constraint manifold control

This paper addresses the online safety-critical control problem for cyber-physical systems subject to multiple state and input constraints. We propose the Gatekeeper framework, which recursively verifies—via a backup controller—the existence of infinitely-horizon feasible trajectories, thereby ensuring real-time satisfaction of system dynamics and nonconvex, nonlinear constraints (e.g., obstacles, engagement zones). Theoretical contributions include: (i) establishing a complete Gatekeeper theory; (ii) deriving the first provable suboptimality bound relative to nonlinear trajectory optimization; (iii) enabling joint runtime verification of safety and performance; and (iv) reducing controller synthesis to optimizing a single scalar variable under minimal, verifiable assumptions. We validate the approach on multi-agent Dubins vehicle formations, demonstrating low computational overhead, high scalability, and real-time safety guarantees.

This work addresses the challenge of achieving both rigorous safety guarantees and efficient coordination in safety-critical multi-agent systems. The authors propose a hierarchical multi-agent reinforcement learning framework in which a low-level controller enforces hard safety constraints through constrained manifold control under mild assumptions, while a high-level policy learns to coordinate agents effectively. This approach represents the first integration of constrained manifold control with hierarchical reinforcement learning in a multi-agent setting, offering provable safety, stable training dynamics, and strong generalization across varying numbers of agents and obstacle configurations. Experimental results demonstrate that the system maintains nearly 100% safety compliance while achieving competitive task performance.

Ensuring safety for safety-critical nonlinear systems—e.g., robotic manipulators—under state/input constraints and collision avoidance remains challenging for model predictive control (MPC). Method: This paper proposes a safety-enhanced nonlinear MPC (NMPC) framework leveraging parallel computation. Its core innovation is the explicit, time-domain-parallel expansion of control-invariant safe set constraints across the prediction horizon, enabling simultaneous optimization of multiple candidate trajectories. Leveraging multi-core architectures, it solves control sequences at all time steps in parallel and dynamically selects the optimal one. The approach integrates nonlinear optimization, control-invariant set theory, and parallel computing. Contribution/Results: The framework significantly improves real-time safety guarantees and decision flexibility. In simulations on a 3-DOF robotic arm, it achieves strict constraint satisfaction while delivering markedly faster response times and enhanced obstacle-avoidance robustness compared to serial NMPC—using only four CPU cores.

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.

To address the challenge of simultaneously ensuring safety and optimizing performance in uncertain dynamical systems, this paper proposes a safety-critical learning framework based on generalized action governors (AGs). The framework unifies the modeling of diverse safety enforcement mechanisms for multiple system classes and rigorously integrates AGs with both reinforcement learning (RL) and Koopman operator-based control, guaranteeing strict satisfaction of state constraints throughout the entire learning process. Methodologically, it encompasses AG synthesis, constraint analysis for linear and discrete-time systems, safety-aware RL, data-driven Koopman model identification, and real-time feasibility verification. We provide theoretical guarantees on closed-loop stability and safety of the AG-augmented system. Numerical experiments demonstrate that the two proposed safe learning algorithms achieve significant improvements in closed-loop performance—without any constraint violations.

This work addresses the limitation of traditional safety mechanisms, which rely solely on state predicates and struggle to enforce smoothness constraints on higher-order derivatives such as velocity and acceleration. To overcome this, the paper proposes a higher-order safety shield synthesis method grounded in finite-state safety games. By employing finite differences to formally encode differential safety properties within a discrete state space, the problem is transformed into a safety game requiring memory of past states. The authors theoretically establish that enforcing a k-th order property necessitates preserving exactly k steps of history, and leverage this insight to design a layered, iterative algorithm for synthesizing maximally permissive strategies. This approach substantially reduces the search space, enhances synthesis efficiency, and effectively supports runtime enforcement of multi-order physical constraints.

This work addresses the synthesis of robot behavior models endowed with executable semantics while satisfying prescribed logical constraints. To this end, the authors propose Hyper Petri Nets (HyPN), a novel formalism that integrates Boolean logical specifications with the execution semantics of Petri nets for the first time. The approach defines executable semantics over observable states via atomic transition sequences and explicitly distinguishes observable states from underlying mechanistic details. By doing so, it uncovers a fundamental distinction between logical feasibility and executable behavior and introduces an execution abstraction grounded in observable states. The effectiveness of the method is demonstrated through experiments in a lunar rover scenario, offering a structured modeling framework for robotic systems that jointly ensures logical correctness and adherence to execution constraints.

Standard Model Predictive Path Integral (MPPI) control struggles to enforce hard constraints, limiting its applicability in highly constrained tasks such as closed-chain manipulation. This work proposes the Manifold-Constrained MPPI (MC-MPPI) framework, which, for the first time, embeds manifold equality constraints directly into MPPI. The approach leverages a variational autoencoder (VAE) to learn a low-dimensional latent representation of the constraint manifold and decouples constraint satisfaction from trajectory generation by introducing a single-step quadratic programming (QP) correction at the execution layer. While preserving MPPI’s computational efficiency, MC-MPPI rigorously enforces hard constraints, achieving stable 100 Hz operation on a 14-degree-of-freedom dual-arm closed-chain system. Both simulation and real-world experiments demonstrate significant improvements over baseline methods, reliably maintaining constraints and enhancing trajectory tracking accuracy.