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Hierarchical motion planning at the acceleration level based on task priority matrix for space robot

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Abstract

This paper addresses the motion planning problem for a free-floating redundant space robotic system at the acceleration level considering the strict task priority. The robot is primarily expected to track the prescribed trajectory together with various other tasks, e.g., regulating the base attitude, avoiding collision with obstacles and respecting the joint constraints. Then, the planning problem is reformulated as strictly hierarchical quadratic least-square problems containing both equality and inequality and solved with the proposed task-priority algorithm based on the combination of the task priority matrix method and the active-set method. Besides, a novel velocity-related dynamic potential function is also designed to obtain a smoother motion when approaching obstacles, and further relaxed to the one-dimensional inequality to take full advantage of the robot capacity and dexterity. Simulation results have validated the proposed motion planning strategy imposed on the dual-arm space robot.

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Data availability

Data sharing is not applicable to this article since no datasets were generated or analyzed during the current study.

Abbreviations

\(J^j_i\) :

Joint i of manipulator j

\(C_0, C^j_i\) :

Center of mass (CM) of base and body i of manipulator j

\({\varvec{b}}^j_0\) :

Position vector from \(C_0\) to \(J^j_1\)

\({\varvec{a}}^j_i, {\varvec{b}}^j_i\) :

Position vectors from \(J^j_i\) to \(C^j_i\) and from \(C^j_i\) to \(J^j_{i+1}\)

\({\varvec{r}}_b, {\varvec{r}}^j_{C_i}\) :

Position vectors of \(C_0\) and \(C^j_i\) in the inertia frame

\({\varvec{r}}^j_e\) :

Position vector of end-effector j in the inertia frame

\({\varvec{r}}_s\) :

Position vector of the whole space robotic system CM in the inertia frame

\({\varvec{r}}_{ci}\) :

Position vector of the critical point of link i

\({\varvec{r}}_{bs}\) :

Position vector from \(C_0\) to the system CM

\({\varPsi }_b, {\varPsi }^j_e\) :

Attitude angles of base and end-effector j

\({{\varvec{x}}}_b, {{\varvec{x}}}^j_e\) :

Pose vectors of base and end-effector j

\({\theta }^j\) :

Joint-position vector of manipulator j

\({{\varvec{\omega }}}_b, {{\varvec{\omega }}}^j_e\) :

Angular velocities of base and end-effector j

\({\mathbf{J}}_b, {\mathbf{J}}^j_e\) :

Jacobian matrices corresponding to the motion of base and end-effector j

\({\mathbf{H}}_b\) :

Base inertia matrix

\({\mathbf{H}}^j_m\) :

Inertia matrix of manipulator j

\({\mathbf{H}}^j_{bm}\) :

Coupled inertia matrix between base and manipulator j

\({{\varvec{c}}}_b, {{\varvec{c}}}^j_m\) :

Generalized Coriolis and centrifugal force terms corresponding to base and manipulator j

\({{\varvec{f}}}_b, {{\varvec{f}}}^j_m\) :

Generalized forces and torques exerted to base and end-effector j

\({{\varvec{\tau }}}^j_m\) :

Generalized joint torque of manipulator j

\({{\varvec{v}}}_{ci}\) :

Linear velocity of the critical point \({\varvec{r}}_{ci}\)

\({{\varvec{n}}}_{ci,k}\) :

Unit direction vector pointing from the critical point \({\varvec{r}}_{ci}\) to k-th obstacle

\(\phi _i\) :

Angle between vectors \({{\varvec{v}}}_{ci}\) and \({{\varvec{n}}}_{ci,k}\)

\(d_s\) :

Influence range of artificial potential force

\({\mathbf{F}}_{T}\) :

Task priority matrix (TPM)

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Acknowledgements

This work is supported by National Natural Science Foundation of China (No. U2013206).

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Authors and Affiliations

  1. National Key Laboratory of Aerospace Flight Dynamics, Northwestern Polytechnical University, Xi’an, 710072, People’s Republic of China

    Peng Cai, Xiaokui Yue & Mingming Wang

  2. Research & Development Institute of Northwestern Polytechnical University in Shenzhen, Shenzhen, 518057, People’s Republic of China

    Mingming Wang & Yao Cui

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  1. Peng Cai
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Correspondence to Peng Cai.

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Cai, P., Yue, X., Wang, M. et al. Hierarchical motion planning at the acceleration level based on task priority matrix for space robot. Nonlinear Dyn 107, 2309–2326 (2022). https://doi.org/10.1007/s11071-021-07038-2

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