Legged Robotics

Quadruped mammals coordinate sagittal spinal bending with axial extension and compression during dynamic locomotion. Yet most robotic quadrupeds use rigid trunks, passively compliant spines with fixed properties, or actively controlled spines that track prescribed trajectories. Whether actively regulated spinal compliance can support faster dynamic locomotion remains unclear. We present SPARC, a compact 1.26-kg, 3-DoF sagittal-plane spine that combines revolute and prismatic motion with independently tunable task-space stiffness and damping. A floating-base impedance controller renders the desired task-space compliance, and benchtop tests show that the fitted axial stiffness matches commanded values within 1.5%. We integrate SPARC into an 8-DoF quadruped and evaluate it across 97 bounding trials under three spine configurations: impedance-controlled SPARC, the same SPARC module held near a fixed pose using position control, and a lightweight rigid spine. Impedance-controlled SPARC reaches 1.029 m/s, compared with 0.769 m/s for position-controlled SPARC and 0.673 m/s for the rigid spine. Impedance-controlled SPARC reaches higher speeds with larger axial motion and greater mechanical power exchange, while at matched speed it has a higher electrical cost of transport than the rigid spine, revealing an energetic trade-off. Code and hardware are available at: https://github.com/YueWang996/sparc

Most modern approaches to quadruped locomotion focus on using Deep Reinforcement Learning (DRL) to learn policies from scratch, in an end-to-end manner. Such methods often fail to scale, as every new problem or application requires time-consuming and iterative reward definition and tuning. We present Generalist Contact-Conditioned Policy (GeCCo) --- a low-level policy trained with Deep Reinforcement Learning that is capable of tracking arbitrary contact points with a quadruped robot. We shift from task-specific end-to-end learning to a modular hierarchy in which a single planner-agnostic, contact-conditioned tracking policy serves as a robust interface between planning and control. By maintaining stable contact execution under dynamic uncertainty and planner mismatch, the policy enables high-level planners (e.g., handcrafted, learned, or optimization-based) to be composed and swapped without retraining. We demonstrate the scalability and robustness of our method by evaluating on a wide range of locomotion and manipulation tasks in a common framework and under a single generalist policy. These include a variety of gaits, traversing complex terrains (e.g., stairs and slopes) as well as previously unseen stepping-stones and narrow beams, and interacting with objects (e.g., pressing a button, pushing a barrel). Our framework acquires new behaviors more efficiently, simply by combining a task-specific high-level contact planner and the pre-trained generalist policy. Project website: https://vassil-atn.github.io/gecco.github.io

We present the design and implementation of HASTA (Hopper with Adjustable Stiffness for Terrain Adaptation), a vertical hopping robot with real-time tunable leg stiffness, aimed at optimizing energy efficiency across various ground profiles (a pair of ground stiffness and damping conditions). By adjusting leg stiffness, we aim to maximize apex hopping height, a key metric for energy-efficient vertical hopping. We hypothesize that softer legs perform better on soft, damped ground by minimizing penetration and energy loss, while stiffer legs excel on hard, less damped ground by reducing limb deformation and energy dissipation. Through experimental tests and simulations, we find the best leg stiffness within our selection for each combination of ground stiffness and damping, enabling the robot to achieve maximum steady-state hopping height with a constant energy input. These results support our hypothesis that tunable stiffness improves energy-efficient locomotion in controlled experimental conditions. In addition, the simulation provides insights that could aid in the future development of controllers for selecting leg stiffness.

Robust and accurate proprioceptive state estimation of the main body is crucial for legged robots to execute tasks in extreme environments where exteroceptive sensors, such as LiDARs and cameras, may become unreliable. In this paper, we propose DogLegs, a state estimation system for legged robots that fuses the measurements from a body-mounted inertial measurement unit (Body-IMU), joint encoders, and multiple leg-mounted IMUs (Leg-IMU) using an extended Kalman filter (EKF). The filter system contains the error states of all IMU frames. The Leg-IMUs are used to detect foot contact, thereby providing zero-velocity measurements to update the state of the Leg-IMU frames. Additionally, we compute the relative position constraints between the Body-IMU and Leg-IMUs by the leg kinematics and use them to update the main body state and reduce the error drift of the individual IMU frames. Field experimental results have shown that our proposed DogLegs system achieves better state estimation accuracy compared to the traditional leg odometry method (using only Body-IMU and joint encoders) across various terrains. We make our code and datasets publicly available to benefit the research community (https://github.com/YibinWu/DogLegs).

This paper presents the Kinetics Observer, a novel proprioceptive state estimator for legged robots designed to provide the feedback required for versatile locomotion and physical interaction with the environment, with enhanced robustness to contact slippage. Its core contribution is a tight coupling between whole-body kinematics and external wrenches through a contact dynamics model, enabling the consistent fusion of leg kinematics, IMU, and wrench sensor measurements for real-time joint estimation of centroidal kinematics, contact rest poses, contact wrenches, and disturbance wrenches. By exploiting contact wrench measurements as correction terms, the proposed observer increases sensing redundancy, which provides observability of contact slippage relative to the centroid frame and enhanced robustness to modeling and sensor errors. The approach is experimentally evaluated on two humanoid robots across three scenarios totaling thirteen walking sequences, including long-distance walking with repeated contact changes, locomotion over slippery obstacles, and non-coplanar multicontact motion.

Legged locomotion on flowing ground ({\em e.g.} granular media) is unlike locomotion on hard ground because feet experience both solid- and fluid-like forces during surface penetration. Recent bio-inspired legged robots display speed relative to body size on hard ground comparable to high performing organisms like cockroaches but suffer significant performance loss on flowing materials like sand. In laboratory experiments we study the performance (speed) of a small (2.3 kg) six-legged robot, SandBot, as it runs on a bed of granular media (1 mm poppy seeds). For an alternating tripod gait on the granular bed, standard gait control parameters achieve speeds at best two orders of magnitude smaller than the 2 body lengths/s ($\approx 60$ cm/s) for motion on hard ground. However, empirical adjustment of these control parameters away from the hard ground settings, restores good performance, yielding top speeds of 30 cm/s. Robot speed depends sensitively on the packing fraction $φ$ and the limb frequency $ω$, and a dramatic transition from rotary walking to slow swimming occurs when $φ$ becomes small enough and/or $ω$ large enough. We propose a kinematic model of the rotary walking mode based on generic features of penetration and slip of a curved limb in granular media. The model captures the dependence of robot speed on limb frequency and the transition between walking and swimming modes but highlights the need for a deeper understanding of the physics of granular media.