Value iteration based approximate dynamic programming for mobile robot trajectory tracking with persistent inputs

This paper presents a value iteration based approximate dynamic programming technique to solve the trajectory tracking problem of unicycle like wheeled mobile robots. Given a reference trajectory (2D), an error model is derived to form a nonlinear affine system. The robot is supposed to track the reference trajectory asymptotically. The solution of the error model is used to define the value function (cost-to-go function), which is a measure of the robot's tracking error and the cost of applying its actuator inputs (in this case, linear and angular velocities of the robot). A critic neural network approximates the value function to determine the optimal control inputs that are applied to the robot's actuators. A set of computer simulations is conducted to evaluate the performance of the proposed approximate dynamic programming method. The robot's trajectory tracking performance using the proposed method is also compared with that of the conventional approximate linearization technique in order to show the superiority of the value iteration based approximate dynamic programming.