Velocity-Level Control with Compliance to Acceleration-Level Constraints: A Novel Scheme for Manipulator Redundancy Resolution

Manipulators are subject to physical constraints at different levels, i.e., joint angle limits, joint velocity limits, and acceleration limits. Effective resolution of redundant manipulators with compliance to the physical constraints is a fundamental issue for safe operation. Existing results generally resolve the manipulator redundancy either at the velocity level or the acceleration level. On the one hand, the velocity-level redundancy resolution scheme is able to deal with the joint angle and joint velocity limits successfully but cannot address the joint acceleration limit. On the other hand, although the existing acceleration-level redundancy resolution scheme is able to overcome the failure of the velocity-level one in complying with acceleration constraints, it is at the cost of making the system equation more complicated, e.g., the dependence on the time derivative of the Jacobian matrix. Whether it is possible to conduct redundancy resolution at the velocity level but with the compliance to joint angle constraints, joint velocity constraints, and joint acceleration constraints remains an open problem in past decades. This paper gives a positive answer to this pending problem by providing a novel scheme. In the proposed scheme, the redundancy resolution problem is formulated as a quadratic program subject to joint angle, velocity, and acceleration constraints with the joint velocity being the decision variable and joint velocity norm as the performance index, which is widely adopted and closely related to the energy consumption. Then, a projection neural network is designed and proposed to online solve the problem with the joint acceleration constraint handled. Theoretical analysis is performed to guarantee the global convergence of the proposed projection neural network to the optimal solution to the redundancy resolution problem. Besides, simulation results based on a PUMA 560 industrial manipulator are presented and compared to verify the theoretical result and substantiate the efficacy and superiority of the proposed scheme.