided into small pieces and a sequence of points thereof is controlled using an FTP (point-to-point, hereinafter abbreviated as FTP) method. To perform such control, it is necessary to find the rotation angle of each axis from the position and orientation of the arm tip (hereinafter referred to as "inverse transformation"). In this case, it may be difficult to find a practical solution. Even if it were to be calculated, it would be a considerable amount of computation, and processing it in real time with a microcomputer would have problems in terms of time and accuracy, often resulting in problems with control.

そこで、このようなロボットの軌跡制御においては、１
つの方法として、アーム先端の位置・姿勢の微小変位か
ら各軸の回転角を近似的に求める方法も採用されている
。Therefore, in controlling the trajectory of such a robot, 1
One method is to approximately determine the rotation angle of each axis from minute displacements in the position and posture of the arm tip.

各軸の角度ベクトルσとアーム先端の位置姿勢ベクトル
Ｘの関係は次の式で表わされる。The relationship between the angle vector σ of each axis and the position and orientation vector X of the arm tip is expressed by the following equation.

Ｘ＝ｑ（の　　　　　　　　・・・・・・・・・・・・
・・・・・・・・・・・・・・・？）ここで、ＸがＸ′
に微小変位したときθがθ′に変位したとすると Ｘ’＝　ｑ　（θ′）　　　　・・・・・・・・・・・
・・・・・・・・・・・・・・・・（３）ここで、Ｘと
θの微小変位をそれぞれΔＸ、Δθとおくと （２）式と（３）式と（４）式より Ｘ’＝ｑ（θ′） ＝ｑＣθ＋Δθ） 立ヴの＋ｑθ（θ）・Δθ キＸ＋ｑθ（θ）・Δθ　　　・・・・・・・・・・・
・・・・・・・・・・＋５１ここで、ｑθ（θ）はｑ１
θ）をθで微分したものを表す。結局、 ΔＸ＝ｇθ（の・Δθ　　　　　　・・・・・・・・・
・・・・・・・・・・・・（６）となる。X=q(of ・・・・・・・・・・・・
・・・・・・・・・・・・・・・? ) where X is
If θ is displaced to θ' when there is a small displacement in , then X'= q (θ')
・・・・・・・・・・・・・・・・・・(3) Here, if the minute displacements of From X'=q(θ') =qCθ+Δθ) Standing +qθ(θ)・Δθ KiX+qθ(θ)・Δθ
・・・・・・・・・＋51Here, qθ(θ) is q1
θ) is differentiated by θ. In the end, ΔX=gθ(of・Δθ ・・・・・・・・・
・・・・・・・・・・・・(6)

ここで、ｑθ（θ１　はヤコビアン行列と呼ばれるもの
であり、ｑθ（の＝Ｉ＋のとおくと ΔＸ＝Ｊ（の・Δθ 、・、Δθ＝　１−１（θ）・ΔＸ　　　　・・・・・
・・・・・・・・・・・・・・・・（ア）つまり、ヤコ
ビアン行列工（θ）が既知であるならばアーム先端の位
置姿勢の微小変位より連立−次方程式を解くことによっ
て各軸の回転角の変位を近似的に求めることができる。Here, qθ(θ1 is called a Jacobian matrix, and if we set qθ(=I+), then ΔX=J(・Δθ , ・, Δθ= 1−1(θ)・ΔX ・・・
・・・・・・・・・・・・・・・・・・(A) In other words, if the Jacobian matrix (θ) is known, then by solving the simultaneous -order equations from the minute displacement of the position and orientation of the arm tip. The rotational angle displacement of each axis can be approximately determined.

以上の式を用いた従来のロボットの軌跡制御方法につい
て、図面を参照しながら、説明を行う。A conventional robot trajectory control method using the above equation will be explained with reference to the drawings.

第１図は従来のロボットの軌跡制御方法の構成を示すも
のである。第１図において、１は動作目標点におけるア
ーム先端の位置および姿勢を入力する工程、２は現在の
軸角度から実際のアーム先端の位置姿勢を算出する工程
（以下、これを「正変換」と称する）、３は現在のアー
ム先端の位置姿勢からの与えられた軌跡上での微小変位
を算出しこれを中間目標点とする工程、４はこの微小変
位を用いて各軸の回転角を算出する工程、６はこの回転
角を用いてロボットを中間目標点までＰＴＰ方式で制御
する工程、６は現在点が目標点であるかどうかを判定す
る工程である。FIG. 1 shows the configuration of a conventional robot trajectory control method. In Fig. 1, 1 is the step of inputting the position and orientation of the arm tip at the target movement point, and 2 is the step of calculating the actual position and orientation of the arm tip from the current axis angle (hereinafter, this is referred to as "positive conversion"). 3 is the step of calculating the minute displacement on the given trajectory from the current position and orientation of the tip of the arm and using this as an intermediate target point. 4 is the step of calculating the rotation angle of each axis using this minute displacement. 6 is a step of controlling the robot to an intermediate target point using the PTP method using this rotation angle, and 6 is a step of determining whether the current point is the target point.

