Redundant arm kinematic control with recurrent loop

Abstract

A new method for generating redundant arm inverse kinematic solutions based on the iterative update of joint vectors is presented. A novel neural network architecture with a recurrent loop is then formed based on the proposed method. In the proposed method, the pseudoinverse of the gradient of a Lyapunov function is defined in the joint space to update the joint vector toward a solution. This differs from the conventional methods based on the Jacobian pseudoinverse or Jacobian transpose. This paper establishes explicit convergence control schemes to achieve fast and stable convergence: 1) the convergence speed is enhanced by modifying the convergence dynamics based on terminal attractors, and 2) the convergence stability is ensured by the adaptive selection of update intervals based on the stability condition derived in this paper. The proposed neural network consists of a feedforward network and a feedback network forming a recurrent loop. The feedforward network is a multilayer network with hidden units having sinusoidal activation functions. As such, it computes accurately the forward kinematic solutions with simple training. The feedback network is derived from the feedforward network and computes joint vector updates. The proposed neural network has definite advantages over conventional neural networks for robot arm kinematic control, because it can not only handle redundant arm kinematic control, but can also provide an accurate computation of forward and inverse kinematic solutions with very simple training. The simulation results demonstrate that the proposed method is effective for the real-time kinematic control of a redundant arm as well as the real-time generation of collision-free joint trajectories.