Solving the Inverse Kinematics Problem of Multiple Redundant Manipulators with Collision Avoidance in Dynamic Environments

Abstract

This article presents an approach for collision-free kinematics of multiple redundant manipulators in complex environments. The approach describes a representation of task space and joint limit constraints for redundant manipulators and handles collision-free constraints by micromanipulator dynamic model and velocity obstacles. A new algorithm based on Newton-based and first-order techniques is proposed to generate collision-free inverse kinematics solutions. The present approach is applied in simulation for the redundant manipulators in a various working environments with dynamic obstacles. The physical experiments using a Baxter robot in a various working environments with dynamic obstacles are also performed. The results demonstrate the effectiveness of the proposed approach compared with existing methods regarding working environment and computational cost.

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Acknowledgements

This work has been supported by the National Natural Science Foundation of China [Project Number: 91848101] and the Foundation for Innovative Research Groups of the National Natural Science Foundation of China [Grant Number: 51521003].

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Correspondence to Jingdong Zhao.

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Appendices

Appendix A: DH Parameters of Micromanipulator Dynamic Model and Right Arm Model

i/Sm αi− 1/αm− 1(rad) ai− 1/am− 1(m) di/dm(m) 𝜃i/𝜃m (rad) joint limit(rad) rm(m)
0 0 0 0 − 0.7854 / /
1 0 0.83288 0.129626 q 1 (− 1.7016, + 1.7016) /
2 − 1.5708 0.069 0.27053 q 2 (− 2.147, + 1.047) /
3 1.5708 0.102 0 q3 + 1.5708 (− 3.0541, + 3.0541) /
S 1 0 0 0 0 / 0.08
S 2 0 0 0.128 0 / 0.07
S 3 0 0.069 0.134 0 / 0.085
4 − 1.5708 0 0 q4 − 1.5708 (− 0.05, + 2.618) /
5 1.5708 0.10359 0 q5 + 1.5708 (− 3.059, + 3.059) /
S 4 0 0 0 0 / 0.065
S 5 0 0 0.16641 0 / 0.065
6 − 1.5708 0.01 0.10359 q6 − 1.5708 (− 1.5707, + 2.094) /
7 1.5708 0 0.115975 q7 + 1.5708 (− 3.059, + 3.059) /

Appendix B: DH Parameters of the Human Model

A h αh− 1(rad) ah− 1(m) dh(m) 𝜃h (rad) rh(m)
A 1 0 0 0.7 0 0.1
A 2 0 0 − 0.25 0 0.08
A3(A6) + (−)1.5708 0 0.2 − (+)1.5708 0.08
A4(A7) 0 0 0.2 0 0.08
A5(A8) 0 0 0.15 0 0.07

Appendix C: DH Parameters of Sphere Obstacles and Left Arm Model

i/Ah αi− 1/αh− 1(rad) ai− 1/ah− 1(m) di/dh(m) 𝜃i/𝜃h (rad) joint limit(rad) rh(m)
0 0 0 0 0.7854 / /
1 0 0.83288 0.129626 q 1 (− 1.7016, + 1.7016) /
2 − 1.5708 0.069 0.27053 q 2 (− 2.147, + 1.047) /
3 1.5708 0.102 0 q3 + 1.5708 (− 3.0541, + 3.0541) /
A 1 0 0 0 0 / 0.08
A 2 0 0 0.128 0 / 0.07
A 3 0 0.069 0.134 0 / 0.085
4 − 1.5708 0 0 q4 − 1.5708 (− 0.05, + 2.618) /
5 1.5708 0.10359 0 q5 + 1.5708 (− 3.059, + 3.059) /
A 4 0 0 0 0 / 0.065
A 5 0 0 0.16641 0 / 0.065
A 6 0 0.01 0.10359 0 / 0.075
6 − 1.5708 0 0 q6 − 1.5708 (− 1.5707, + 2.094) /
7 1.5708 0 0.115975 q7 + 1.5708 (− 3.059, + 3.059) /
A 7 0 0 0.015 0 / 0.055
A 8 0 0 0.124 0 / 0.055
A 9 0 0 0.115 0 / 0.055

Appendix D: DH Parameters of Sphere Obstacles and Kuka Arm Model

i/Ah αi− 1/αh− 1(rad) ai− 1/ah− 1(m) di/dh(m) 𝜃i/𝜃h (rad) joint limit(rad) rh(m)
1 1.5708 0 0.36 q 1 (− 2.967, + 2.967) /
2 − 1.5708 0 0 q 2 (− 2.094, + 2.094) /
A 1 0 0 0 0 / 0.08
A 2 0 0 0.21 0 / 0.07
3 − 1.5708 0 0.21 q 3 (− 2.967, + 2.967) /
4 1.5708 0 0 q 4 (− 2.094, + 2.094) /
A 3 0 0 0 0 / 0.075
A 4 0 0 0 0.21 / 0.07
5 1.5708 0 0.19 q 5 (− 2.967, + 2.967) /
6 − 1.5708 0 0 q 6 (− 2.094, + 2.094) /
A 5 0 0 0 0 / 0.075
7 0 0 0.126 q 7 (− 2.967, + 2.967) /
A 6 0 0 0 0.02 / 0.065

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Zhao, L., Zhao, J. & Liu, H. Solving the Inverse Kinematics Problem of Multiple Redundant Manipulators with Collision Avoidance in Dynamic Environments. J Intell Robot Syst 101, 30 (2021). https://doi.org/10.1007/s10846-020-01279-w

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Keywords

  • Inverse kinematics
  • Multiple manipulators
  • Collision avoidance
  • Dynamic obstacles