arXiv subjects

Zachary Olkin

Publications and source records attributed to Zachary Olkin.

8 recordsLinked to original sources

arXiv2026

Terrain Consistent Reference-Guided RL for Humanoid Navigation Autonomy

We present a method for training reference-guided, perceptive reinforcement learning locomotion policies for humanoid robots in which reference trajectories are modulated in training to be consistent with terrain geometry. Aiming to deploy our method with standard navigation autonomy infrastructure, we synthesize SE(2)-controllable reference trajectories inside the RL training loop, projecting desired footsteps onto valid footholds and adjusting swing-foot and center-of-mass trajectories to match the terrain. The resulting policy exposes a clean SE(2) velocity interface compatible with standard navigation planners. In simulation, environmentally-conditioned references significantly improve reference tracking performance compared to environment agnostic references. On hardware, we integrate the policy with an MPC + control barrier function planner and demonstrate long-horizon (>70m) closed-loop autonomous navigation on the Unitree G1 through outdoor environments containing rough terrain and consecutive flights of stairs, with all sensing and computation onboard.

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arXiv2026

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.

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arXiv2026

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.

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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

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

Locomotion on Constrained Footholds via Layered Architectures and Model Predictive Control

Computing stabilizing and optimal control actions for legged locomotion in real time is difficult due to the nonlinear, hybrid, and high dimensional nature of these robots. The hybrid nature of the system introduces a combination of discrete and continuous variables which causes issues for numerical optimal control. To address these challenges, we propose a layered architecture that separates the choice of discrete variables and a smooth Model Predictive Controller (MPC). The layered formulation allows for online flexibility and optimality without sacrificing real-time performance through a combination of gradient-free and gradient-based methods. The architecture leverages a sampling-based method for determining discrete variables, and a classical smooth MPC formulation using these fixed discrete variables. We demonstrate the results on a quadrupedal robot stepping over gaps and onto terrain with varying heights. In simulation, we demonstrate the controller on a humanoid robot for gap traversal. The layered approach is shown to be more optimal and reliable than common heuristic-based approaches and faster to compute than pure sampling methods.

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arXiv2025

Layered Nonlinear Model Predictive Control for Robust Stabilization of Hybrid Systems

Computing the receding horizon optimal control of nonlinear hybrid systems is typically prohibitively slow, limiting real-time implementation. To address this challenge, we propose a layered Model Predictive Control (MPC) architecture for robust stabilization of hybrid systems. A high level "hybrid" MPC is solved at a slow rate to produce a stabilizing hybrid trajectory, potentially sub-optimally, including a domain and guard sequence. This domain and guard sequence is passed to a low level "fixed mode" MPC which is a traditional, time-varying, state-constrained MPC that can be solved rapidly, e.g., using nonlinear programming (NLP) tools. A robust version of the fixed mode MPC is constructed by using tracking error tubes that are not guaranteed to have finite size for all time. Using these tubes, we demonstrate that the speed at which the fixed mode MPC is re-calculated is directly tied to the robustness of the system, thereby justifying the layered approach. Finally, simulation examples of a five link bipedal robot and a controlled nonlinear bouncing ball are used to illustrate the formal results.

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arXiv2024

Bilevel Optimization for Real-Time Control with Application to Locomotion Gait Generation

Model Predictive Control (MPC) is a common tool for the control of nonlinear, real-world systems, such as legged robots. However, solving MPC quickly enough to enable its use in real-time is often challenging. One common solution is given by real-time iterations, which does not solve the MPC problem to convergence, but rather close enough to give an approximate solution. In this paper, we extend this idea to a bilevel control framework where a "high-level" optimization program modifies a controller parameter of a "low-level" MPC problem which generates the control inputs and desired state trajectory. We propose an algorithm to iterate on this bilevel program in real-time and provide conditions for its convergence and improvements in stability. We then demonstrate the efficacy of this algorithm by applying it to a quadrupedal robot where the high-level problem optimizes a contact schedule in real-time. We show through simulation that the algorithm can yield improvements in disturbance rejection and optimality, while creating qualitatively new gaits.

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