D-SafeMPC: Diffusion-Driven Safe Model Predictive Control with Discrete-Time Control Barrier Functions

Forward Trajectory Steering for Hamilton-Jacobi Reachability Analysis

Hamilton-Jacobi (HJ) reachability provides a mathematically rigorous framework for safe control of dynamical systems, but its practical application is bottlenecked by the computational complexity of solving Hamilton-Jacobi-Isaacs variational inequality PDEs in high dimensions. Physics-informed neural networks (PINNs) have recently emerged as a promising alternative to classical mesh-based solvers, yet their performance is highly sensitive to the choice of collocation sampling. In order to learn accurate safety value functions, existing PINNs-based HJ reachability solvers must rely on complex training pipelines and auxiliary supervision. In this work, we propose STEER2REACH (S2R), a PINNs-based HJ reachability solver that requires minimal modification on top of standard PINNs training. S2R's key contribution is a lightweight, low-overhead adaptive collocation sampling distribution constructed by steering forward trajectories using a combination of the optimal control and disturbance signals induced by the current value function, with injected stochastic exploration noise. We demonstrate that despite its simplicity, S2R achieves competitive--and in some cases improved--performance on safety metrics while reducing relative L2 error across a range of reachability benchmarks compared with SoTA MPC-guided HJ reachability solvers, all without requiring multi-stage training or MPC-based supervision.

Safe, high-precision reinforcement learning-based optimal control of surgical continuum robots: A monotone tube boundary approach with prescribed-time control capability

Integrating Predictive Sampling and Diffusion Policy for Adaptive Control in Simulated Robotic Arms

This paper presents a hybrid control approach that combines Predictive Sampling and Diffusion Policy to achieve smooth and adaptive motion in robotic arms. Traditional control systems such as PID and Model Predictive Control provide stability but have limited adaptability under uncertain or changing conditions. In contrast, diffusion models can generate smooth control actions but do not ensure physical consistency. In the proposed method, Predictive Sampling is used to plan short term control actions based on the robot dynamics, while the Diffusion Policy refines these actions through a learning based denoising process. The system is implemented on a 2R robotic arm using the MuJoCo simulator with Python and PyTorch. Experimental results show that the hybrid controller produces smoother trajectories, reduces torque noise, and improves overall motion stability when compared to conventional control methods. The results demonstrate how combining model based and data driven techniques can enhance adaptive control in robotic systems.

Koopman-based model predictive control for nonlinear systems with bounded model uncertainty

Constrained Close Loop Model Predictive Control Architecture for Deformable Linear Objects for Dynamic Motions

Deformable linear objects (DLOs) exhibit highly nonlinear dynamic behavior, complicating their control during high-speed maneuvers. Furthermore, the lack of a generic spatial representation and the difficulty of real-time state estimation hinder effective closed-loop manipulation. Building upon our previously established state estimation framework and control architecture, this paper introduces a constrained, closed-loop model predictive control (MPC) approach for highly dynamic DLO manipulation. We integrate hardware and environmental limits into the MPC as soft constraints, enabling tasks like dynamic tracking with endpoint wall avoidance. Additionally, we demonstrate challenging maneuvers, such as swinging a DLO through a narrow slot in open-loop. Furthermore, we enhance our prior state estimation method by incorporating mid-object via points, significantly improving shape reconstruction and enabling the prediction of non-monotonically curved geometries. Finally, we present an extensive evaluation of the complete control architecture using two simulated and five physical DLOs. This analysis assesses the critical influence of kinematic segment discretization, object dynamics, and distribution shifts on overall tracking performance, thereby validating the efficacy and robustness of the approach.

Real-Time Model Predictive Control Algorithms for Autonomous Spacecraft Guidance

This report studies and compares four families of Model Predictive Control (MPC) algorithms for autonomous spacecraft rendezvous guidance: Linear MPC, Tube MPC, Fast/Embedded MPC, and Successive Convexification (SCvx). Using the Clohessy-Wiltshire-Hill (CWH) relative-motion model, we show that the marginal stability of the underlying dynamics causes the condition number of the condensed Hessian to grow sharply with the prediction horizon, which explains why gradient-based solvers such as Fast MPC diverge under long-horizon stress tests while exact linear-algebra solvers (ADMM with Cholesky factorisation) remain unaffected. Tube MPC is validated across five standard rendezvous manoeuvres (Translation, R-bar, V-bar, Natural Motion Circumnavigation, and Corkscrew) using a single fixed controller configuration, and a two-sided, provably correct bound is derived to bracket the worst-case tracking error directly from the cost weight matrices. The framework is further extended to track an arbitrary, non-closed-form reference trajectory through online-recomputed linearisation, with the safety guarantee holding throughout. Finally, to assess feasibility for real flight software, the core numerical routines (Cholesky factorisation and the Riccati equation solver) are re-implemented from first principles, without external libraries, and validated against standard scientific computing tools to machine precision. Taken together, these results support Tube MPC as a robust and computationally realistic controller for onboard, real-time spacecraft rendezvous guidance.