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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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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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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DOI: https://doi.org/10.1007/s10846-020-01279-w