arXiv subjects

Zhenyu Gan

Publications and source records attributed to Zhenyu Gan.

15 recordsLinked to original sources

arXiv2026

Closing the Loop on the Poppy Humanoid: Bipedal Locomotion with Linear-Quadratic Control and Learned Cost Functions

The Poppy Humanoid is an open-source, low-cost robot suitable for research and education in artificial intelligence. However, we are unaware of any published methodology that achieves reliable, unassisted bipedal locomotion on the standard Poppy hardware. This paper contributes a functional closed-loop walking controller for Poppy, based on the linear-quadratic regulator (LQR) framework for trajectory tracking. Starting with data collected from open-loop playback of a nominal walking trajectory, our proposed method learns a quadratic cost function for an LQR controller that substantially improves the reliability of the motion. The closed-loop controller is validated empirically, demonstrating statistically significant improvements in walking performance compared to open-loop trajectory playback.

cs.RO↗

arXiv2025

Beyond Topology: A Morphological Symmetry Graph Representation for Locomotion Policy Learning

Reinforcement learning has enabled impressive locomotion skills on articulated robots, but common policy representations remain only weakly aligned with robot physics. Generic networks ignore kinematic structure, while graph-based policies encode connectivity without specifying how physical quantities transform across symmetric body parts. We introduce a morphological symmetry graph representation for locomotion policy learning and instantiate it in MS-PPO. Starting from the robot's topological graph, our representation augments each observation and action space with the permutation and sign transformations induced by morphological symmetry. This yields a symmetry-equivariant graph actor and a symmetry-invariant graph critic, enforcing the desired policy and value constraints by construction rather than through reward shaping or data augmentation. We evaluate MS-PPO on a variety of locomotion tasks using both Unitree Go2 quadruped and Unitree G1 humanoid, including command tracking, asymmetric joint failures, out-of-distribution command generalization, and zero-shot sim-to-real deployment. Experiments show improved symmetry generalization, robustness, sample efficiency, and model efficiency over topology- and symmetry-aware baselines.

cs.RO↗

arXiv2025

Towards Dynamic Quadrupedal Gaits: A Symmetry-Guided RL Hierarchy Enables Free Gait Transitions at Varying Speeds

Quadrupedal robots exhibit a wide range of viable gaits, but generating specific footfall sequences often requires laborious expert tuning of numerous variables, such as touch-down and lift-off events and holonomic constraints for each leg. This paper presents a unified reinforcement learning framework for generating versatile quadrupedal gaits by leveraging the intrinsic symmetries and velocity-period relationship of dynamic legged systems. We propose a symmetry-guided reward function design that incorporates temporal, morphological, and time-reversal symmetries. By focusing on preserved symmetries and natural dynamics, our approach eliminates the need for predefined trajectories, enabling smooth transitions between diverse locomotion patterns such as trotting, bounding, half-bounding, and galloping. Implemented on the Unitree Go2 robot, our method demonstrates robust performance across a range of speeds in both simulations and hardware tests, significantly improving gait adaptability without extensive reward tuning or explicit foot placement control. This work provides insights into dynamic locomotion strategies and underscores the crucial role of symmetries in robotic gait design.

cs.RO↗

arXiv2025

Transformable Modular Robots: A CPG-Based Approach to Independent and Collective Locomotion

Modular robotics enables the development of versatile and adaptive robotic systems with autonomous reconfiguration. This paper presents a modular robotic system in which each module has independent actuation, battery power, and control, allowing both individual mobility and coordinated locomotion. A hierarchical Central Pattern Generator (CPG) framework governs motion, with a low-level CPG controlling individual modules and a high-level CPG synchronizing inter-module coordination, enabling smooth transitions between independent and collective behaviors. To validate the system, we conduct simulations in MuJoCo and hardware experiments, evaluating locomotion across different configurations. We first analyze single-module motion, followed by two-module cooperative locomotion. Results demonstrate the effectiveness of the CPG-based control framework in achieving robust, flexible, and scalable locomotion. The proposed modular architecture has potential applications in search and rescue, environmental monitoring, and autonomous exploration, where adaptability and reconfigurability are essential.

