No abstract

Abstract-The paper suggests a new approach to navigation of mobile robots, based on nonlinear model predictive control and using a navigation function as a control Lyapunov function. In this approach, the nonlinear optimal control problem is treated using randomized algorithms. The advantage of the proposed combination of navigation functions for robot motion planning with randomized algorithms within an MPC framework, is that the control design offers stability by design, is platform independent, and allows the designer to tradeoff performance for (computation) speed, according to the application requirements.

The note combines (weak) control Lyapunov function-based nonlinear receding horizon control, with randomized optimization. This approach is applied to the problem of robot navigation in the presence of state and input constraints. It is shown that under certain conditions, relaxing the definiteness requirements on the terminal cost function allows one to select control inputs through a Monte-Carlo optimization scheme in a way that preserves the stability and convergence properties of the closed loop system. While the particular randomized optimization scheme used here can be substituted for the nonlinear optimal control method of choice, the introduction of randomization in receding horizon optimization is anticipated to offer additional trade-offs between performance and computation speed compared to the fixed-overhead nonlinear optimal control strategies typically employed.