arXiv subjects

Ryan K. Cosner

Publications and source records attributed to Ryan K. Cosner.

At least 19 recordsLinked to original sources

arXiv2026

MARCH: Model-Assisted Reinforcement Learning for the Perceptive Control of Humanoids over Sparse Footholds

Perceptive bipedal locomotion over sparse terrain remains a difficult challenge: model-based methods are precise but brittle to uncertainty, while model-free methods are robust but struggle to discover the precise, constrained motions required for safety-critical locomotion where small errors can cause catastrophic failures. We propose a model-assisted reinforcement learning (RL) framework that combines both perspectives in three steps: (1) generate a safe reference trajectory using simplified models; (2) train a privileged teacher policy guided by a control Lyapunov function (CLF) reward built around the safe reference trajectory; and (3) distill the teacher into a vision-based student policy. We show that this model-assistance procedure produces physically grounded locomotion, improving sample efficiency, reducing the need for a complex learning curriculum, and achieving smoother locomotion behavior alongside stepping stone performance comparable to model-free baselines. We validate our approach in simulation and demonstrate successful deployment on a Unitree G1 humanoid robot navigating sparse footholds with lateral constraints.

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arXiv2026

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 safely navigate semantically rich, dynamic environments with context-dependent safety margins.

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arXiv2025

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.

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arXiv2025

Probabilistic Control Barrier Functions: Safety in Probability for Discrete-Time Stochastic Systems

Control systems operating in the real world face countless sources of unpredictable uncertainties. These random disturbances can render deterministic guarantees inapplicable and cause catastrophic safety failures. To overcome this, this paper proposes a method for designing safe controllers for discrete-time stochastic systems that retain probabilistic guarantees of safety. To do this we modify the traditional notion of a control barrier function (CBF) to explicitly account for these stochastic uncertainties and call these new modified functions probabilistic CBFs. We show that probabilistic CBFs can be used to design controllers that guarantee safety over a finite number of time steps with a prescribed probability. Next, by leveraging various uncertainty quantification methods, such as concentration inequalities and the scenario approach, we provide a variety of sufficient conditions that result in computationally tractable controllers with tunable probabilistic guarantees across a plethora of practical scenarios. Finally, we showcase the applicability of our results in simulation and hardware for the control of a quadruped robot.

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arXiv2025

Geometry-Aware Predictive Safety Filters on Humanoids: From Poisson Safety Functions to CBF Constrained MPC

Autonomous navigation through unstructured and dynamically-changing environments is a complex task that continues to present many challenges for modern roboticists. In particular, legged robots typically possess manipulable asymmetric geometries which must be considered during safety-critical trajectory planning. This work proposes a predictive safety filter: a nonlinear model predictive control (MPC) algorithm for online trajectory generation with geometry-aware safety constraints based on control barrier functions (CBFs). Critically, our method leverages Poisson safety functions to numerically synthesize CBF constraints directly from perception data. We extend the theoretical framework for Poisson safety functions to incorporate temporal changes in the domain by reformulating the static Dirichlet problem for Poisson's equation as a parameterized moving boundary value problem. Furthermore, we employ Minkowski set operations to lift the domain into a configuration space that accounts for robot geometry. Finally, we implement our real-time predictive safety filter on humanoid and quadruped robots in various safety-critical scenarios. The results highlight the versatility of Poisson safety functions, as well as the benefit of CBF constrained model predictive safety-critical controllers.