cs.RO↗

arXiv2025

Gait Transitions in Load-Pulling Quadrupeds: Insights from Sled Dogs and a Minimal SLIP Model

Quadrupedal animals employ diverse galloping strategies to optimize speed, stability, and energy efficiency. However, the biomechanical mechanisms that enable adaptive gait transitions during high-speed locomotion under load remain poorly understood. In this study, we present new empirical and modeling insights into the biomechanics of load-pulling quadrupeds, using sprint sled dogs as a model system. High-speed video and force recordings reveal that sled dogs often switch between rotary and transverse galloping gaits within just a few strides and without any observable changes in speed, stride duration, or terrain, providing clear evidence of locomotor multistability during high-speed load-pulling. To investigate the mechanical basis of these transitions, a physics-based quadrupedal Spring-Loaded Inverted Pendulum model with hybrid dynamics and prescribed footfall sequences to reproduce the asymmetric galloping patterns observed in racing sled dogs. Through trajectory optimization, we replicate experimentally observed gait sequences and identify swing-leg stiffness modulation as a key control mechanism for inducing transitions. This work provides a much-needed biomechanical perspective on high-speed animal draft and establishes a modeling framework for studying locomotion in pulling quadrupeds, with implications for both biological understanding and the design of adaptive legged systems.

eess.SY↗

arXiv2025

Iteratively Learning Muscle Memory for Legged Robots to Master Adaptive and High Precision Locomotion

This paper presents a scalable and adaptive control framework for legged robots that integrates Iterative Learning Control (ILC) with a biologically inspired torque library (TL), analogous to muscle memory. The proposed method addresses key challenges in robotic locomotion, including accurate trajectory tracking under unmodeled dynamics and external disturbances. By leveraging the repetitive nature of periodic gaits and extending ILC to nonperiodic tasks, the framework enhances accuracy and generalization across diverse locomotion scenarios. The control architecture is data-enabled, combining a physics-based model derived from hybrid-system trajectory optimization with real-time learning to compensate for model uncertainties and external disturbances. A central contribution is the development of a generalized TL that stores learned control profiles and enables rapid adaptation to changes in speed, terrain, and gravitational conditions-eliminating the need for repeated learning and significantly reducing online computation. The approach is validated on the bipedal robot Cassie and the quadrupedal robot A1 through extensive simulations and hardware experiments. Results demonstrate that the proposed framework reduces joint tracking errors by up to 85% within a few seconds and enables reliable execution of both periodic and nonperiodic gaits, including slope traversal and terrain adaptation. Compared to state-of-the-art whole-body controllers, the learned skills eliminate the need for online computation during execution and achieve control update rates exceeding 30x those of existing methods. These findings highlight the effectiveness of integrating ILC with torque memory as a highly data-efficient and practical solution for legged locomotion in unstructured and dynamic environments.

cs.RO↗

arXiv2025

Refining Motion for Peak Performance: Identifying Optimal Gait Parameters for Energy-Efficient Quadrupedal Bounding

Energy efficiency is a critical factor in the performance and autonomy of quadrupedal robots. While previous research has focused on mechanical design and actuation improvements, the impact of gait parameters on energetics has been less explored. In this paper, we hypothesize that gait parameters, specifically duty factor, phase shift, and stride duration, are key determinants of energy consumption in quadrupedal locomotion. To test this hypothesis, we modeled the Unitree A1 quadrupedal robot and developed a locomotion controller capable of independently adjusting these gait parameters. Simulations of bounding gaits were conducted in Gazebo across a range of gait parameters at three different speeds: low, medium, and high. Experimental tests were also performed to validate the simulation results. The findings demonstrate that optimizing gait parameters can lead to significant reductions in energy consumption, enhancing the overall efficiency of quadrupedal locomotion. This work contributes to the advancement of energy-efficient control strategies for legged robots, offering insights directly applicable to commercially available platforms.

