An improved approach for constrained robust model predictive control

This paper presents an architecture for the navigation of an autonomous mobile robot evolving in environments with obstacles. Instead of addressing motion planning and control in different contexts, these issues are described in connected modules with performance requirement considerations. The planning problem is formulated as a constrained receding horizon planning problem and is solved in real time with an efficient computational method that combines nonlinear control theory, B-spline basis function and nonlinear programming. An integral sliding mode controller is used for trajectory tracking. Closed-loop stability of the tracking errors is guaranteed in spite of unknown disturbances. It is also shown that this strategy is particularly useful if integral sliding mode control is combined with other methods to further robustify against perturbations. The effectiveness, perfect performance of obstacle avoidance, real time and high robustness properties are demonstrated by experimental results.

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“…One can note that constraints (7) and (8) [16]. However, it takes into account the computation time δt.…”

Section: Remarkmentioning

confidence: 99%

Performance-based reactive navigation for non-holonomic mobile robots

et al. 2009

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Section: Introductionmentioning

confidence: 99%

“…With the development of MPC, robust MPC with state feedback has been studied extensively [1], [3], [9]. A main approach for robust MPC synthesis is to design a state-feedback control law that minimizes a "worst-case" infinite horizon objective function by solving linear matrix inequalities (LMIs) [1]. In order to reduce conservativeness, Cuzzola et al in [1] proposed using several Lyapunov functions to replace a single Lyapunov function and solving LMIs corresponding to a different vertex of the uncertainty's polytope.…”

Section: Introductionmentioning

confidence: 99%

Robust Model Predictive Control for Piecewise Affine Systems

Zou

2007

Circuits Syst Signal Process

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In this paper, we study a robust model predictive control (MPC) strategy for piecewise affine (PWA) systems with uncertainty that is described as a set of polytopic parameter-varying models in a polytope corresponding to each partition of the PWA systems. First, an infinite horizon MPC technique for guaranteeing robust stability is developed for uncertain PWA systems. According to the condition of the PWA system states, the sequence of piecewise linear feedback controller at each sampling time is derived on-line by solving a convex optimization problem involving linear matrix inequalities. The feasible PWA control law design can robustly stabilize the uncertain PWA systems. However, the on-line optimization problems may lead to a computational burden. Then we further propose an improved robust MPC algorithm. When the current state is outside of the region of PWA systems containing the origin, the proposed on-line robust MPC algorithm is utilized; once the current state enters the region with the origin, sequence attraction domains where the origin is included are constructed off-line one within another, and the explicit control laws corresponding to different attraction domains can drive the state to the origin. The two algorithms are illustrated with a numerical example. The simulation results show that both controller design methods can stabilize the PWA systems with polytopic uncertainty, and the improved algorithm can reduce the on-line computation cost.

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“…Recent 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].…”

Section: Introductionmentioning

confidence: 99%

Decentralized robust receding horizon control for multi-vehicle guidance

Kuwata

Richards

Schouwenaars

et al. 2006

2006 American Control Conference

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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.

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An improved approach for constrained robust model predictive control

Cited by 360 publications

References 9 publications

Performance-based reactive navigation for non-holonomic mobile robots

Performance-based reactive navigation for non-holonomic mobile robots

Robust Model Predictive Control for Piecewise Affine Systems

Decentralized robust receding horizon control for multi-vehicle guidance

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