Accelerating and Scaling MPC-Guided Reinforcement Learning for Humanoid Locomotion and Manipulation

In humanoid motion control, model predictive control (MPC) offers physically grounded prediction and constraint handling, while reinforcement learning (RL) enables robust whole-body skills through large-scale simulation. However, using MPC inside RL often requires time-consuming problem construction or excessive training overhead, making such frameworks difficult to justify in practice. This work studies efficient training-time MPC guidance for humanoid locomotion and manipulation, termed MPC-RL. We introduce a centroidal-dynamics MPC reward formulation that leverages guidance from MPC trajectories in training time. To make this practical in massively parallel RL, we develop $π^n$MPC, a parallel-in-horizon and construction-free batched GPU MPC solver that operates directly on time-varying dynamics to avoid high memory usage and pre-compilation. Through a variety of comparative studies and hardware validations, we have found that MPC-RL achieves superior performance in locomotion and manipulation skills. The code base is available at https://github.com/junhengl/mpc-rl.

Stability of Control Lyapunov Function Guided Reinforcement Learning

Reinforcement learning (RL) has become the de facto method for achieving locomotion on humanoid robots in practice, yet stability analysis of the corresponding control policies is lacking. Recent work has attempted to merge control theoretic ideas with reinforcement learning through control guided learning. A notable example of this is the use of a control Lyapunov function (CLF) to synthesize the reinforcement learning rewards, a technique known as CLF-RL, which has shown practical success. This paper investigates the stability properties of optimal controllers using CLF-RL with the goal of bridging experimentally observed stability with theoretical guarantees. The RL problem is viewed as an optimal control problem and exponential stability is proven in both continuous and discrete time using both core CLF reward terms and the additional terms used in practice. The theoretical bounds are numerically verified on systems such as the double integrator and cart-pole. Finally, the CLF guided rewards are implemented for a walking humanoid robot to generate stable periodic orbits.

On Surprising Effects of Risk-Aware Domain Randomization for Contact-Rich Sampling-based Predictive Control

Domain randomization (DR) is widely used in policy learning to improve robustness to modeling error, but remains underexplored in contact-rich sampling-based predictive control (SPC), where rollout quality is highly sensitive to uncertainty. In this work, we take the first step by studying risk-aware DR in predictive sampling on a simple yet representative Push-T task, comparing average, optimistic, and pessimistic rollout aggregations under randomized model instances. Our initial results suggest that DR affects not only robustness to model error, but also the effective cost landscape seen by the sampling-based optimizer, by reshaping the basin of attraction around contact-producing actions. This opens up potential for exploring better grounded risk-aware contact-rich SPC under model uncertainty. Video: https://youtu.be/f1F0ALXxhSM

Full-Body Dynamic Safety for Robot Manipulators: 3D Poisson Safety Functions for CBF-Based Safety Filters

Collision avoidance for robotic manipulators requires enforcing full-body safety constraints in high-dimensional configuration spaces. Control Barrier Function (CBF) based safety filters have proven effective in enabling safe behaviors, but enforcing the high number of constraints needed for safe manipulation leads to theoretic and computational challenges. This work presents a framework for full-body collision avoidance for manipulators in dynamic environments by leveraging 3D Poisson Safety Functions (PSFs). In particular, given environmental occupancy data, we sample the manipulator surface at a prescribed resolution and shrink free space via a Pontryagin difference according to this resolution. On this buffered domain, we synthesize a globally smooth CBF by solving Poisson's equation, yielding a single safety function for the entire environment. This safety function, evaluated at each sampled point, yields task-space CBF constraints enforced by a real-time safety filter via a multi-constraint quadratic program. We prove that keeping the sample points safe in the buffered region guarantees collision avoidance for the entire continuous robot surface. The framework is validated on a 7-degree-of-freedom manipulator in dynamic environments.

HALO: Hybrid Auto-encoded Locomotion with Learned Latent Dynamics, Poincaré Maps, and Regions of Attraction

Reduced-order models are powerful for analyzing and controlling high-dimensional dynamical systems. Yet constructing these models for complex hybrid systems such as legged robots remains challenging. Classical approaches rely on hand-designed template models (e.g., LIP, SLIP), which, though insightful, only approximate the underlying dynamics. In contrast, data-driven methods can extract more accurate low-dimensional representations, but it remains unclear when stability and safety properties observed in the latent space meaningfully transfer back to the full-order system. To bridge this gap, we introduce HALO (Hybrid Auto-encoded Locomotion), a framework for learning latent reduced-order models of periodic hybrid dynamics directly from trajectory data. HALO employs an autoencoder to identify a low-dimensional latent state together with a learned latent Poincaré map that captures step-to-step locomotion dynamics. This enables Lyapunov analysis and the construction of an associated region of attraction in the latent space, both of which can be lifted back to the full-order state space through the decoder. Experiments on a simulated hopping robot and full-body humanoid locomotion demonstrate that HALO yields low-dimensional models that retain meaningful stability structure and predict full-order region-of-attraction boundaries.

