Analysis, Verification and Comparison on Feedback‐Aided MA Equivalence and Zhang Equivalency of Minimum‐Kinetic‐Energy Type for Kinematic Control of Redundant Robot Manipulators

Abstract

By following and generalizing Ma et al.'s inspiring work and Zhang et al.'s inspiring work, this paper proposes and investigates three kinds of equivalent relationships with error-feedback information incorporated for the minimum-kinetic-energy (MKE) redundancy resolution. Specifically, these three equivalent relationships are divided into two big classes in terms of scheme formulations: one is termed MKE-type Ma equivalence (MKE-ME); the other is MKE-type Zhang equivalency (MKE-ZE), which can be further subdivided into MKE-ZE-I and MKE-ZE-II. Also, the equivalent analyses as well as the primary distinctions about three such equivalent relationships are presented. The simulation results based on a PUMA560 robot manipulator and a three-link planar robot manipulator not only verify the efficacy of the corresponding velocity-level and acceleration-level schemes of MKE-ME, MKE-ZE-I and MKE-ZE-II, but also substantiate their reasonableness and effectiveness of these three equivalent relationships. More importantly, the comparative numerical results show their respective characteristics and advantages for kinematic control of redundant robot manipulators.

Improved recurrent neural networks for online solution of Moore‐Penrose inverse applied to redundant manipulator kinematic control

“…Figure 5 shows the kinematics structure of such a manipulator. For this robot manipulator, the joint vector = [ 1 , 2 , 3 ] T ∈ R 3 and the end-effector position vector r = [r x , r y ] T ∈ R 2 are related by the following forward-kinematic equation [31]:…”

Refined Self-Motion Scheme With Zero Initial Velocities and Time-Varying Physical Limits via Zhang Neurodynamics Equivalency

“…Zhang neurodynamics equivalency (ZNDE) inspired by Ma equivalency (Ma, 1996 ; Ma et al, 1996 ), is actually a class of practice-accepted approximation, which is derived from Zhang neurodynamics (Chen and Zhang, 2018 ; Qin et al, 2021 ). Some schemes of complex systems via the ZNDE approach were efficiently simplified (Guo et al, 2013 ; Qiu et al, 2016 , 2018 ). Minimum-velocity-norm schemes of redundant robot manipulators at two different layers were established by Guo et al ( 2013 ), and the equivalent relationship between two manipulator control schemes was also developed via the Zhang neurodynamics method.…”

Velocity‐layer Zhang equivalency for time‐varying joint limits avoidance of redundant robot manipulator

“…Zhang equivalency (ZE) is a category of practice-accepted approximation in reality, which is inspired by the works of Ma et al [25,26]. Preliminary works about the ZE proved that some schemes via the ZE approach were mathematically approximate but practically equivalent [27][28][29][30][31][32]. Specifically, Guo et al [27] studied the equivalent relationship between two robotic schemes at different layers via the ZE approach.…”

“…[25, 26]. Preliminary works about the ZE proved that some schemes via the ZE approach were mathematically approximate but practically equivalent [27–32]. Specifically, Guo et al.…”