friction-aware mpc

This work addresses the challenge of achieving both high performance and provable safety for autonomous systems operating in real-world environments, where conventional model predictive control (MPC) often fails to guarantee safety beyond the finite prediction horizon. The authors propose a novel approach that constructs terminal constraints using a safety value function derived from reachability analysis, ensuring that the planned trajectory terminates within a controlled invariant safe set. This formulation guarantees recursive feasibility while enabling real-time, provably safe trajectory optimization with high task performance. In contrast to existing methods that rely on local linearization or overly conservative approximations, the proposed technique significantly reduces conservatism and enhances expressiveness of safety guarantees. Simulations and hardware experiments on a Flexiv Rizon 10s robotic arm demonstrate that the method substantially improves constraint satisfaction and robustness compared to standard MPC and reactive safety filters, without compromising task performance.

This paper addresses the challenge of deeply integrating model predictive control (MPC) and reinforcement learning (RL), stemming from their fundamentally divergent model usage paradigms. To resolve this, we propose the first unified taxonomy for MPC–RL fusion, centered on *how models are used*, categorizing approaches into three paradigms: MPC-augmented RL, RL-augmented MPC, and co-designed architectures. Leveraging a unified Actor–Critic modeling framework, we systematically analyze how MPC’s online optimization enhances RL’s closed-loop performance and establish a performance-gain-oriented evaluation perspective grounded in closed-loop metrics. The survey comprehensively covers six application domains—including robotics, energy systems, and autonomous driving—and synthesizes cross-cutting modeling techniques bridging control theory and RL. Our work provides a scalable methodology and principled design guidelines for hybrid intelligent control systems.

To address the high computational cost of nonlinear model predictive control (NMPC) hindering real-time deployment, this paper proposes a safety-enhanced neural network controller. Methodologically, we introduce a novel verifiable neural architecture that integrates online feasibility verification and forward-integration dynamics; upon detecting output infeasibility or performance degradation, the controller automatically reverts to a precomputed safe candidate solution—thereby rigorously enforcing state and input constraints while guaranteeing closed-loop stability and convergence. Evaluated on three standard nonlinear NMPC benchmarks, the approach achieves sub-0.2 ms average inference latency, accelerating computation by several orders of magnitude over conventional NMPC solvers. It significantly outperforms unsafe “naïve” neural controllers and, for the first time, enables high-speed NMPC approximation with deterministic safety guarantees.

Addressing the critical challenge of ensuring long-term safety for sampling-based model predictive control (MPC) in black-box nonlinear systems under limited prediction horizons, this paper proposes a novel framework integrating neural control barrier functions (Neural CBFs) with variational inference MPC (VIMPC). It is the first work to embed Neural CBFs into sampling-based MPC, leveraging constraint-aware importance sampling and low-variance resampling to achieve rigorous, horizon-wide safety guarantees—albeit with mild relaxation of recursive feasibility. The method enables real-time deployment (sub-millisecond latency on CPU) and exhibits robustness to cost function design: safety is preserved even when the cost function is poorly specified. Comprehensive simulations and real-world hardware experiments demonstrate substantial improvements in both safety assurance and computational efficiency.

To address the high online computational latency of Model Predictive Control (MPC), which hinders real-time deployment, this paper proposes a data-driven, nonparametric acceleration framework. The method constructs an upper bound on the optimal cost from an offline MPC solution dataset and employs a greedy lookup strategy to replace online optimization with table-based inference. It establishes, for the first time, explicit theoretical guarantees on recursive feasibility and bounded suboptimality, quantifying the trade-off between dataset size and performance bounds. Experimental results demonstrate that the proposed approach accelerates MPC by 100–1000× compared to conventional implementations, while incurring only negligible performance degradation. Crucially, control quality—measured in terms of stability, constraint satisfaction, and closed-loop performance—is rigorously preserved. This work thus introduces a new paradigm for low-latency, real-time control grounded in data-driven approximation with provable guarantees.

This study addresses the lack of a systematic synthesis in research on integrating reinforcement learning (RL) with model predictive control (MPC) for linear systems by proposing the first multidimensional taxonomy tailored to this domain. Drawing on a comprehensive literature review up to 2025, the work establishes a classification framework along five dimensions: RL role, algorithm type, MPC formulation, cost function structure, and application area, followed by an integrative cross-dimensional analysis. The study elucidates representative integration strategies, traces methodological evolution, and identifies key challenges—including computational burden, sample efficiency, robustness, and closed-loop guarantees—thereby offering a structured reference and practical guidance for both theoretical analysis and architectural design in RL–MPC systems.

This work addresses the excessive conservatism of traditional control methods in safety-critical systems, which often compromises optimal performance and feasibility. To overcome this limitation, the authors propose a novel framework that embeds Control Barrier Functions (CBFs) as terminal constraints within Model Predictive Control (MPC), thereby rigorously guaranteeing safety while significantly reducing conservatism and enlarging the set of reachable states. The approach enables warm-starting of the underlying nonlinear optimization problem to accelerate convergence and is supported by constructive theoretical proofs ensuring formal correctness. Simulation results demonstrate a 1.7–2.7× reduction in infeasible regions and successful tracking of reference trajectories entirely residing within regions deemed unsafe by conventional CBF formulations, thereby validating the method’s superiority and effectiveness.

This work investigates how to achieve optimal policies in Markov decision processes (MDPs) that incorporate future information—such as reference trajectories or predictions—by leveraging model predictive control (MPC). The authors formulate MPC as a class of parameterized policies and train them end-to-end via reinforcement learning. Their key contribution lies in establishing, for the first time, the precise structural conditions under which MPC can exactly represent the optimal value function and policy, thereby providing a theoretical foundation for MPC as a structured function approximator with formal guarantees. Empirical validation on a point-mass racing task with future reference trajectories demonstrates that the proposed approach learns policies approaching optimality, confirming its effectiveness.

This study addresses the finite-horizon budget allocation problem under non-stationary changes in return efficiency by formulating it as a closed-loop economic control problem. The authors employ a receding-horizon model predictive control (MPC) approach to dynamically optimize budget allocation, accounting for execution noise and operational constraints. Through comparison with reactive strategies, the research demonstrates that non-stationarity alone is insufficient for MPC to outperform reactive methods; MPC achieves significant and sustained superiority only when the return efficiency exhibits predictable structures that the model can effectively capture, thereby enabling advantageous intertemporal trade-offs. In contrast, under scenarios of random drift or stationarity, MPC offers no notable performance advantage over reactive approaches.

Existing reinforcement learning (RL) methods lack formal safety guarantees for nonlinear engineering systems such as autonomous vehicles and soft robotics, while model predictive control (MPC) suffers from trade-offs between model fidelity and real-time feasibility. This paper proposes an MPC-RL co-design framework: during training, an MPC-based online safety envelope guides RL policy learning; during deployment, a lightweight safety filter—grounded in Lipschitz continuity analysis—enforces dynamic constraints strictly without online optimization, ensuring real-time compliance. The approach integrates model predictive control, deep RL, and Lipschitz robustness analysis. Evaluated on a nonlinear aeroelastic wing testbed, the method achieves 32% improvement in disturbance rejection, 27% reduction in actuator energy consumption, and zero constraint violations with stable trajectory tracking under severe turbulence.