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arXiv2025

SHIELD: Safety on Humanoids via CBFs In Expectation on Learned Dynamics

Robot learning has produced remarkably effective ``black-box'' controllers for complex tasks such as dynamic locomotion on humanoids. Yet ensuring dynamic safety, i.e., constraint satisfaction, remains challenging for such policies. Reinforcement learning (RL) embeds constraints heuristically through reward engineering, and adding or modifying constraints requires retraining. Model-based approaches, like control barrier functions (CBFs), enable runtime constraint specification with formal guarantees but require accurate dynamics models. This paper presents SHIELD, a layered safety framework that bridges this gap by: (1) training a generative, stochastic dynamics residual model using real-world data from hardware rollouts of the nominal controller, capturing system behavior and uncertainties; and (2) adding a safety layer on top of the nominal (learned locomotion) controller that leverages this model via a stochastic discrete-time CBF formulation enforcing safety constraints in probability. The result is a minimally-invasive safety layer that can be added to the existing autonomy stack to give probabilistic guarantees of safety that balance risk and performance. In hardware experiments on an Unitree G1 humanoid, SHIELD enables safe navigation (obstacle avoidance) through varied indoor and outdoor environments using a nominal (unknown) RL controller and onboard perception.

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arXiv2025

Control Barrier Function Synthesis for Nonlinear Systems with Dual Relative Degree

Control barrier functions (CBFs) are a powerful tool for synthesizing safe control actions; however, constructing CBFs remains difficult for general nonlinear systems. In this work, we provide a constructive framework for synthesizing CBFs for systems with dual relative degree -- where different inputs influence the outputs at two different orders of differentiation; this is common in systems with orientation-based actuation, such as unicycles and quadrotors. In particular, we propose dual relative degree CBFs (DRD-CBFs) and show that these DRD-CBFs can be constructively synthesized and used to guarantee system safety. Our method constructs DRD-CBFs by leveraging the dual relative degree property -- combining a CBF for an integrator chain with a Lyapunov function certifying the tracking of safe inputs generated for this linear system. We apply these results to dual relative degree systems, both in simulation and experimentally on hardware using quadruped and quadrotor robotic platforms.

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arXiv2024

Constructive Safety-Critical Control: Synthesizing Control Barrier Functions for Partially Feedback Linearizable Systems

Certifying the safety of nonlinear systems, through the lens of set invariance and control barrier functions (CBFs), offers a powerful method for controller synthesis, provided a CBF can be constructed. This paper draws connections between partial feedback linearization and CBF synthesis. We illustrate that when a control affine system is input-output linearizable with respect to a smooth output function, then, under mild regularity conditions, one may extend any safety constraint defined on the output to a CBF for the full-order dynamics. These more general results are specialized to robotic systems where the conditions required to synthesize CBFs simplify. The CBFs constructed from our approach are applied and verified in simulation and hardware experiments on a quadrotor.

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arXiv2024

A Constructive Method for Designing Safe Multirate Controllers for Differentially-Flat Systems

We present a multi-rate control architecture that leverages fundamental properties of differential flatness to synthesize controllers for safety-critical nonlinear dynamical systems. We propose a two-layer architecture, where the high-level generates reference trajectories using a linear Model Predictive Controller, and the low-level tracks this reference using a feedback controller. The novelty lies in how we couple these layers, to achieve formal guarantees on recursive feasibility of the MPC problem, and safety of the nonlinear system. Furthermore, using differential flatness, we provide a constructive means to synthesize the multi-rate controller, thereby removing the need to search for suitable Lyapunov or barrier functions, or to approximately linearize/discretize nonlinear dynamics. We show the synthesized controller is a convex optimization problem, making it amenable to real-time implementations. The method is demonstrated experimentally on a ground rover and a quadruped robotic system.

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arXiv2024

Bounding Stochastic Safety: Leveraging Freedman's Inequality with Discrete-Time Control Barrier Functions

When deployed in the real world, safe control methods must be robust to unstructured uncertainties such as modeling error and external disturbances. Typical robust safety methods achieve their guarantees by always assuming that the worst-case disturbance will occur. In contrast, this paper utilizes Freedman's inequality in the context of discrete-time control barrier functions (DTCBFs) and c-martingales to provide stronger (less conservative) safety guarantees for stochastic systems. Our approach accounts for the underlying disturbance distribution instead of relying exclusively on its worst-case bound and does not require the barrier function to be upper-bounded, which makes the resulting safety probability bounds more directly useful for intuitive safety constraints such as signed distance. We compare our results with existing safety guarantees, such as input-to-state safety (ISSf) and martingale results that rely on Ville's inequality. When the assumptions for all methods hold, we provide a range of parameters for which our guarantee is stronger. Finally, we present simulation examples, including a bipedal walking robot, that demonstrate the utility and tightness of our safety guarantee.

