A GNN for repetitive motion generation of four-wheel omnidirectional mobile manipulator with nonconvex bound constraints

This paper proposes a gradient neural network (GNN) to solve the repetitive motion generation scheme of the omnidirectional four-wheel mobile manipulator. The overall kinematics model of the omnidirectional mobile platform and the manipulator fixed on omnidirectional platform are established. First, the analysis of the current repetitive movement generation (RMG) scheme for the kinematic control of the manipulator can find that the position error does not theoretically converge to zero and fluctuates. This paper analyzes the phenomenon from a theoretical viewpoint and reveals that the current RMG scheme has position errors associated with joint errors. Then, to solve the shortcomings of the current solution, an orthogonal projection repetitive motion generation (OPRMG) method is proposed, which theoretically eliminates position errors and decouples joint space and Cartesian space. Using the gradient descent method to establish the corresponding GNN aided with the speed compensation, and provide theoretical analysis to reflect the stability. Moreover, the joint speed limit in the RMG scheme is extended to nonconvex constraints. The advantages of the OPRMG scheme are demonstrated by the simulation results of the omnidirectional mobile manipulator (OMM) synthesized by the current GNNRMG and the proposed GNNOPRMG. In addition, by adjusting the feedback coefficient, the high performance of the OPRMG scheme can be verified by simulation and comparison of the position error (PE) and joint error (JE) of the OMM.