Decentralized Robust Receding Horizon Control for Multi-vehicle Guidance Yoshiaki Kuwata, Arthur Richards, Tom Schouwenaars, and Jonathan P. How Abstract— This paper presents a decentralized robust Model Predictive Control algorithm for multi-vehicle trajectory opti- mization. The algorithm is an extension of a previous robust safe but knowledgeable (RSBK) algorithm that uses the constraint tightening technique to achieve robustness, an invariant set to ensure safety, and a cost-to-go function to generate an intelligent trajectory around obstacles in the environment. Although the RSBK algorithm was shown to solve faster than the previous robust MPC algorithms, the approach was based on a centralized calculation that is impractical for a large group of vehicles. This paper decentralizes the algorithm by ensuring that each vehicle always has a feasible solution under the action of disturbances. The key advantage of this algorithm is that it only requires local knowledge of the environment and the other vehicles while guaranteeing robust feasibility of the entire fleet. The new approach also facilitates a significantly more general implementation architecture for the decentralized trajectory optimization, which further decreases the delay due to computation time. Keywords: Model Predictive Control (MPC), Constrained, Decentralized, Invariant set, Robust Feasibility I. INTRODUCTION Model Predictive Control (MPC) or Receding Horizon Control (RHC) has been successfully applied to trajectory optimization problems for unmanned vehicles [1]–[2] be- cause it can systematically handle constraints such as vehicle dynamics, flight envelope limitations, and no-fly zones. Re- cent research has focused on robust MPC, which is robust to external disturbances or inherent discrepancies between the model and the real process, and numerous techniques have been proposed in the past decade [3]–[4]. Recent work [8] extended a new form of the constraint tightening approach in Ref. [9] to address the computational complexity of the on-line optimization. The main improve- ment was that the new algorithm did not explicitly require that the system states reach the target over the planning horizon. Instead, the controller only requires that the states can be driven to a robust control invariant set, which is updated as the system evolves. This enables the use of much shorter planning horizons and the online optimizations can be solved much faster. The robust MPC approach was also combined with a cost-to-go function that provides a good estimate of the path beyond the planning horizon to Y. Kuwata, Dept. of Aeronautics and Astronautics, MIT, Cambridge, MA 02139, USA, kuwata@mit.edu A. Richards, Lecturer, University of Bristol, Dept. of Aerospace Engi- neering, Arthur.Richards@bristol.ac.uk T. Schouwenaars, Dept. of Aeronautics and Astronautics, MIT, Cam- bridge, MA 02139, USA, toms@mit.edu J. How, Associate Professor, Dept. of Aeronautics and Astronautics, MIT, Cambridge, MA 02139, USA, jhow@mit.edu the goal [2] to create a Robust Safe But Knowledgeable (RSBK) algorithm. While the RSBK algorithm was shown to have a significant computational improvement over the original RMPC algorithm, a centralized planning approach is impractical for a team of multiple vehicles. Using a technique similar to Ref. [10], this paper develops a distributed plan- ning algorithm (DRSBK) that guarantees robust feasibility of the vehicle paths without iterating, which is crucial for real-time implementation. The primary computational benefit of the DRSBK algo- rithm over RSBK is that each vehicle only calculates its own trajectory. The interactions with all other vehicles are handled as constraints. We also define a local neighborhood of each UAV that includes all other vehicles that could have a direct conflict with that vehicle. By limiting the number of vehicles considered to only those within a local region of each UAV, the number of constraints in each subproblem is reduced, which further simplifies the DRSBK computation. Using only local communication, DRSBK is shown to maintains the robust feasibility of the entire fleet. The algorithm generalizes the implementation approaches of Refs. [9], [11] to have several of the vehicles computing their trajectories simultaneously. This greatly reduces the delay incurred in the other, more rigid implementation approaches. The paper is organized as follows. Section III gives an overview of RSBK algorithm, which is extended to the decentralized case with only local communications in Sec- tion IV. Finally, Section V shows simulation results. II. PROBLEM STATEMENT In this paper, the index or subscript p, q denotes the vehicle index, index k denotes the current time step, and index j denotes the prediction step. There are total of n vehicles whose dynamics are described by LTI model x p (k + 1) = A p x p (k)+ B p u p (k)+ w p (k) (1) for p =1,...,n, where x p (k) is the state vector, u p (k) is the input vector, and w p (k) is the disturbance vector for the p th vehicle. The disturbances w p (k) are unknown but lie in known bounded sets w p (k) ∈W p . The environment has obstacles to be avoided, and the vehicles have flight envelope limitations. The general output sets Y p capture these local constraints of each vehicle p =1,...,n y p (k)= C p x p (k)+ D p u p (k) ∈Y p . (2) The coupling between vehicles is captured by a further set of constraints c =1,...,m applied to the sum of outputs Proceedings of the 2006 American Control Conference Minneapolis, Minnesota, USA, June 14-16, 2006 WeC19.6 1-4244-0210-7/06/$20.00 ©2006 IEEE 2047