An obstacle avoidance model predictive control scheme for mobile robots subject to nonholonomic constraints: A sum-of-squares approach

The paper addresses the obstacle avoidance motion planning problem for ground vehicles operating in uncertain environments. By resorting to set-theoretic ideas and sum of squares (SOS) decomposition techniques, a receding horizon control algorithm is proposed for robots modeled by polynomial systems subject to input, state and nonholonomic constraints. Sequences of inner ellipsoidal approximations of the exact one-step controllable sets are computed for all admissible obstacle scenarios and then on-line exploited to determine the more adequate control action to be applied in a receding horizon fashion. The results here proposed are a significant generalization of existing algorithms which are tailored only for linear time invariant plant descriptions. The resulting framework guarantees uniformly ultimate boundedness and constraints fulfilment regardless of any obstacle scenario occurrence.