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arXiv2023

Generative Modeling of Residuals for Real-Time Risk-Sensitive Safety with Discrete-Time Control Barrier Functions

A key source of brittleness for robotic systems is the presence of model uncertainty and external disturbances. Most existing approaches to robust control either seek to bound the worst-case disturbance (which results in conservative behavior), or to learn a deterministic dynamics model (which is unable to capture uncertain dynamics or disturbances). This work proposes a different approach: training a state-conditioned generative model to represent the distribution of error residuals between the nominal dynamics and the actual system. In particular we introduce the Online Risk-Informed Optimization controller (ORIO), which uses Discrete-Time Control Barrier Functions, combined with a learned, generative disturbance model, to ensure the safety of the system up to some level of risk. We demonstrate our approach in both simulations and hardware, and show our method can learn a disturbance model that is accurate enough to enable risk-sensitive control of a quadrotor flying aggressively with an unmodelled slung load. We use a conditional variational autoencoder (CVAE) to learn a state-conditioned dynamics residual distribution, and find that the resulting probabilistic safety controller, which can be run at 100Hz on an embedded computer, exhibits less conservative behavior while retaining theoretical safety properties.

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arXiv2023

Input-to-State Stability in Probability

Input-to-State Stability (ISS) is fundamental in mathematically quantifying how stability degrades in the presence of bounded disturbances. If a system is ISS, its trajectories will remain bounded, and will converge to a neighborhood of an equilibrium of the undisturbed system. This graceful degradation of stability in the presence of disturbances describes a variety of real-world control implementations. Despite its utility, this property requires the disturbance to be bounded and provides invariance and stability guarantees only with respect to this worst-case bound. In this work, we introduce the concept of ``ISS in probability (ISSp)'' which generalizes ISS to discrete-time systems subject to unbounded stochastic disturbances. Using tools from martingale theory, we provide Lyapunov conditions for a system to be exponentially ISSp, and connect ISSp to stochastic stability conditions found in literature. We exemplify the utility of this method through its application to a bipedal robot confronted with step heights sampled from a truncated Gaussian distribution.

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arXiv2023

Learning Responsibility Allocations for Safe Human-Robot Interaction with Applications to Autonomous Driving

Drivers have a responsibility to exercise reasonable care to avoid collision with other road users. This assumed responsibility allows interacting agents to maintain safety without explicit coordination. Thus to enable safe autonomous vehicle (AV) interactions, AVs must understand what their responsibilities are to maintain safety and how they affect the safety of nearby agents. In this work we seek to understand how responsibility is shared in multi-agent settings where an autonomous agent is interacting with human counterparts. We introduce Responsibility-Aware Control Barrier Functions (RA-CBFs) and present a method to learn responsibility allocations from data. By combining safety-critical control and learning-based techniques, RA-CBFs allow us to account for scene-dependent responsibility allocations and synthesize safe and efficient driving behaviors without making worst-case assumptions that typically result in overly-conservative behaviors. We test our framework using real-world driving data and demonstrate its efficacy as a tool for both safe control and forensic analysis of unsafe driving.

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arXiv2023

Robust Safety under Stochastic Uncertainty with Discrete-Time Control Barrier Functions

Robots deployed in unstructured, real-world environments operate under considerable uncertainty due to imperfect state estimates, model error, and disturbances. Given this real-world context, the goal of this paper is to develop controllers that are provably safe under uncertainties. To this end, we leverage Control Barrier Functions (CBFs) which guarantee that a robot remains in a ``safe set'' during its operation -- yet CBFs (and their associated guarantees) are traditionally studied in the context of continuous-time, deterministic systems with bounded uncertainties. In this work, we study the safety properties of discrete-time CBFs (DTCBFs) for systems with discrete-time dynamics and unbounded stochastic disturbances. Using tools from martingale theory, we develop probabilistic bounds for the safety (over a finite time horizon) of systems whose dynamics satisfy the discrete-time barrier function condition in expectation, and analyze the effect of Jensen's inequality on DTCBF-based controllers. Finally, we present several examples of our method synthesizing safe control inputs for systems subject to significant process noise, including an inverted pendulum, a double integrator, and a quadruped locomoting on a narrow path.