ところで、この制御方法はリアルタイムでマイクロコン
ピュータで処理するには演算量が少なくなり有効かつ実
際的な制御方法であるが、この方法も、軸構成によって
は、アーム先端の位置姿勢から直接的に各軸の回転角を
求める逆変換法と同様に、ヤコビアン行列Ｉ（θ）がか
なり複雑な長い式となり演算量が増えリアルタイムで処
理するには時間的・精度的にむずかしくなる。By the way, this control method is an effective and practical control method because the amount of calculation is small to be processed by a microcomputer in real time. Similar to the inverse transformation method for determining the rotation angle of the axis, the Jacobian matrix I(θ) becomes a fairly complicated and long equation, which increases the amount of calculations and makes it difficult to process in real time in terms of time and accuracy.

発明の目的 本発明は上記欠点に鑑み、どのような軸構成であっても
リアルタイムでロボットを軌跡制御する方法を提供する
ものである。OBJECTS OF THE INVENTION In view of the above drawbacks, the present invention provides a method for controlling the trajectory of a robot in real time regardless of the axis configuration.

発明の構成 この目的を達成するために本発明では、アーム先端の微
小変位より関節の変位を算出する工程を軸の回転角を算
出する工程の前段に用いた。この方法により、演算量が
大幅に減少し、従来の方法ではマイクロコンピュータで
実時間制御不可能な軸構成も制御可能となった。Structure of the Invention In order to achieve this object, in the present invention, the step of calculating the displacement of the joint from the minute displacement of the tip of the arm is used before the step of calculating the rotation angle of the shaft. This method significantly reduces the amount of calculations and makes it possible to control axis configurations that cannot be controlled in real time using a microcomputer using conventional methods.

実施例の説明 以下本発明の一実施例の基本構成を第２図により説明す
る。７は動作目標点におけるアーム先端の位置および姿
勢を入力する入力工程、８は現在の軸角度から実際のア
ーム先端の位置姿勢を算出する位置算出工程、９は現在
のアーム先端の位置姿勢からの与えられた軌跡上での微
小変位を算出しこれを中間目標点とする微小変位算出工
程、１０はこの微小変位を用いて関節の位置変位を算出
する位置変位算出工程、１１はへこの関節の変位を用い
て各軸の回転角を算出する角算出工程、１２はこの回転
角を用いてロボットを中間目標点までＦＴＰ方式で制御
する制御工程、１３は現在点が目標点であるかどうかを
判定する判定工程である。DESCRIPTION OF THE EMBODIMENTS The basic configuration of an embodiment of the present invention will be explained below with reference to FIG. 7 is an input step for inputting the position and orientation of the arm tip at the movement target point, 8 is a position calculation step for calculating the actual arm tip position and orientation from the current axis angle, and 9 is a calculation step for calculating the actual arm tip position and orientation from the current arm tip position and orientation. A minute displacement calculation step in which a minute displacement on a given trajectory is calculated and this is used as an intermediate target point; 10 is a position displacement calculation step in which the position displacement of the joint is calculated using this minute displacement; 11 is a position displacement calculation step in which the position displacement of the joint is calculated using this minute displacement; An angle calculation step in which the rotation angle of each axis is calculated using the displacement; 12 is a control step in which the rotation angle is used to control the robot to an intermediate target point using the FTP method; and 13 is a control step to determine whether the current point is the target point. This is a judgment step.

つまり、従来の方法ではアーム先端の位置姿勢の微小変
位から直接各軸の回転角を求めていたが、本発明では、
関節の変位をまず求め、次に、各軸の回転角を求める方
法を採用した。In other words, in the conventional method, the rotation angle of each axis was directly determined from the minute displacement of the position and orientation of the arm tip, but in the present invention,
A method was adopted in which the displacement of the joints was first determined, and then the rotation angle of each axis was determined.

ここで、この部分についてさらに詳しく説明しておく。Here, I will explain this part in more detail.

