mpc torque optimization

Real-time Model Predictive Control (MPC) for resource-constrained microcontrollers—e.g., ARM Cortex-M7—is severely limited by memory footprint and computational latency, hindering deployment on ultra-lightweight robotic platforms. Method: We propose a structured Alternating Direction Method of Multipliers (ADMM) solver tailored for embedded MPC, leveraging problem decomposition, hand-optimized embedded C code, and fixed-point arithmetic to minimize both memory usage and execution time. Contribution/Results: Our solver achieves nearly 10× speedup over the state-of-the-art OSQP solver and, for the first time, enables MPC closed-loop control at >500 Hz on a 27-g quadrotor. It supports high-bandwidth trajectory tracking and dynamic obstacle avoidance. Crucially, we tightly integrate ADMM with the inherent structural properties of MPC—such as block-banded sparsity and separable constraints—yielding the first lightweight, real-time MPC framework deployable on microcontrollers. This work provides a practical, optimal-control-based solution for autonomous navigation in miniature robotics.

Real-time autonomous navigation for embedded unmanned aerial vehicles (UAVs) faces a fundamental challenge: conventional nonlinear model predictive control (NMPC) cannot meet millisecond-level closed-loop timing requirements under severe computational constraints. Method: This paper proposes an embedded-friendly hierarchical NMPC architecture that decouples long-horizon safety-aware planning from short-horizon high-frequency tracking. The planning layer employs a large-horizon, low-frequency (~100 ms) NMPC to ensure global feasibility and obstacle avoidance; the tracking layer uses a small-horizon, high-frequency (~5 ms) lightweight MPC for responsive trajectory following. Contribution/Results: We establish theoretical guarantees on recursive feasibility and obstacle-avoidance safety. Engineering deployment is achieved via constraint simplification, hierarchical optimization, and real-time C++ implementation on ARM processors. Experimental validation on a quadrotor demonstrates a 5× increase in planning horizon, significantly improved navigation success rate and trajectory quality over monolithic NMPC baselines in complex static environments.

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.

To address the high computational cost of nonlinear model predictive control (NMPC) hindering real-time deployment, this paper proposes a safety-enhanced neural network controller. Methodologically, we introduce a novel verifiable neural architecture that integrates online feasibility verification and forward-integration dynamics; upon detecting output infeasibility or performance degradation, the controller automatically reverts to a precomputed safe candidate solution—thereby rigorously enforcing state and input constraints while guaranteeing closed-loop stability and convergence. Evaluated on three standard nonlinear NMPC benchmarks, the approach achieves sub-0.2 ms average inference latency, accelerating computation by several orders of magnitude over conventional NMPC solvers. It significantly outperforms unsafe “naïve” neural controllers and, for the first time, enables high-speed NMPC approximation with deterministic safety guarantees.

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 challenges of joint tuning of cost weights and low-level controller gains in torque-level nonlinear model predictive control (nMPC) for the UR10e robotic arm, as well as the high risk of poor sim-to-real transfer. We propose a digital twin–based automatic parameter optimization framework. Innovatively, we employ the SAASBO high-dimensional Bayesian optimization algorithm to efficiently search for optimal nMPC parameter configurations within a safety-certified digital twin simulation environment, enabling end-to-end co-tuning across simulation and real hardware. Experimental results demonstrate: (i) a 41.9% reduction in end-effector trajectory tracking error and a 2.5% decrease in online solver time in simulation; and (ii) a 25.8% improvement in tracking accuracy on the physical platform. These results validate the proposed framework’s superior balance of accuracy, real-time performance, and sim-to-real transferability.

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.

This work addresses the high computational cost of model predictive control (MPC) in real-time control of a 3-degree-of-freedom robotic arm by proposing a behavior cloning–based neural network surrogate. An expert controller is constructed by integrating inverse kinematics with MPC, and a static deep multilayer perceptron (MLP) is trained to emulate its input–output mapping. The study demonstrates that this static architecture outperforms temporal models, indicating that instantaneous state information suffices to replicate MPC behavior. Experimental results show a task success rate of 84.98% under relaxed tolerances, with inference latency reduced by a factor of three compared to MPC. However, under stringent accuracy requirements, the approach exhibits steady-state errors, revealing room for improvement in precision. These findings highlight the efficiency and potential of lightweight static networks for real-time robotic control.

To address the challenge of jointly ensuring motion stability and manipulation force control in legged mobile manipulation, this paper proposes a full-order inverse-dynamics-based whole-body model predictive control (MPC) framework. The method directly optimizes joint torques within a single prediction horizon, unifying whole-body motion planning and contact force generation to achieve dynamically consistent and constraint-complete natural coupling behavior. It integrates Pinocchio for rigid-body dynamics modeling, CasADi for automatic differentiation, and Fatrop for efficient interior-point optimization, enabling real-time control at 80 Hz on a Unitree B2 quadrupedal platform equipped with a Z1 manipulator. Experimental validation demonstrates robust performance across diverse dynamic manipulation tasks—including dragging heavy objects, pushing boxes, and wiping whiteboards—significantly enhancing both robustness and generalization capability of legged mobile manipulation.

This work addresses the challenges of high training overhead and complex problem formulation in combining model predictive control (MPC) with reinforcement learning (RL) for humanoid robot motion control. To this end, the authors propose an MPC-RL framework that leverages a centroidal dynamics-based MPC during training to generate guiding trajectories and designs an MPC-informed reward mechanism to enhance learning efficiency. Furthermore, they develop πⁿMPC, a just-in-time compiled, batched GPU-parallel MPC solver capable of handling time-varying dynamics, which substantially reduces computational costs. Experimental results demonstrate that the proposed approach outperforms existing methods across a range of locomotion and manipulation tasks, achieving both high performance and computational efficiency on real hardware.