cs.RO↗

arXiv2025

16 Ways to Gallop: Energetics and Body Dynamics of High-Speed Quadrupedal Gaits

Galloping is a common high-speed gait in both animals and quadrupedal robots, yet its energetic characteristics remain insufficiently explored. This study systematically analyzes a large number of possible galloping gaits by categorizing them based on the number of flight phases per stride and the phase relationships between the front and rear legs, following Hildebrand's framework for asymmetrical gaits. Using the A1 quadrupedal robot from Unitree, we model galloping dynamics as a hybrid dynamical system and employ trajectory optimization (TO) to minimize the cost of transport (CoT) across a range of speeds. Our results reveal that rotary and transverse gallop footfall sequences exhibit no fundamental energetic difference, despite variations in body yaw and roll motion. However, the number of flight phases significantly impacts energy efficiency: galloping with no flight phases is optimal at lower speeds, whereas galloping with two flight phases minimizes energy consumption at higher speeds. We validate these findings using a quadratic programming (QP)-based controller, developed in our previous work, in Gazebo simulations. These insights advance the understanding of quadrupedal locomotion energetics and may inform future legged robot designs for adaptive, energy-efficient gait transitions.

cs.RO↗

arXiv2024

Harnessing Natural Oscillations for High-Speed, Efficient Asymmetrical Locomotion in Quadrupedal Robots

This study explores the dynamics of asymmetrical bounding gaits in quadrupedal robots, focusing on the integration of torso pitching and hip motion to enhance speed and stability. Traditional control strategies often enforce a fixed posture, minimizing natural body movements to simplify the control problem. However, this approach may overlook the inherent dynamical advantages found in natural locomotion. By considering the robot as two interconnected segments, we concentrate on stance leg motion while allowing passive torso oscillation, drawing inspiration from natural dynamics and underactuated robotics principles. Our control scheme employs Linear Inverted Pendulum (LIP) and Spring-Loaded Inverted Pendulum (SLIP) models to govern front and rear leg movements independently. This approach has been validated through extensive simulations and hardware experiments, demonstrating successful high-speed locomotion with top speeds nearing 4 m/s and reduced ground reaction forces, indicating a more efficient gait. Furthermore, unlike conventional methods, our strategy leverages natural torso oscillations to aid leg circulation and stride length, aligning robot dynamics more closely with biological counterparts. Our findings suggest that embracing the natural dynamics of quadrupedal movement, particularly in asymmetrical gaits like bounding, can lead to more stable, efficient, and high-speed robotic locomotion. This investigation lays the groundwork for future studies on versatile and dynamic quadrupedal gaits and their potential applications in scenarios demanding rapid and effective locomotion.

cs.RO↗

arXiv2024

Lipschitz-Regularized Critics Lead to Policy Robustness Against Transition Dynamics Uncertainty

Uncertainties in transition dynamics pose a critical challenge in reinforcement learning (RL), often resulting in performance degradation of trained policies when deployed on hardware. Many robust RL approaches follow two strategies: enforcing smoothness in actor or actor-critic modules with Lipschitz regularization, or learning robust Bellman operators. However, the first strategy does not investigate the impact of critic-only Lipschitz regularization on policy robustness, while the second lacks comprehensive validation in real-world scenarios. Building on this gap and prior work, we propose PPO-PGDLC, an algorithm based on Proximal Policy Optimization (PPO) that integrates Projected Gradient Descent (PGD) with a Lipschitz-regularized critic (LC). The PGD component calculates the adversarial state within an uncertainty set to approximate the robust Bellman operator, and the Lipschitz-regularized critic further improves the smoothness of learned policies. Experimental results on two classic control tasks and one real-world robotic locomotion task demonstrate that, compared to several baseline algorithms, PPO-PGDLC achieves better performance and predicts smoother actions under environmental perturbations.

