Available online at www.sciencedirect.com Journal of the Franklin Institute ] (]]]]) ]]]–]]] An obstacle avoidance model predictive control scheme for mobile robots subject to nonholonomic constraints: A sum-of-squares approach G. Franzè n , W. Lucia DIMES – Università della Calabria Rende (CS), 87036, Italy Received 14 October 2014; received in revised form 29 January 2015; accepted 12 March 2015 Abstract 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. & 2015 The Franklin Institute. Published by Elsevier Ltd. All rights reserved. 1. Introduction Motion planning and autonomous vehicle control problems in uncertain environments are of paramount importance in several human applications where guaranteed real time feasibility, safety against uncertainties and disturbances are required. Despite extensive research, this problem still represents a real challenge that becomes more complex by taking into account the limited perception abilities and computational power resources of the robot, as well as restrictions on the vehicle mobility www.elsevier.com/locate/jfranklin http://dx.doi.org/10.1016/j.jfranklin.2015.03.021 0016-0032/& 2015 The Franklin Institute. Published by Elsevier Ltd. All rights reserved. n Corresponding author. E-mail addresses: franze@dimes.unical.it (G. Franzè), wlucia@dimes.unical.it (W. Lucia). Please cite this article as: G. Franzè, W. Lucia, An obstacle avoidance model predictive control scheme for mobile robots subject to nonholonomic constraints: A sum-of-squares approach, Journal of the Franklin Institute. (2015), http://dx.doi.org/10.1016/j.jfranklin.2015.03.021