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Obstacle Avoidance Path Planning of Space Manipulator Based on Improved Artificial Potential Field Method

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Abstract

This paper proposes an approach about obstacle collision-free motion planning of space manipulator by utilizing a Configuration-Oriented Artificial Potential Field method in 3-D space environment. Firstly, the artificial potential field method, which is usually used in 2-D space, is extended to 3-D space. Secondly, improving the artificial potential field method enables to carry out obstacle avoidance planning for the configuration of entire space manipulator (including the end-effector and links). Finally, the approach is combined with the inverse kinematics calculation which is based on the Generalized Jacobian Matrix for planning a collision-free motion of space manipulator. At the end of the article, by simulating the method mentioned above, the validity of the proposed method is verified.

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Abbreviations

r 0 ∈ R 3 :

Position vector of the center of mass (CM) of base with respect to inertial coordinates

r i ∈ R 3 (i = 1, …, n):

Position vector of CM of link i with respect to inertial coordinates

r g ∈ R 3 :

Position vector of the system CM with respect to inertial coordinates

b 0 ∈ R 3 :

Position vector from CM of base to joint 1 with respect to inertial coordinates

p i  ∊ R 3 (i = 1, … , n):

Position vector of joint i with respect to inertial coordinates

p e  ∈ R 3 :

Position vector of end-effector with respect to inertial coordinates

v 0 ∊ R 3 :

Linear velocity of base at certain time

v e ∊ R 3 :

Linear velocity of end-effector at certain time

ω 0 ∊ R 3 :

Angular velocity of base at certain time

ω e  ∊ R 3 :

Angular velocity of end-effector at certain time

k i  ∊ R 3 (i = 1, … , n):

The unit direction vector of z-axle of frame i Σ i (i = 1, … , n)

θ i :

Joint angle i

Θ ∊ R n :

Joint angle vector

m i :

Mass of link i

M :

System mass

r i :

Radius of link i

l i :

Length of link i

η = cos (ψ/2):

Scalar part of quaternion representation

q = k sin (ψ/2):

Vector parts of quaternion representation

\( \tilde{r} \) :

Cross-product operator (equal to “×”), i.e.: if \( r = \left[ {\begin{array}{*{20}c} {r_{x} } \\ {r_{y} } \\ {r_{z} } \\ \end{array} } \right] \), then \( \tilde{r} = \left[ {\begin{array}{*{20}c} 0 & { - r_{z} } & {r_{y} } \\ {r_{z} } & 0 & { - r_{x} } \\ { - r_{y} } & {r_{x} } & 0 \\ \end{array} } \right] \)

I i  ∊ R 3×3 :

Inertia matrix of link i with respect to itself CM (all of links are regarded as cylinder)

Ψ b  ∊ R 3 :

Attitude of base expressed in terms of x–y–z Euler angles

ε :

The threshold that is selected is used to judge whether manipulator is singular

λ m :

The maximum damping value setting for user in singular area

\( \rho (q) = \left\| {q - q(g)} \right\| \) :

Euclidean distance from q to q g

ξ g , ξ m , η :

corresponding directly proportional position gain coefficient

ρ 0 :

Positive constant, indicate the maximum distance in which obstacle regions can affect movement of attracted point

ρ(q):

The minimum distance of position and attitude in obstacle regions C obs , that is to say, for all q ′ ∊ C obs

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Acknowledgments

This work is supported by the Program for Changjiang Scholars and Innovative Research Team in University (No. IRT1109), the Program for Liaoning Science and Technology Research in University (No. LS2010008), the Program for Liaoning Innovative Research Team in University (No. LT2011018), Natural Science Foundation of Liaoning Province (201102008), the Program for Liaoning Key Lab of Intelligent Information Processing and Network Technology in University and by “Liaoning BaiQianWan Talents Program (2010921010, 2011921009)”.

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  1. Key Laboratory of Advanced Design and Intelligent Computing (Dalian University), Ministry of Education, Dalian, 116622, People’s Republic of China

    S. Liu, Q. Zhang & D. Zhou

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  1. S. Liu
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  2. Q. Zhang
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  3. D. Zhou
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Correspondence to Q. Zhang.

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Liu, S., Zhang, Q. & Zhou, D. Obstacle Avoidance Path Planning of Space Manipulator Based on Improved Artificial Potential Field Method. J. Inst. Eng. India Ser. C 95, 31–39 (2014). https://doi.org/10.1007/s40032-014-0099-z

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