Distributed model predictive control (DMPC) is promising in achieving optimal cooperative control in multirobot systems (MRS). However, real-time DMPC implementation relies on numerical optimization tools to periodically calculate local control sequences online. This process is computationally demanding and lacks scalability for large-scale, nonlinear MRS. This article proposes a novel distributed learning-based predictive control framework for scalable multirobot control. Unlike conventional DMPC methods that calculate open-loop control sequences, our approach centers around a computationally fast and efficient distributed policy learning algorithm that generates explicit closed-loop DMPC policies for MRS without using numerical solvers. The policy learning is executed incrementally and forward in time in each prediction interval through an online distributed actor-critic implementation. The control policies are successively updated in a receding-horizon manner, enabling fast and efficient policy learning with the closed-loop stability guarantee. The learned control policies could be deployed online to MRS with varying robot scales, enhancing scalability and transferability for large-scale MRS. Furthermore, we extend our methodology to address the multirobot safe learning challenge through a force field-inspired policy learning approach. We validate our approach's effectiveness, scalability, and efficiency through extensive experiments on cooperative tasks of large-scale wheeled robots and multirotor drones. Our results demonstrate the rapid learning and deployment of DMPC policies for MRS with scales up to 10 000 units.

In recent years, safe reinforcement learning (RL) with the actor-critic structure has gained significant interest for continuous control tasks. However, achieving near-optimal control policies with safety and convergence guarantees remains challenging. Moreover, few works have focused on designing RL algorithms that handle time-varying safety constraints. This article proposes a safe RL algorithm for optimal control of nonlinear systems with time-varying state and control constraints. The algorithm's novelty lies in two key aspects. Firstly, the approach introduces a unique barrier force-based control policy structure to ensure control safety during learning. Secondly, a multistep policy evaluation mechanism is employed, enabling the prediction of policy safety risks under time-varying constraints and guiding safe updates. Theoretical results on learning convergence, stability, and robustness are proven. The proposed algorithm outperforms several state-of-the-art RL algorithms in the simulated Safety Gym environment. It is also applied to the real-world problem of integrated path following and collision avoidance for two intelligent vehicles - a differential-drive vehicle and an Ackermann-drive one. The experimental results demonstrate the impressive sim-to-real transfer capability of our approach, while showcasing satisfactory online control performance.

Koopman operators are of infinite dimension and capture the characteristics of nonlinear dynamics in a lifted global linear manner. The finite data-driven approximation of Koopman operators results in a class of linear predictors, useful for formulating linear model predictive control (MPC) of nonlinear dynamical systems with reduced computational complexity. However, the robustness of the closed-loop Koopman MPC under modeling approximation errors and possible exogenous disturbances is still a crucial issue to be resolved. Aiming at the above problem, this paper presents a robust tube-based MPC solution with Koopman operators, i.e., r-KMPC, for nonlinear discrete-time dynamical systems with additive disturbances. The proposed controller is composed of a nominal MPC using a lifted Koopman model and an off-line nonlinear feedback policy. The proposed approach does not assume the convergence of the approximated Koopman operator, which allows using a Koopman model with a limited order for controller design. Fundamental properties, e.g., stabilizability, observability, of the Koopman model are derived under standard assumptions with which, the closed-loop robustness and nominal point-wise convergence are proven. Simulated examples are illustrated to verify the effectiveness of the proposed approach.