Multi-phase NMPC Strategy for Safe Navigation in Unknown Environments using Polynomial Zonotopes

Abstract

This study presents a novel approach for guiding robots through cluttered and unknown environments. The approach utilizes multi-phase non-linear model predictive control (NMPC) and polynomial zonotopes (PZs) to describe collision-free areas (CFAs). Laser sensor data is processed to obtain the CFA, which is divided into convex subregions. These subregions are then transformed into PZs, which provide constraints for the optimal control problem (OCP) of the NMPC. Compared to conventional half-space representations, PZs require fewer constraints, resulting in a more efficient method for describing the same polytopes. The proposed approach employs a multi-phase method that divides the trajectory into segments and applies individual subregion convex constraints to each segment. This result is a reduction in the number of constraints per segment. Numerical experiments with a wheeled mobile robot are conducted to demonstrate the effectiveness of the proposed approach.