arXiv subjects

Aaron D. Ames

Publications and source records attributed to Aaron D. Ames.

At least 73 records · Page 4Linked to original sources

arXiv2026

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.

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arXiv2025

CLF-RL: Control Lyapunov Function Guided Reinforcement Learning

Reinforcement learning (RL) has shown promise in generating robust locomotion policies for bipedal robots, but often suffers from tedious reward design and sensitivity to poorly shaped objectives. In this work, we propose a structured reward shaping framework that leverages model-based trajectory generation and control Lyapunov functions (CLFs) to guide policy learning. We explore two model-based planners for generating reference trajectories: a reduced-order linear inverted pendulum (LIP) model for velocity-conditioned motion planning, and a precomputed gait library based on hybrid zero dynamics (HZD) using full-order dynamics. These planners define desired end-effector and joint trajectories, which are used to construct CLF-based rewards that penalize tracking error and encourage rapid convergence. This formulation provides meaningful intermediate rewards, and is straightforward to implement once a reference is available. Both the reference trajectories and CLF shaping are used only during training, resulting in a lightweight policy at deployment. We validate our method both in simulation and through extensive real-world experiments on a Unitree G1 robot. CLF-RL demonstrates significantly improved robustness relative to the baseline RL policy and better performance than a classic tracking reward RL formulation.

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arXiv2025

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.

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arXiv2025

Combinatorial Control Barrier Functions: Nested Boolean and p-choose-r Compositions of Safety Constraints

This paper investigates the problem of composing multiple control barrier functions (CBFs) -- and matrix control barrier functions (MCBFs) -- through logical and combinatorial operations. Standard CBF formulations naturally enable conjunctive (AND) combinations, but disjunctive (OR) and more general logical structures introduce nonsmoothness and possibly a combinatorial blow-up in the number of logical combinations. We introduce the framework of combinatorial CBFs that addresses p-choose-r safety specifications and their nested composition. The proposed framework ensures safety for the exact safe set in a scalable way, using the original number of primitive constraints. We establish theoretical guarantees on safety under these compositions, and we demonstrate their use on a patrolling problem in a multi-agent system.

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arXiv2025

KALIKO: Kalman-Implicit Koopman Operator Learning For Prediction of Nonlinear Dynamical Systems

Long-horizon dynamical prediction is fundamental in robotics and control, underpinning canonical methods like model predictive control. Yet, many systems and disturbance phenomena are difficult to model due to effects like nonlinearity, chaos, and high-dimensionality. Koopman theory addresses this by modeling the linear evolution of embeddings of the state under an infinite-dimensional linear operator that can be approximated with a suitable finite basis of embedding functions, effectively trading model nonlinearity for representational complexity. However, explicitly computing a good choice of basis is nontrivial, and poor choices may cause inaccurate forecasts or overfitting. To address this, we present Kalman-Implicit Koopman Operator (KALIKO) Learning, a method that leverages the Kalman filter to implicitly learn embeddings corresponding to latent dynamics without requiring an explicit encoder. KALIKO produces interpretable representations consistent with both theory and prior works, yielding high-quality reconstructions and inducing a globally linear latent dynamics. Evaluated on wave data generated by a high-dimensional PDE, KALIKO surpasses several baselines in open-loop prediction and in a demanding closed-loop simulated control task: stabilizing an underactuated manipulator's payload by predicting and compensating for strong wave disturbances.

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arXiv2025

Robust Adaptive Safe Robotic Grasping with Tactile Sensing

Robotic grasping requires safe force interaction to prevent a grasped object from being damaged or slipping out of the hand. In this vein, this paper proposes an integrated framework for grasping with formal safety guarantees based on Control Barrier Functions. We first design contact force and force closure constraints, which are enforced by a safety filter to accomplish safe grasping with finger force control. For sensory feedback, we develop a technique to estimate contact point, force, and torque from tactile sensors at each finger. We verify the framework with various safety filters in a numerical simulation under a two-finger grasping scenario. We then experimentally validate the framework by grasping multiple objects, including fragile lab glassware, in a real robotic setup, showing that safe grasping can be successfully achieved in the real world. We evaluate the performance of each safety filter in the context of safety violation and conservatism, and find that disturbance observer-based control barrier functions provide superior performance for safety guarantees with minimum conservatism.