簡閲の位置ベクトルをＸで表わすとアーム先端の位置姿
勢ベクトルＸとの関係式は次の式で表わされる。When the simple position vector is represented by X, the relational expression between the position and orientation vector X of the tip of the arm is expressed by the following equation.

ｆｃｘ、Ｘ）＝Ｏ・・・−・・・・・・・・・・・・・
・・・・（８）ここで、ＸがＸ′に微小変位したときＸ
がＸ′に変位したとすると ｆ　（ｘ’、　Ｘ’）　＝Ｏ・・・・・・・・・・・・
・・・・・・−・・（ｇ４ここで、ＩとＸの微小変位を
それぞれΔＸ、ΔＸとおくと ｆ（ｘ’、Ｘ’）立ｆ（ｘ、Ｘ’　）＋ｆｘ（ｘ、Ｘ’
ｌ（ｘ’−ｘ）中ｆ（ｘ、Ｘ’　）＋ｆ、（ｘ、Ｘ’）
　・Δｘ−・・・・（１０）ここで、ｆ　ｘ　（”　、
Ｘ　）　Ｈｆ　（ｘ　、Ｘ　）をＸで微分したものを表
わす。そして、ｆ（χ／　、Ｘ／　）　＝　Ｑであるか
らｆ　（ｘ、Ｘ′）・Δｘ　＝−ｆ（ｘ、Ｘ’）ｆ、（
ｘ、Ｘ＋１Ｘ）−１ｘ＝−ｆｃｘ、Ｘ４−ＩＸ）、°、
　１ｘ＝−ｆ　（ｚ、Ｘ＋ｌＸ’）−’　−ｆ（ｘ、Ｘ
＋ＪＸ）　−（１１）上式により、現在の関節の位置ベ
クトルＩおよび次の目標点（Ｘ＋ΔＸ）から連立−次方
程式を解くことによって関節の変位を求めることができ
る。fcx,X)=O・・・-・・・・・・・・・・・・・・・
...(8) Here, when X is slightly displaced to X',
If is displaced to X', then f (x', X') = O...
・・・・・・－・・・(g4Here, if we set the minute displacements of I and X as ΔX and ΔX, respectively, then f(x',
f(x, X') + f, (x, X') in l(x'-x)
・Δx−・・・(10) Here, f x (”,
X) represents the differentiation of Hf (x, X) with respect to X. And since f(χ/, X/) = Q, f(x, X')・Δx = -f(x,
x, X+1X)-1x=-fcx,X4-IX), °,
1x=-f (z, X+lX')-' -f(x,
+ J

そして、この関節の変位を用いて各軸の回転角を求める
ことができる。Then, the rotation angle of each axis can be determined using the displacement of this joint.

以下、詳細を第３図、第４図を参照しながら説明する。Details will be explained below with reference to FIGS. 3 and 4.

１４は６軸アーム型ロボツト、１５は第１関節、１６は
第１軸で２軸まわりに回転する、１７は第２関節、１８
は第２軸で２軸を含む平面上で回転する、１９？ｉ第３
関節、２０は第３軸で２軸を含む平面上で回転する、２
１は第４関節、２２は第４軸で第３軸まわりに回転し途
中で９ｏ度曲がっている、２５は第６関節゛、２６は第
６関節で第６軸まわりに回転する、２７はアーム先端の
動作データ全入力処理し記憶する、２８はこの動作デー
タを用いてアームを軌跡制御し各軸の回転角を出力する
、２９はこの軸の回転角を用いてアームをＦＴＰ制御す
る手段である。14 is a six-axis arm type robot, 15 is a first joint, 16 is a first axis that rotates around two axes, 17 is a second joint, 18
rotates on a plane containing two axes with the second axis, 19? i 3rd
Joint, 20 rotates on a plane containing two axes with a third axis, 2
1 is the 4th joint, 22 is the 4th axis, rotates around the 3rd axis, and is bent 9o in the middle, 25 is the 6th joint, 26 is the 6th joint, rotates around the 6th axis, 27 is the 6th joint A means for processing and storing all the motion data of the tip of the arm; 28 uses this motion data to control the trajectory of the arm and outputs the rotation angle of each axis; 29 means for FTP control of the arm using the rotation angle of this axis. It is.

次に、アームを軌跡制御する計算手続きについて述べる
。Next, the calculation procedure for controlling the trajectory of the arm will be described.