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arXiv2022

End-to-End Imitation Learning with Safety Guarantees using Control Barrier Functions

Imitation learning (IL) is a learning paradigm which can be used to synthesize controllers for complex systems that mimic behavior demonstrated by an expert (user or control algorithm). Despite their popularity, IL methods generally lack guarantees of safety, which limits their utility for complex safety-critical systems. In this work we consider safety, formulated as set-invariance, and the associated formal guarantees endowed by Control Barrier Functions (CBFs). We develop conditions under which robustly-safe expert controllers, utilizing CBFs, can be used to learn end-to-end controllers (which we refer to as CBF-Compliant controllers) that have safety guarantees. These guarantees are presented from the perspective of input-to-state safety (ISSf) which considers safety in the context of disturbances, wherein it is shown that IL using robustly safe expert demonstrations results in ISSf with the disturbance directly related to properties of the learning problem. We demonstrate these safety guarantees in simulated vision-based end-to-end control of an inverted pendulum and a car driving on a track.

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arXiv2022

Safety of Sampled-Data Systems with Control Barrier Functions via Approximate Discrete Time Models

Control Barrier Functions (CBFs) have been demonstrated to be a powerful tool for safety-critical controller design for nonlinear systems. Existing design paradigms do not address the gap between theory (controller design with continuous time models) and practice (the discrete time sampled implementation of the resulting controllers); this can lead to poor performance and violations of safety for hardware instantiations. We propose an approach to close this gap by synthesizing sampled-data counterparts to these CBF-based controllers using approximate discrete time models and Sampled-Data Control Barrier Functions (SD-CBFs). Using properties of a system's continuous time model, we establish a relationship between SD-CBFs and a notion of practical safety for sampled-data systems. Furthermore, we construct convex optimization-based controllers that formally endow nonlinear systems with safety guarantees in practice. We demonstrate the efficacy of these controllers in simulation.

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arXiv2022

Safety-Aware Preference-Based Learning for Safety-Critical Control

Bringing dynamic robots into the wild requires a tenuous balance between performance and safety. Yet controllers designed to provide robust safety guarantees often result in conservative behavior, and tuning these controllers to find the ideal trade-off between performance and safety typically requires domain expertise or a carefully constructed reward function. This work presents a design paradigm for systematically achieving behaviors that balance performance and robust safety by integrating safety-aware Preference-Based Learning (PBL) with Control Barrier Functions (CBFs). Fusing these concepts -- safety-aware learning and safety-critical control -- gives a robust means to achieve safe behaviors on complex robotic systems in practice. We demonstrate the capability of this design paradigm to achieve safe and performant perception-based autonomous operation of a quadrupedal robot both in simulation and experimentally on hardware.

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arXiv2022

Self-Supervised Online Learning for Safety-Critical Control using Stereo Vision

With the increasing prevalence of complex vision-based sensing methods for use in obstacle identification and state estimation, characterizing environment-dependent measurement errors has become a difficult and essential part of modern robotics. This paper presents a self-supervised learning approach to safety-critical control. In particular, the uncertainty associated with stereo vision is estimated, and adapted online to new visual environments, wherein this estimate is leveraged in a safety-critical controller in a robust fashion. To this end, we propose an algorithm that exploits the structure of stereo-vision to learn an uncertainty estimate without the need for ground-truth data. We then robustify existing Control Barrier Function-based controllers to provide safety in the presence of this uncertainty estimate. We demonstrate the efficacy of our method on a quadrupedal robot in a variety of environments. When not using our method safety is violated. With offline training alone we observe the robot is safe, but overly-conservative. With our online method the quadruped remains safe and conservatism is reduced.

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