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arXiv2025

Minimizing Conservatism in Safety-Critical Control for Input-Delayed Systems via Adaptive Delay Estimation

Input delays affect systems such as teleoperation and wirelessly autonomous connected vehicles, and may lead to safety violations. One promising way to ensure safety in the presence of delay is to employ control barrier functions (CBFs), and extensions thereof that account for uncertainty: delay adaptive CBFs (DaCBFs). This paper proposes an online adaptive safety control framework for reducing the conservatism of DaCBFs. The main idea is to reduce the maximum delay estimation error bound so that the state prediction error bound is monotonically non-increasing. To this end, we first leverage the estimation error bound of a disturbance observer to bound the state prediction error. Second, we design two nonlinear programs to update the maximum delay estimation error bound satisfying the prediction error bound, and subsequently update the maximum state prediction error bound used in DaCBFs. The proposed method ensures the maximum state prediction error bound is monotonically non-increasing, yielding less conservatism in DaCBFs. We verify the proposed method in an automated connected truck application, showing that the proposed method reduces the conservatism of DaCBFs.

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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

From Bundles to Backstepping: Geometric Control Barrier Functions for Safety-Critical Control on Manifolds

Control barrier functions (CBFs) have a well-established theory in Euclidean spaces, yet still lack general formulations and constructive synthesis tools for systems evolving on manifolds common in robotics and aerospace applications. In this paper, we develop a general theory of geometric CBFs on bundles and, for control-affine systems, recover the standard optimization-based CBF controllers and their smooth analogues. Then, by generalizing kinetic energy-based CBF backstepping to Riemannian manifolds, we provide a constructive CBF synthesis technique for geometric mechanical systems, as well as easily verifiable conditions under which it succeeds. Further, this technique utilizes mechanical structure to avoid computations on higher-order tangent bundles. We demonstrate its application to an underactuated satellite on SO(3).

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arXiv2025

Architecture Is All You Need: Diversity-Enabled Sweet Spots for Robust Humanoid Locomotion

Robust humanoid locomotion in unstructured environments requires architectures that balance fast low-level stabilization with slower perceptual decision-making. We show that a simple layered control architecture (LCA), a proprioceptive stabilizer running at high rate, coupled with a compact low-rate perceptual policy, enables substantially more robust performance than monolithic end-to-end designs, even when using minimal perception encoders. Through a two-stage training curriculum (blind stabilizer pretraining followed by perceptual fine-tuning), we demonstrate that layered policies consistently outperform one-stage alternatives in both simulation and hardware. On a Unitree G1 humanoid, our approach succeeds across stair and ledge tasks where one-stage perceptual policies fail. These results highlight that architectural separation of timescales, rather than network scale or complexity, is the key enabler for robust perception-conditioned locomotion.

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arXiv2025

Safety-Critical Control with Bounded Inputs: A Closed-Form Solution for Backup Control Barrier Functions

Verifying the safety of controllers is critical for many applications, but is especially challenging for systems with bounded inputs. Backup control barrier functions (bCBFs) offer a structured approach to synthesizing safe controllers that are guaranteed to satisfy input bounds by leveraging the knowledge of a backup controller. While powerful, bCBFs require solving a high-dimensional quadratic program at run-time, which may be too costly for computationally-constrained systems such as aerospace vehicles. We propose an approach that optimally interpolates between a nominal controller and the backup controller, and we derive the solution to this optimization problem in closed form. We prove that this closed-form controller is guaranteed to be safe while obeying input bounds. We demonstrate the effectiveness of the approach on a double integrator and a nonlinear fixed-wing aircraft example.

