New Pseudoinverse-Based Path-Planning Scheme With PID Characteristic for Redundant Robot Manipulators in the Presence of Noise

In this paper, a new path-planning scheme based on pseudoinverse-type formulation for redundant robot manipulators with the existence of noise is proposed and investigated. Such a pseudoinverse-based path-planning (PPP) scheme contains the proportional, integral, and derivative information of the desired Cartesian path (of the end-effector), and can thus be viewed as a nonlinear proportional-integral-derivative (PID) controller for redundant robot manipulators. In other words, the proposed PPP scheme has the PID characteristic in terms of the desired Cartesian path. Theoretical results are given to show that the Cartesian error synthesized by the proposed PPP scheme has the property of global and exponential convergence (that is to say, the error trajectory is asymptotically stable) and to indicate that such a scheme has the capability to suppress noise. Simulation results based on a four-link planar robot manipulator with the existence of zero, constant, and bounded time-varying noises are presented to further substantiate the efficacy and superiority of the proposed PPP scheme for the path planning of redundant robot manipulators. The physical realizability of the proposed PPP scheme is also demonstrated by applying this scheme to a practical six-link planar robot manipulator.