# Adaptive Critic Based Optimal Kinematic Control for a Robot Manipulator

## TL;DR

This paper introduces a novel adaptive critic control method for robot manipulators that guarantees convergence to optimality and stability, validated through simulations and real-world experiments with a 6-DOF robot.

## Contribution

It proposes a new critic weight update law within the SNAC framework that ensures convergence and stability in kinematic control tasks.

## Key findings

- Guaranteed convergence to optimal cost
- Stable control of robot manipulator
- Validated with real robot experiments

## Abstract

This paper is concerned with the optimal kinematic control of a robot manipulator where the robot end effector position follows a task space trajectory. The joints are actuated with the desired velocity profile to achieve this task. This problem has been solved using a single network adaptive critic (SNAC) by expressing the forward kinematics as input affine system. Usually in SNAC, the critic weights are updated using back propagation algorithm while little attention is given to convergence to the optimal cost. In this paper, we propose a critic weight update law that ensures convergence to the desired optimal cost while guaranteeing the stability of the closed loop kinematic control. In kinematic control, the robot is required to reach a specific target position. This has been solved as an optimal regulation problem in the context of SNAC based kinematic control. When the robot is required to follow a time varying task space trajectory, then the kinematic control has been framed as an optimal tracking problem. For tracking, an augmented system consisting of tracking error and reference trajectory is constructed and the optimal control policy is derived using SNAC framework. The stability and performance of the system under the proposed novel weight tuning law is guaranteed using Lyapunov approach. The proposed kinematic control scheme has been validated in simulations and experimentally executed using a real six degrees of freedom (DOF) Universal Robot (UR) 10 manipulator.