A new discrete-time repetitive motion planning scheme based on pseudoinverse formulation for redundant robot manipulators with joint constrains

Recently, a repetitive motion planning (RMP) scheme with guaranteed precision has been developed for redundant robot manipulators. However, the RMP scheme does not consider joint constrains. As a result, such a scheme may not perform effectively when the joint configuration exceeds its physical limit. In this paper, we provide a further study by proposing a new discrete-time RMP (DTRMP) scheme based on the pseudoinverse formulation for redundant robot manipulators with joint constrains. Specifically, by using the direct derivation and by introducing the feedback, the handling of joint physical limit is formulated as an implicit dynamic equation. Then, the combined kinematic equation of the constrained redundant robot manipulators is obtained, and the resultant continuous-time RMP (CTRMP) scheme with the pseudoinverse-based formulation is established. By utilizing a numerical difference rule to discretize the CTRMP scheme, the new DTRMP scheme is thus developed for redundant robot manipulators with joint constrains. Theoretical analysis and computer simulations under a constrained five-link robot manipulator validate the effectiveness and superiority of the proposed DTRMP scheme. The experiment results of implementing the proposed scheme on the constrained practical Panda robot manipulator further indicate the scheme applicability and feasibility.