cs.LG↗

arXiv2024

Breaking Symmetries Leads to Diverse Quadrupedal Gaits

Symmetry manifests itself in legged locomotion in a variety of ways. No matter where a legged system begins to move periodically, the torso and limbs coordinate with each other's movements in a similar manner. Also, in many gaits observed in nature, the legs on both sides of the torso move in exactly the same way, sometimes they are just half a period out of phase. Furthermore, when some animals move forward and backward, their movements are strikingly similar as if the time had been reversed. This work aims to generalize these phenomena and propose formal definitions of symmetries in legged locomotion using group theory terminology. Symmetries in some common quadrupedal gaits such as pronking, bounding, half-bounding, and galloping have been discussed. Moreover, a spring-mass model has been used to demonstrate how breaking symmetries can alter gaits in a legged system. Studying the symmetries may provide insight into which gaits may be suitable for a particular robotic design, or may enable roboticists to design more agile and efficient robot controllers by using certain gaits.

cs.RO↗

arXiv2024

Towards Dynamic Quadrupedal Gaits: A Symmetry-Guided RL Hierarchy Enables Free Gait Transitions at Varying Speeds

eess.SY↗

arXiv2023

Energetic Analysis on the Optimal Bounding Gaits of Quadrupedal Robots

It is often overlooked by roboticists when designing locomotion controllers for their legged machines, that energy consumption plays an important role in selecting the best gaits for locomotion at high speeds or over long distances. The purpose of this study is to examine four similar asymmetrical quadrupedal gaits that are frequently observed in legged animals in nature. To understand how a specific footfall pattern will change the energetics of a legged system, we first developed a full body model of a quadrupedal robot called A1. And for each gait we created a hybrid system with desired footfall sequence and rigid impacts. In order to find the most energy efficient gait, we used optimal control methods to formulate the problem as a trajectory optimization problem with proper constraints and objective function. This problem was implemented and solved in a nonlinear programming framework called FROST. Based on the optimized trajectories for each gait, we investigated the values of cost of transport and the work done by all joints. Moreover, we analyzed the exchange of angular momentum in different components of the system during the whole stride cycle. According to the simulation results, bounding with two flight phases is likely to be the most energy efficient gait for A1 across a wide range of speed.

cs.RO↗

arXiv2022

Practice Makes Perfect: an iterative approach to achieve precise tracking for legged robots

Precise trajectory tracking for legged robots can be challenging due to their high degrees of freedom, unmodeled nonlinear dynamics, or random disturbances from the environment. A commonly adopted solution to overcome these challenges is to use optimization-based algorithms and approximate the system with a simplified, reduced-order model. Additionally, deep neural networks are becoming a more promising option for achieving agile and robust legged locomotion. These approaches, however, either require large amounts of onboard calculations or the collection of millions of data points from a single robot. To address these problems and improve tracking performance, this paper proposes a method based on iterative learning control. This method lets a robot learn from its own mistakes by exploiting the repetitive nature of legged locomotion within only a few trials. Then, a torque library is created as a lookup table so that the robot does not need to repeat calculations or learn the same skill over and over again. This process resembles how animals learn their muscle memories in nature. The proposed method is tested on the A1 robot in a simulated environment, and it allows the robot to pronk at different speeds while precisely following the reference trajectories without heavy calculations.

cs.RO↗

arXiv2019

Leveraging the Template and Anchor Framework for Safe, Online Robotic Gait Design

Online control design using a high-fidelity, full-order model for a bipedal robot can be challenging due to the size of the state space of the model. A commonly adopted solution to overcome this challenge is to approximate the full-order model (anchor) with a simplified, reduced-order model (template), while performing control synthesis. Unfortunately it is challenging to make formal guarantees about the safety of an anchor model using a controller designed in an online fashion using a template model. To address this problem, this paper proposes a method to generate safety-preserving controllers for anchor models by performing reachability analysis on template models while bounding the modeling error. This paper describes how this reachable set can be incorporated into a Model Predictive Control framework to select controllers that result in safe walking on the anchor model in an online fashion. The method is illustrated on a 5-link RABBIT model, and is shown to allow the robot to walk safely while utilizing controllers designed in an online fashion.

cs.RO↗