Journal Paper: Distributed Robust Receding Horizon Control for Multi-vehicle Guidance

Kuwata, Y.; Richards, A.G.; Schouwenaars, T. & How, J.P., Distributed Robust Receding Horizon Control for Multi-vehicle Guidance, IEEE Transactions on Control Systems Technology, Vol. 15, No. 4, July 2007, Pages 627--641.

Abstract: This paper presents a new distributed robust Model Predictive Control algorithm for multi-vehicle trajectory optimization and demonstrates the approach with numerical simulations and multi-vehicle experiments. The technique builds on the robust-safe-but-knowledgeable (RSBK) algorithm, which is developed in this paper for the multi-vehicle case. RSBK uses constraint tightening to achieve robustness to external disturbances, an invariant set to ensure safety in the presence of changes to the environment, and a cost-to-go function to generate an intelligent trajectory around known obstacles. The key advantage of this RSBK algorithm is that it enables the use of much shorter planning horizons while still preserving the robust feasibility guarantees of previously proposed approaches. The second contribution of this paper is a distributed version of the RSBK algorithm, which is more suitable for real-time execution. In the distributed RSBK (DRSBK) algorithm, each vehicle only optimizes for its own decisions by solving a subproblem of reduced size, which results in shorter computation times. Furthermore, the algorithm retains the robust feasibility guarantees of the centralized approach while requiring that each agent only have local knowledge of the environment and neighbor vehicles’ plans. This new approach also facilitates the use of a significantly more general implementation architecture for the distributed trajectory optimization, which further decreases the delay due to computation time.

Conference Paper: Robust Receding Horizon Control using Generalized Constraint Tightening

Y. Kuwata, A. G. Richards, and J. P. How, Robust Receding Horizon Control using Generalized Constraint Tightening, American Control Conference, 2007.

Abstract: This paper presents a decentralized robust Model Predictive Control algorithm for multi-vehicle trajectory optimization. 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.

Conference Paper: Robust Distributed Model Predictive Control with Cooperation

P. Trodden and A. G. Richards, "Robust Distributed Model Predictive Control with Cooperation", European Control Conference, 2007.

Abstract: This paper extends a form of distributed model predictive control (MPC) for subsystems with decoupled dynamics and with coupled constraints. By use of an objective function that includes knowledge of the coupling between subsystems, cooperative behaviour is promoted with respect to the global objective. The method is robust to persistent disturbances, by the use of the Tube MPC concept, in which an optimization designs a sequence of invariant state sets for the system to follow, rather than a trajectory. Robust stability is guaranteed for any choice of update sequence and objective function. It is demonstrated that, through cooperation, global performance can improve on that obtained by a simple distributed implementation.

Conference Paper: Robust Multiplexed Model Predictive Control

A. G. Richards, K.-V. Ling and J. M. Maciejowski, Robust Multiplexed Model Predictive Control, European Control Conference, 2007.

Abstract: This paper extends the recently developed multiplexed model predictive control (MMPC) concept to ensure satisfaction of hard constraints despite the action of persistent, unknown but bounded disturbances. MMPC uses asynchronous control moves on each input channel instead of synchronised moves on all channels. It offers reduced computation, by dividing the online optimisation into a smaller problem for each channel, and potential performance improvements, as the response to a disturbance is quicker, albeit via only one channel. Robustness to disturbances is introduced using the constraint tightening approach, tailored to suit the asynchronous updates of MMPC and the resulting time-varying optimisations. Numerical results are presented, involving a simple mechanical example and an aircraft control example, showing the potential computational and performance benefits of the new robust MMPC.