Safety Guardrails in the Sky: Realizing Control Barrier Functions on the VISTA F-16 Jet

The advancement of autonomous systems -- from legged robots to self-driving vehicles and aircraft -- necessitates executing increasingly high-performance and dynamic motions without ever putting the system or its environment in harm's way. In this paper, we introduce Guardrails -- a novel runtime assurance mechanism that guarantees dynamic safety for autonomous systems, allowing them to safely evolve on the edge of their operational domains. Rooted in the theory of control barrier functions, Guardrails offers a control strategy that carefully blends commands from a human or AI operator with safe control actions to guarantee safe behavior. To demonstrate its capabilities, we implemented Guardrails on an F-16 fighter jet and conducted flight tests where Guardrails supervised a human pilot to enforce g-limits, altitude bounds, geofence constraints, and combinations thereof. Throughout extensive flight testing, Guardrails successfully ensured safety, keeping the pilot in control when safe to do so and minimally modifying unsafe pilot inputs otherwise.

Chasing Autonomy: Dynamic Retargeting and Control Guided RL for Performant and Controllable Humanoid Running

Humanoid robots have the promise of locomoting like humans, including fast and dynamic running. Recently, reinforcement learning (RL) controllers that can mimic human motions have become popular as they can generate very dynamic behaviors, but they are often restricted to single motion play-back which hinders their deployment in long duration and autonomous locomotion. In this paper, we present a pipeline to dynamically retarget human motions through an optimization routine with hard constraints to generate improved periodic reference libraries from a single human demonstration. We then study the effect of both the reference motion and the reward structure on the reference and commanded velocity tracking, concluding that a goal-conditioned and control-guided reward which tracks dynamically optimized human data results in the best performance. We deploy the policy on hardware, demonstrating its speed and endurance by achieving running speeds of up to 3.3 m/s on a Unitree G1 robot and traversing hundreds of meters in real-world environments. Additionally, to demonstrate the controllability of the locomotion, we use the controller in a full perception and planning autonomy stack for obstacle avoidance while running outdoors.

MIRROR: Visual Motion Imitation via Real-time Retargeting and Teleoperation with Parallel Differential Inverse Kinematics

Real-time humanoid teleoperation requires inverse kinematics (IK) solvers that are both responsive and constraint-safe under kinematic redundancy and self-collision constraints. While differential IK enables efficient online retargeting, its locally linearized updates are inherently basin-dependent and often become trapped near joint limits, singularities, or active collision boundaries, leading to unsafe or stagnant behavior. We propose a GPU-parallelized, continuation-based differential IK that improves escape from such constraint-induced local minima while preserving real-time performance, promoting safety and stability. Multiple constrained IK quadratic programs are evaluated in parallel, together with a self-collision avoidance control barrier function (CBF), and a Lyapunov-based progression criterion selects updates that reduce the final global task-space error. The method is paired with a visual skeletal pose estimation pipeline that enables robust, real-time upper-body teleoperation on the THEMIS humanoid robot hardware in real-world tasks.

Safe-SAGE: Social-Semantic Adaptive Guidance for Safe Engagement through Laplace-Modulated Poisson Safety Functions

Traditional safety-critical control methods, such as control barrier functions, suffer from semantic blindness, exhibiting the same behavior around obstacles regardless of contextual significance. This limitation leads to the uniform treatment of all obstacles, despite their differing semantic meanings. We present Safe-SAGE (Social-Semantic Adaptive Guidance for Safe Engagement), a unified framework that bridges the gap between high-level semantic understanding and low-level safety-critical control through a Poisson safety function (PSF) modulated using a Laplace guidance field. Our approach perceives the environment by fusing multi-sensor point clouds with vision-based instance segmentation and persistent object tracking to maintain up-to-date semantics beyond the camera's field of view. A multi-layer safety filter is then used to modulate system inputs to achieve safe navigation using this semantic understanding of the environment. This safety filter consists of both a model predictive control layer and a control barrier function layer. Both layers utilize the PSF and flux modulation of the guidance field to introduce varying levels of conservatism and multi-agent passing norms for different obstacles in the environment. Our framework enables legged robots to navigate semantically rich, dynamic environments with context-dependent safety margins while maintaining rigorous safety guarantees.

Layered Safety: Enhancing Autonomous Collision Avoidance via Multistage CBF Safety Filters

This paper presents a general end-to-end framework for constructing robust and reliable layered safety filters that can be leveraged to perform dynamic collision avoidance over a broad range of applications using only local perception data. Given a robot-centric point cloud, we begin by constructing an occupancy map which is used to synthesize a Poisson safety function (PSF). The resultant PSF is employed as a control barrier function (CBF) within two distinct safety filtering stages. In the first stage, we propose a predictive safety filter to compute optimal safe trajectories based on nominal potentially-unsafe commands. The resultant short-term plans are constrained to satisfy the CBF condition along a finite prediction horizon. In the second stage, instantaneous velocity commands are further refined by a real-time CBF-based safety filter and tracked by the full-order low-level robot controller. Assuming accurate tracking of velocity commands, we obtain formal guarantees of safety for the full-order system. We validate the optimality and robustness of our multistage architecture, in comparison to traditional single-stage safety filters, via a detailed Pareto analysis. We further demonstrate the effectiveness and generality of our collision avoidance methodology on multiple legged robot platforms across a variety of real-world dynamic scenarios.