integrate sdf into mpc

This paper addresses real-time motion planning for vehicles in confined spaces, focusing on collision avoidance with polygonal obstacles. To overcome the computational bottleneck of traditional mixed-integer programming (MIP), it proposes a convex, integer-free modeling framework for polygonal collision constraints. The method integrates two key innovations into a model predictive control (MPC) architecture: (1) SVM-based reconstruction of polygonal boundaries to enhance collision detection accuracy; and (2) a minimum signed directed edge (MSDE) distance function—convex, differentiable, and computationally lightweight—to formulate obstacle-avoidance constraints. Experimental results demonstrate that the SVM-enhanced boundary representation significantly improves parking maneuver accuracy in narrow environments, while the MSDE formulation enables millisecond-scale online optimization on an RC car platform, with only marginal degradation in obstacle avoidance performance. The approach thus achieves an effective trade-off between geometric fidelity and real-time computational efficiency.

This work addresses the challenge of real-time local planning in cluttered environments, where conventional optimization-based approaches suffer from high computational overhead due to frequent collision checks. The authors propose a geometrically exact polygonal signed distance function (PSDF) and construct a branch-free, weight-free tensorized geometry pipeline that enables efficient GPU batch computation and automatic differentiation. Integrated into a sequential quadratic programming framework, this pipeline yields PSDF-MPC, a real-time model predictive controller. Notably, the method achieves the first efficient GPU-parallel implementation of PSDF, decouples CPU and GPU workloads, and renders obstacle-avoidance constraint evaluation complexity independent of the number of obstacles. Experiments demonstrate that PSDF surpasses existing methods in both accuracy and efficiency for distance queries, while PSDF-MPC exhibits strong real-time performance and robust collision avoidance in both simulation and physical robot trials.

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 limitations of conventional model predictive control (MPC) in autonomous driving motion planning—namely, restricted solution spaces due to convex approximations and the difficulty of balancing real-time performance with global optimality—this paper proposes a safety-enhanced reinforcement learning (RL) and MPC co-optimization framework. Methodologically, it incorporates an energy-function-based safety index constraint and designs state-dependent, online-updated Lagrange multipliers to embed safety requirements into both RL policy optimization and MPC solving, enabling joint safe optimization of reference trajectory generation and local control. Its key contribution is the first integration of a safety index function with an adaptive Lagrange multiplier mechanism, overcoming convex approximation constraints and enabling broader exploration of globally optimal solutions. Evaluated in highway scenarios, the approach achieves a 23.6% improvement in collision avoidance rate and an 18.4% reduction in jerk (trajectory smoothness), while maintaining millisecond-level real-time responsiveness—outperforming baseline MPC and standard safety-aware RL methods.

Real-time trajectory generation for obstacle avoidance in dynamic environments suffers from reliance on explicit obstacle boundary representations, low computational efficiency, and suboptimal trajectories. Method: This paper proposes a real-time planning and control framework integrating Model Predictive Control (MPC) with discrete-time high-order Control Barrier Functions (DHOCBFs). It automatically generates convex polyhedral obstacle representations from grid maps—bypassing the need for prior geometric knowledge (e.g., explicit boundary equations)—and directly derives DHOCBFs to ensure safety for both convex and non-convex obstacles. Global optimality is further enforced via optimization-driven path planning. Contribution/Results: Experiments in tightly constrained dynamic scenarios demonstrate significant improvements in computational speed and trajectory feasibility compared to baseline CBF methods, while yielding shorter, safer, and dynamically feasible trajectories.

This paper addresses mapless, collision-free navigation for aerial robots in unknown environments using only onboard ranging sensors. Method: We propose a neural-augmented nonlinear model predictive control (Neural NMPC) framework featuring a two-stage neural architecture: a convolutional encoder implicitly maps single-frame range images to a signed distance field (SDF), and an MLP embeds this representation into NMPC position constraints—ensuring recursive feasibility and closed-loop stability. The framework requires no explicit mapping or external localization, operating directly on raw range measurements for real-time, velocity-level obstacle avoidance. Contribution/Results: Evaluated in both simulation and real-world forest environments, our approach significantly outperforms state-of-the-art local navigators and demonstrates strong robustness against odometry drift.

This work addresses the challenge of autonomous vehicle path planning by proposing a staged framework that balances safety, comfort, dynamic feasibility, and computational efficiency. The approach first generates a coarse trajectory using Dijkstra’s graph search, then constructs a spatially varying convex lateral safety corridor. This discrete obstacle-avoidance result is explicitly embedded into a model predictive control (MPC) formulation as continuous feasible constraints. To refine the trajectory, the MPC optimization incorporates the third derivative of lateral offset as a smoothness penalty term. Evaluated across multiple overtaking scenarios, the method significantly reduces lateral acceleration, curvature, and jerk while improving computational performance—achieving 28.08% and 29.52% reductions in computation time on straight and curved road segments, respectively.

This work addresses the challenge of real-time, safe, and robust model predictive control for high-dimensional uncertain nonlinear systems over long horizons. The authors propose a GPU-parallelized System Level Synthesis (SLS) framework that, for the first time, embeds reachability constraints directly into the SLS formulation and jointly optimizes the nominal trajectory, tracking controller, and closed-loop reachable set. By integrating sequential quadratic programming, an ADMM-accelerated QP solver, associative scanning, and adaptive caching, the method generates online control policies in under 20 milliseconds on average for systems with 61–75 states, handling up to 2×10⁵ variables and 8×10⁴ constraints. Compared to CPU and GPU baselines, it achieves 97.7% and 71.8% speedups in nominal trajectory computation, respectively, and a 237× acceleration in SLS and reachability calculations, enabling millisecond-scale, scalable, and empirically 100% safe nonlinear MPC.

This work addresses the geometric complexity of collision avoidance for polyhedral robots navigating environments populated with polyhedral obstacles by proposing an iterative convex optimization framework that integrates exact polyhedral distance computation with control barrier functions. By computing closest points between convex polyhedra to construct supporting hyperplanes, the method generates linear discrete-time control barrier constraints. Coupled with local linearization of system dynamics and robot geometry, this formulation transforms the original non-convex problem into a sequence of convex optimization problems. Notably, this approach is the first to embed exact polyhedral distance within an MPC-DCBF framework, preserving geometric fidelity while guaranteeing convexity at each optimization step. Experiments demonstrate real-time, collision-free navigation in complex mazes, multi-robot settings, and three-dimensional scenarios, achieving millisecond-level computational performance.