AC-SMPC: Differentiable Actor--Critic MPC with State Constraints for Safe and Fast Robot Navigation

A key limitation on the use of diffusion models in robotic planning is their inability to inherently enforce safety or dynamical constraints, which often results in physically infeasible or unsafe outputs. Hybrid approaches that employ model predictive control (MPC) to address this problem can be unstable, as poor trajectory initializations from the diffusion model prevent the MPC from converging to a safe and feasible solution. To overcome these challenges, we propose D-SafeMPC, which enhances the interaction between diffusion and control. Our method guides the reverse diffusion process with control barrier functions (CBFs) and control Lyapunov functions (CLFs) and employs an iterative-projection scheme where an MPC refines the trajectory at each denoising step. This steers sampling toward safe, goal-directed regions and provides reliable MPC warm starts. In simulations on a Franka manipulator across four scenarios (one static-obstacle and three dynamic-obstacle settings) and in a sim-to-real experiment on a physical Franka robot, D-SafeMPC improves safety, task success rates, and planning efficiency over state-of-the-art baselines. To facilitate reproducibility, our source code and experimental configurations are available in a repository at https://github.com/erdiphd/D-SafeMPC

Ensuring safe physical interaction between torque-controlled manipulators and humans is essential for deploying robots in everyday environments. Model Predictive Control (MPC) has emerged as a suitable framework thanks to its capacity to handle hard constraints, provide strong guarantees and zero-shot adaptability through predictive reasoning. However, Gradient-Based MPC (GB-MPC) solvers have demonstrated limited performance for collision avoidance in complex environments. Sampling-based approaches such as Model Predictive Path Integral (MPPI) control offer an alternative via stochastic rollouts, but enforcing safety via additive penalties is inherently fragile, as it provides no formal constraint satisfaction guarantees. We propose a collision avoidance framework called COSMIK-MPPI combining MPPI with the toolbox for human motion estimation RT-COSMIK and the Constraints-as-Terminations transcription, which enforces safety by treating constraint violations as terminal events, without relying on large penalty terms or explicit human motion prediction. The proposed approach is evaluated against state-of-the-art GB-MPC and vanilla MPPI in simulation and on a real manipulator arm. Results show that COSMIK-MPPI achieves a 100% task success rate with a constant computation time (22 ms), largely outperforming GB-MPC. In simulated infeasible scenarios, COSMIK-MPPI consistently generates collision-free trajectories, contrary to vanilla MPPI. These properties enabled safe execution of complex real-world human-robot interaction tasks in shared workspaces using an affordable markerless human motion estimator, demonstrating a robust, compliant, and practical solution for predictive collision avoidance (cf. results showcased at https://exquisite-parfait-ffa925.netlify.app)

Model Predictive Control (MPC) is widely used for autonomous-vehicle (AV) motion planning, but its real-time applicability is often limited by the need for accurate models and online solution of nonlinear, nonconvex optimization problems in dynamic road environments. Actor-critic reinforcement learning offers a promising alternative for online policy generation, yet its policy-learning process often lacks explicit control-theoretic structure. This article proposes a learning predictive control (LPC) framework with deep Koopman operators for efficient real-time motion planning under nonconvex constraints. To address nonlinear and uncertain vehicle dynamics, a deep-Koopman-based predictor is used to lift the system into an interpretable linear observable space in a data-driven manner. Unlike traditional MPC, which computes open-loop control sequences, the proposed LPC framework yields a closed-loop state-feedback policy within each prediction interval through receding-horizon actor-critic learning. To ensure safety under nonconvex environmental constraints, LPC constructs convex local surrogate representations of obstacles and defines corresponding potential-field functions. These functions and their gradients are directly embedded into the actor-critic structure, enabling efficient, safety-aware policy learning. Extensive simulations and real-world experiments on the HongQi-EHS3 platform demonstrate favorable performance in diverse obstacle-avoidance scenarios in terms of safety, computational efficiency, and driving comfort, compared with benchmark methods such as CBF-MPC and LMPCC.