physics-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.

Existing motion planning methods for nonholonomic systems under nonconvex constraints lack theoretical guarantees of convergence. Method: This paper proposes an output-tracking model predictive control (MPC) framework, incorporating slack variables, designing a terminal set and terminal cost tailored to nonholonomic dynamics, and establishing rigorous closed-loop asymptotic convergence and goal reachability under verifiable, realistic assumptions. Contribution/Results: To the best of our knowledge, this is the first MPC-based planning approach that provides theoretical completeness for nonholonomic systems subject to nonconvex constraints. Comprehensive simulations and experiments on canonical nonconvex scenarios demonstrate the method’s feasibility, closed-loop stability, and computational efficiency—thereby bridging a critical gap between empirical practice and theoretical rigor in nonholonomic motion planning.

Addressing the challenge of simultaneously ensuring safety and task performance for autonomous systems in complex scenarios, this paper proposes a synergistic framework integrating Model Predictive Control (MPC) with Hamilton–Jacobi (HJ) reachability analysis. The method employs online HJ-based computation of safety constraint sets, which are embedded into the MPC optimization problem to guarantee recursive feasibility and satisfaction of safety boundaries—even in high-dimensional state spaces—while preserving MPC’s explicit task-objective optimization capability. Compared to conventional safety-augmented MPC or standalone reachability approaches, our framework achieves a +23.6% improvement in safety constraint satisfaction rate in simulations of a 4D Dubins car and a 6-DOF KUKA iiwa manipulator, with only marginal degradation in task performance and strong scalability to higher dimensions. The core innovation lies in the tightly coupled modeling of safety verification and performance optimization.

Model predictive control (MPC) for neural state-space models (NSSMs) of vehicle dynamics faces severe computational challenges due to the non-convexity and high dimensionality of the resulting optimization problem. Method: This paper proposes Model Predictive Inference Control (MPIC), a novel paradigm that reformulates motion planning as a Bayesian state estimation task. We design a particle smoothing algorithm based on an ensemble of unscented Kalman filters, achieving high estimation accuracy while improving sampling efficiency and real-time performance. Contribution/Results: Unlike gradient-based MPC methods, MPIC overcomes the exponential growth in computational complexity with neural network scale under learned dynamics. In extensive multi-scenario simulations, MPIC significantly improves both solution efficiency and trajectory quality, enabling, for the first time, efficient closed-loop control using large-scale NSSM-based MPC.

Modeling robot contact dynamics and achieving real-time control remain critical challenges in manipulation and locomotion tasks. This paper proposes a lightweight inverse-dynamics trajectory optimization framework that integrates contact-implicit modeling, efficient Hessian approximation, and sparse nonlinear programming structure, substantially reducing computational overhead for contact-sensitive model predictive control (MPC). The open-source real-time MPC solver achieves >100 Hz closed-loop control on a 20-degree-of-freedom bimanual robot platform—marking the first hardware demonstration enabling simultaneous high-dynamic legged locomotion and complex dexterous manipulation under robust contact control. Key contributions include: (i) overcoming the real-time feasibility bottleneck of contact-implicit MPC; and (ii) establishing a unified optimization paradigm that jointly ensures modeling fidelity, computational efficiency, and hardware deployability.

This work addresses the limited exploration capability and difficulty in converging to global optima inherent in sampling-based controllers for path planning. To overcome these challenges, the authors propose integrating motion primitives into the Model Predictive Path Integral (MPPI) framework. By fusing motion primitive-guided structured sampling with perturbed control sequences within the real-time optimization loop, the method substantially enhances exploration efficiency and global optimality in the control space while preserving MPPI’s intrinsic fast response characteristics. Evaluations on quadrotor obstacle navigation tasks demonstrate that the proposed algorithm significantly improves both exploratory behavior and real-time performance, thereby validating its superiority over conventional approaches.

This work addresses the sensitivity to parameters, poor stability, and low computational efficiency commonly observed in gradient-based optimization algorithms for nonlinear model predictive control (NMPC). To overcome these limitations, the authors propose the Search and Accelerate (SaA) algorithm, which integrates adaptive line search, a trust-region mechanism, and gradient acceleration strategies. Specifically designed for box-constrained optimization problems, SaA requires no prior knowledge of the Lipschitz constant and operates effectively with default parameter settings, ensuring broad applicability. Theoretical analysis establishes its convergence and stability properties, while extensive experiments across 600 benchmark instances demonstrate its superior efficiency and robustness. Notably, SaA significantly reduces the NMPC control update cycle, positioning it as a compelling general-purpose alternative to existing gradient-based optimizers.

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 study addresses the challenge of balancing efficiency and maneuverability in multi-fin oscillatory-propulsion underwater robots during cruising. The authors propose a novel approach that embeds a Strouhal number constraint (St = 0.25–0.35) directly into the objective function of model predictive control (MPC). Grounded in first-principles fluid dynamics, this method enables direct optimization of energy efficiency within the MPC framework by integrating a quasi-steady hydrodynamic model and a two-stage non-convex optimization algorithm, achieving real-time operation at 25 Hz on onboard hardware. Experimental results demonstrate an 8.8%–32% reduction in mechanical power consumption across cruising speeds of 0.1–0.3 m/s, successful execution of high-speed maneuvers up to 0.4 m/s—unattainable with conventional methods—and precise tracking of commanded forces.

This study addresses the spurious feasibility issue in variable-impedance model predictive control, where treating joint stiffness as an instantaneous decision variable yields solutions outside the physically realizable set. The work identifies this problem as stemming from modeling error rather than approximation inaccuracies and introduces a dimensionless parameter α = ωₛT to quantify the mismatch between parametrization and the physical feasibility set. Using one-dimensional spring-loaded hopping and planar spring-inverted pendulum models, the authors analytically derive critical (α_crit) and infeasibility (α_infeas) thresholds. By augmenting the state vector with stiffness as a dynamic variable, the proposed method fundamentally eliminates the feasibility gap. Numerical simulations and log-scale regression (R² = 0.99) confirm that trajectory deviations—primarily manifesting as center-of-mass trajectory and stance-phase timing distortions—monotonically increase as α decreases, while the proposed approach constructively restores physical feasibility.