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arXiv2025

RoMoCo: Robotic Motion Control Toolbox for Reduced-Order Model-Based Locomotion on Bipedal and Humanoid Robots

We present RoMoCo, an open-source C++ toolbox for the synthesis and evaluation of reduced-order model-based planners and whole-body controllers for bipedal and humanoid robots. RoMoCo's modular architecture unifies state-of-the-art planners and whole-body locomotion controllers under a consistent API, enabling rapid prototyping and reproducible benchmarking. By leveraging reduced-order models for platform-agnostic gait generation, RoMoCo enables flexible controller design across diverse robots. We demonstrate its versatility and performance through extensive simulations on the Cassie, Unitree H1, and G1 robots, and validate its real-world efficacy with hardware experiments on the Cassie and G1 humanoids.

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arXiv2025

Chasing Stability: Humanoid Running via Control Lyapunov Function Guided Reinforcement Learning

Achieving highly dynamic behaviors on humanoid robots, such as running, requires controllers that are both robust and precise, and hence difficult to design. Classical control methods offer valuable insight into how such systems can stabilize themselves, but synthesizing real-time controllers for nonlinear and hybrid dynamics remains challenging. Recently, reinforcement learning (RL) has gained popularity for locomotion control due to its ability to handle these complex dynamics. In this work, we embed ideas from nonlinear control theory, specifically control Lyapunov functions (CLFs), along with optimized dynamic reference trajectories into the reinforcement learning training process to shape the reward. This approach, CLF-RL, eliminates the need to handcraft and tune heuristic reward terms, while simultaneously encouraging certifiable stability and providing meaningful intermediate rewards to guide learning. By grounding policy learning in dynamically feasible trajectories, we expand the robot's dynamic capabilities and enable running that includes both flight and single support phases. The resulting policy operates reliably on a treadmill and in outdoor environments, demonstrating robustness to disturbances applied to the torso and feet. Moreover, it achieves accurate global reference tracking utilizing only on-board sensors, making a critical step toward integrating these dynamic motions into a full autonomy stack.

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arXiv2025

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.

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arXiv2025

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.

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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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arXiv2025

A Layered Control Perspective on Legged Locomotion: Embedding Reduced Order Models via Hybrid Zero Dynamics

Reduced-order models (ROMs) provide a powerful means of synthesizing dynamic walking gaits on legged robots. Yet this approach lacks the formal guarantees enjoyed by methods that utilize the full-order model (FOM) for gait synthesis, e.g., hybrid zero dynamics. This paper aims to unify these approaches through a layered control perspective. In particular, we establish conditions on when a ROM of locomotion yields stable walking on the full-order hybrid dynamics. To achieve this result, given an ROM we synthesize a zero dynamics manifold encoding the behavior of the ROM -- controllers can be synthesized that drive the FOM to this surface, yielding hybrid zero dynamics. We prove that a stable periodic orbit in the ROM implies an input-to-state stable periodic orbit of the FOM's hybrid zero dynamics, and hence the FOM dynamics. This result is demonstrated in simulation on a linear inverted pendulum ROM and a 5-link planar walking FOM.

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arXiv2025

Matrix Control Barrier Functions

This paper generalizes the control barrier function framework by replacing scalar-valued functions with matrix-valued ones. Specifically, we develop barrier conditions for safe sets defined by matrix inequalities -- both semidefinite and indefinite. Matrix inequalities can be used to describe a richer class of safe sets, including nonsmooth ones. The safety filters constructed from our proposed matrix control barrier functions via semidefinite programming (CBF-SDP) are shown to be continuous. Our matrix formulation naturally provides a continuous safety filter for Boolean-based control barrier functions, notably for disjunctions (OR), without relaxing the safe set. We illustrate the effectiveness of the proposed framework with applications in drone network connectivity maintenance and nonsmooth obstacle avoidance, both in simulations and hardware experiments.

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