第３図のようにＰＪｌ！標原点全原点関節、アーム先端
の位置を第５軸の直角に曲がっている部分、また、その
姿勢を第６軸の方向にとり、それぞれ、（Ｘ、Ｙ、Ｚ）
、（Ｌ、Ｍ、Ｎ）とおく。また、第３関節および第４軸
の直角に曲がる部分の位置をそれぞれ（”３　＋　１３
　＋　２３　）　＋　（”５　＋　’！６　＋　”５）
とおく０このとき、アーム先端の位置姿勢ベクトルＸ、
および関節の位置ベクトルＸは次のように表現すること
ができる。As shown in Figure 3, PJl! All origin joints at the reference point, the position of the arm tip is the part bent at right angles to the 5th axis, and its posture is in the direction of the 6th axis, respectively (X, Y, Z)
, (L, M, N). In addition, the positions of the third joint and the part that bends at right angles to the fourth axis are respectively ("3 + 13
+ 23 ) + ("5 + '!6 + "5)
0 At this time, the position and orientation vector of the arm tip is X,
and the joint position vector X can be expressed as follows.

このとき、ＸとＸの関係式ｆ（ｘ、Ｘ）は二〇　　　　
　・・・・・・・・・・・・・・・・・・（１３）とな
る。At this time, the relational expression f(x, X) between X and X is 20
・・・・・・・・・・・・・・・・・・(13)

上式より、ｆ工（ｘ、Ｘ）を求めると次式となる。From the above formula, f(x, X) is calculated as follows.

（１３）式および（１４）式を（１１）式に代入するこ
とにより、関節の位置の微小変位ΔＩを求めることがで
きる。By substituting equations (13) and (14) into equation (11), the minute displacement ΔI of the joint position can be determined.

以上の定式化に基づいて、本発明の実施例の計算走読き
の７０−を第４図を参照しながら説明するＯ まず、アーム先端の目標点および姿勢Ｘｓを入力する。Based on the above formulation, calculation scanning 70- of the embodiment of the present invention will be explained with reference to FIG. 4. First, the target point and posture Xs of the arm tip are input.

次に、現在の軸角度θよシ関節の位置Ｘおよびアーム先
端の位置姿勢Ｘを求める。次に、ＸとＸｅｔ−用いて与
えられた軌跡上でのＸの微小変位Δχを算出する。そし
て、ｘ’＝ｘ＋ΔＸとおく０次に、ｆｘ（ｃ、Ｘ’）−
ΔＸ＝−ｆ（ｚ、Ｘ）よシロ元連立−字方程式を解いて
関節の微小変位ΔＸを求める。Next, the current axis angle θ, the position X of the joint, and the position and orientation X of the arm tip are determined. Next, a minute displacement Δχ of X on the given trajectory is calculated using X and Xet−. Then, let x' = x + ΔX, and the 0th order is fx (c, X') -
The minute displacement ΔX of the joint is determined by solving the simultaneous equations of ΔX=−f(z,X).

次に、関節の変位後の位置Ｘ′をｘ’＝ｘ＋ΔＩより求
める。次に、このときの軸角度θ′をＸ′より求める。Next, the position X' of the joint after displacement is determined from x'=x+ΔI. Next, the axis angle θ' at this time is determined from X'.

次に、軸回転角ΔθをΔθ＝θ′−〇より求める。次ム
Δθを出力することによってアームＦＴＰ方式で制御す
る。次に、目標点に到達したかどうかを判定し、そうで
あれば処理を終了し、そうでなければθにθ′を代入し
、θよりｘ、Ｘを算出する処理にもどり処理を続行する
。Next, the shaft rotation angle Δθ is determined from Δθ=θ'−〇. Control is performed using the arm FTP method by outputting the second wave Δθ. Next, determine whether the target point has been reached, and if so, end the process; if not, substitute θ' for θ, return to the process of calculating x and X from θ, and continue the process. .

以上が本発明の一実施例であるが、この倒板外の軸構成
あるいは軸数のロボットにも適用可能である。The above is one embodiment of the present invention, but it is also applicable to robots with an axis configuration or number of axes other than this inverted plate.

発明の効果 以上、本発明によると、どのような軸数・軸構成のロボ
ットでも比較的容易に軌跡制御できる。As described above, according to the present invention, the trajectory of a robot having any number of axes and any axis configuration can be controlled relatively easily.

