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.

Input-to-State Safe Backstepping: Robust Safety-Critical Control with Unmatched Uncertainties

Guaranteeing safety in the presence of unmatched disturbances -- uncertainties that cannot be directly canceled by the control input -- remains a key challenge in nonlinear control. This paper presents a constructive approach to safety-critical control of nonlinear systems with unmatched disturbances. We first present a generalization of the input-to-state safety (ISSf) framework for systems with these uncertainties using the recently developed notion of an Optimal Decay CBF, which provides more flexibility for satisfying the associated Lyapunov-like conditions for safety. From there, we outline a procedure for constructing ISSf-CBFs for two relevant classes of systems with unmatched uncertainties: i) strict-feedback systems; ii) dual-relative-degree systems, which are similar to differentially flat systems. Our theoretical results are illustrated via numerical simulations of an inverted pendulum and planar quadrotor.

Walk the PLANC: Physics-Guided RL for Agile Humanoid Locomotion on Constrained Footholds

Bipedal humanoid robots must precisely coordinate balance, timing, and contact decisions when locomoting on constrained footholds such as stepping stones, beams, and planks -- even minor errors can lead to catastrophic failure. Classical optimization and control pipelines handle these constraints well but depend on highly accurate mathematical representations of terrain geometry, making them prone to error when perception is noisy or incomplete. Meanwhile, reinforcement learning has shown strong resilience to disturbances and modeling errors, yet end-to-end policies rarely discover the precise foothold placement and step sequencing required for discontinuous terrain. These contrasting limitations motivate approaches that guide learning with physics-based structure rather than relying purely on reward shaping. In this work, we introduce a locomotion framework in which a reduced-order stepping planner supplies dynamically consistent motion targets that steer the RL training process via Control Lyapunov Function (CLF) rewards. This combination of structured footstep planning and data-driven adaptation produces accurate, agile, and hardware-validated stepping-stone locomotion on a humanoid robot, substantially improving reliability compared to conventional model-free reinforcement-learning baselines.

Distributionally Robust Imitation Learning: Layered Control Architecture for Certifiable Autonomy

Imitation learning (IL) enables autonomous behavior by learning from expert demonstrations. While more sample-efficient than comparative alternatives like reinforcement learning, IL is sensitive to compounding errors induced by distribution shifts. There are two significant sources of distribution shifts when using IL-based feedback laws on systems: distribution shifts caused by policy error and distribution shifts due to exogenous disturbances and endogenous model errors due to lack of learning. Our previously developed approaches, Taylor Series Imitation Learning (TaSIL) and $\mathcal{L}_1$ -Distributionally Robust Adaptive Control (\ellonedrac), address the challenge of distribution shifts in complementary ways. While TaSIL offers robustness against policy error-induced distribution shifts, \ellonedrac offers robustness against distribution shifts due to aleatoric and epistemic uncertainties. To enable certifiable IL for learned and/or uncertain dynamical systems, we formulate \textit{Distributionally Robust Imitation Policy (DRIP)} architecture, a Layered Control Architecture (LCA) that integrates TaSIL and~\ellonedrac. By judiciously designing individual layer-centric input and output requirements, we show how we can guarantee certificates for the entire control pipeline. Our solution paves the path for designing fully certifiable autonomy pipelines, by integrating learning-based components, such as perception, with certifiable model-based decision-making through the proposed LCA approach.

Risk-Aware Safety Filters with Poisson Safety Functions and Laplace Guidance Fields

Robotic systems navigating in real-world settings require a semantic understanding of their environment to properly determine safe actions. This work aims to develop the mathematical underpinnings of such a representation -- specifically, the goal is to develop safety filters that are risk-aware. To this end, we take a two step approach: encoding an understanding of the environment via Poisson's equation, and associated risk via Laplace guidance fields. That is, we first solve a Dirichlet problem for Poisson's equation to generate a safety function that encodes system safety as its 0-superlevel set. We then separately solve a Dirichlet problem for Laplace's equation to synthesize a safe \textit{guidance field} that encodes variable levels of caution around obstacles -- by enforcing a tunable flux boundary condition. The safety function and guidance fields are then combined to define a safety constraint and used to synthesize a risk-aware safety filter which, given a semantic understanding of an environment with associated risk levels of environmental features, guarantees safety while prioritizing avoidance of higher risk obstacles. We demonstrate this method in simulation and discuss how \textit{a priori} understandings of obstacle risk can be directly incorporated into the safety filter to generate safe behaviors that are risk-aware.

Hierarchical Reduced-Order Model Predictive Control for Robust Locomotion on Humanoid Robots

As humanoid robots enter real-world environments, ensuring robust locomotion across diverse environments is crucial. This paper presents a computationally efficient hierarchical control framework for humanoid robot locomotion based on reduced-order models -- enabling versatile step planning and incorporating arm and torso dynamics to better stabilize the walking. At the high level, we use the step-to-step dynamics of the ALIP model to simultaneously optimize over step periods, step lengths, and ankle torques via nonlinear MPC. The ALIP trajectories are used as references to a linear MPC framework that extends the standard SRB-MPC to also include simplified arm and torso dynamics. We validate the performance of our approach through simulation and hardware experiments on the Unitree G1 humanoid robot. In the proposed framework the high-level step planner runs at 40 Hz and the mid-level MPC at 500 Hz using the onboard mini-PC. Adaptive step timing increased the push recovery success rate by 36%, and the upper body control improved the yaw disturbance rejection. We also demonstrate robust locomotion across diverse indoor and outdoor terrains, including grass, stone pavement, and uneven gym mats.

Compatibility of Multiple Control Barrier Functions for Constrained Nonlinear Systems

Control barrier functions (CBFs) are a powerful tool for the constrained control of nonlinear systems; however, the majority of results in the literature focus on systems subject to a single CBF constraint, making it challenging to synthesize provably safe controllers that handle multiple state constraints. This paper presents a framework for constrained control of nonlinear systems subject to box constraints on the systems' vector-valued outputs using multiple CBFs. Our results illustrate that when the output has a vector relative degree, the CBF constraints encoding these box constraints are compatible, and the resulting optimization-based controller is locally Lipschitz continuous and admits a closed-form expression. Additional results are presented to characterize the degradation of nominal tracking objectives in the presence of safety constraints. Simulations of a planar quadrotor are presented to demonstrate the efficacy of the proposed framework.

Safe Navigation under State Uncertainty: Online Adaptation for Robust Control Barrier Functions

Measurements and state estimates are often imperfect in control practice, posing challenges for safety-critical applications, where safety guarantees rely on accurate state information. In the presence of estimation errors, several prior robust control barrier function (R-CBF) formulations have imposed strict conditions on the input. These methods can be overly conservative and can introduce issues such as infeasibility, high control effort, etc. This work proposes a systematic method to improve R-CBFs, and demonstrates its advantages on a tracked vehicle that navigates among multiple obstacles. A primary contribution is a new optimization-based online parameter adaptation scheme that reduces the conservativeness of existing R-CBFs. In order to reduce the complexity of the parameter optimization, we merge several safety constraints into one unified numerical CBF via Poisson's equation. We further address the dual relative degree issue that typically causes difficulty in vehicle tracking. Experimental trials demonstrate the overall performance improvement of our approach over existing formulations.