Nonlinear Control of a Robot Manipulator with a Nonholonomic Jerk Constraint

Abstract

We study the control of a prismatic‐prismatic‐revolute (PPR) robot manipulator subject to a nonholonomic jerk constraint, i.e., a third‐order nonintegrable design constraint. The mathematical model is obtained using the method of Lagrange multipliers. The control inputs are two forces and a torque applied to the prismatic joints and the revolute joint, respectively. The control objective is to control the robot end‐effector movement while keeping the transverse jerk component as zero. The main result of the paper is the construction of a feedback control algorithm that transfers the manipulator from any initial equilibrium configuration to the zero equilibrium configuration in finite time. The effectiveness of the algorithm is illustrated through a simulation example.

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

“…They are similar to the human arm, elephant trunk and snake in the real world [17,18,24]. A fundamental issue in controlling redundant robot manipulators is the redundancy-resolution problem, which is related to the kinematic control of redundant robot manipulators and has attracted extensive attention in scientific researches and engineering applications [1,2,6,[14][15][16][17][18][19][20][21][25][26][27]. The general description of such a redundancy-resolution problem is that, given the desired end-effector Cartesian path r d (t) ∈ R m , the corresponding joint trajectory (t) ∈ R n needs to be generated in real time t. The conventional solution to the redundancy-resolution problem is the pseudoinverse-based method, which is formulated as one minimum-norm particular solution plus a homogeneous solution [21][22][23].…”

“…They are similar to the human arm, elephant trunk and snake in the real world . A fundamental issue in controlling redundant robot manipulators is the redundancy‐resolution problem, which is related to the kinematic control of redundant robot manipulators and has attracted extensive attention in scientific researches and engineering applications . The general description of such a redundancy‐resolution problem is that, given the desired end‐effector Cartesian path , the corresponding joint trajectory needs to be generated in real time t .…”