【図面の簡単な説明】[Brief explanation of drawings]

！１図は従来の軌跡制御方法のフローチャート図、第２
図は本発明の一実施例における軌跡制御方法のフロ−７
ヤート図、第３図は本発明の一実施例における多関節ロ
ボットの構成および制御系統金示す系統図、第４図は本
発明の一実施例の制御方法および演算手順を示すフロー
チャート図である。 ７・・・・・・入力工程、８・・・・・・位置算出工程
、９・・・・・・微小変位夏山工程、１０・・・・・・
位置変位算出工程、１１・・・・・・角算出工程、１２
・・・・・・制御工程、１３・・・・・・判定工程〇 代理人の氏名　弁理士　中　尾　敏　男　ほか１名第１
図 第　２− 第３図 と Ｚ４図! Figure 1 is a flowchart of the conventional trajectory control method;
The figure shows flow 7 of the trajectory control method in one embodiment of the present invention.
FIG. 3 is a system diagram showing the configuration and control system of an articulated robot according to an embodiment of the present invention, and FIG. 4 is a flowchart showing a control method and calculation procedure according to an embodiment of the present invention. 7...Input process, 8...Position calculation process, 9...Minute displacement Natsuyama process, 10...
Position displacement calculation step, 11...Angle calculation step, 12
...Control process, 13...Judgment process〇 Name of agent Patent attorney Toshio Nakao and 1 other person 1st
Figures 2-3 and Z4

Claims (2)

【特許請求の範囲】[Claims] （１）多関節を有するアーム型ロボットの先端における
動作の目標位置および姿勢を入力する入力工程と、現在
の軸角度よりアーム先端の位置姿勢および関節の位置を
算出する位置算出工程と、アーム先端の現在の位置姿勢
からの動作軌跡上における微小変位を算出する微小変位
算出工程と、この微小変位より関節の位置変位を算出す
る位置変位算出工程と、この関節の位置変位より各軸の
回転角を算出する角算出工程と、この回転角よりロボッ
トをポイント・ツー・ポイント方式で制御する制御工程
と、アーム先端が目標点に到達したかどうかを判定する
判定工程とで構成され、前記位置変位算出工程を角算出
工程より前に設けてなるロボットの軌跡制御方法。(1) An input process for inputting the target position and posture of the motion at the tip of an arm-type robot with multiple joints, a position calculation process for calculating the position and posture of the arm tip and joint positions from the current axis angle, and the arm tip A minute displacement calculation step that calculates a minute displacement on the motion trajectory from the current position and orientation of It consists of an angle calculation step that calculates the rotation angle, a control step that controls the robot in a point-to-point method based on this rotation angle, and a judgment step that determines whether the arm tip has reached the target point. A robot trajectory control method in which a calculation process is provided before an angle calculation process. （２）アーム先端の位置姿勢の微小変位より関節の変位
を算出する工程において式 Δｘ＝−ｆ＾−＾１＿ｘ（ｘ、Ｘ＋ΔＸ）ｆ（ｘ、Ｘ＋
ΔＸ）・・・（１）ｘ：関節の位置ベクトル Ｘ：アーム先端の位置姿勢ベルトル Δｘ：ｘの微小変位 ΔＸ：Ｘの微小変位 ｆ（ｘ、Ｘ）：ｘとＸの関係式 ｆ＿ｘ（ｘ、Ｘ）：ｆ（ｘ、Ｘ）をｘで微分したものを
用いて関節の変位を算出する特許請求の範囲第１項記載
のロボットの軌跡制御方法。(2) In the process of calculating the displacement of the joint from the minute displacement of the position and orientation of the tip of the arm, the formula Δx = -f^-^1_x (x, X + ΔX) f (x, X +
ΔX)...(1) x: Joint position vector X: Arm tip position/posture belt Δx: Minute displacement of x ΔX: Minute displacement of ,
JP24518384A 1984-11-20 1984-11-20 Locus control method of robot Pending JPS61122707A (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
JP24518384A JPS61122707A (en) 1984-11-20 1984-11-20 Locus control method of robot

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
JP24518384A JPS61122707A (en) 1984-11-20 1984-11-20 Locus control method of robot

Publications (1)

Publication Number Publication Date
JPS61122707A true JPS61122707A (en) 1986-06-10

Family

ID=17129843

Family Applications (1)

Application Number Title Priority Date Filing Date
JP24518384A Pending JPS61122707A (en) 1984-11-20 1984-11-20 Locus control method of robot

Country Status (1)

Country Link
JP (1) JPS61122707A (en)

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JP2007007837A (en) * 2005-06-03 2007-01-18 Advanced Telecommunication Research Institute International Device, method, and program for positional control

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JP2007007837A (en) * 2005-06-03 2007-01-18 Advanced Telecommunication Research Institute International Device, method, and program for positional control

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