We present a framework for learning a single policy capable of producing all quadruped gaits and transitions. The framework consists of a policy trained with deep reinforcement learning (DRL) to modulate the parameters of a system of abstract oscillators (i.e. Central Pattern Generator), whose output is mapped to joint commands through a pattern formation layer that sets the gait style, i.e. body height, swing foot ground clearance height, and foot offset. Different gaits are formed by changing the coupling between different oscillators, which can be instantaneously selected at any velocity by a user. With this framework, we systematically investigate which gait should be used at which velocity, and when gait transitions should occur from a Cost of Transport (COT), i.e. energy-efficiency, point of view. Additionally, we note how gait style changes as a function of locomotion speed for each gait to keep the most energy-efficient locomotion. While the currently most popular gait (trot) does not result in the lowest COT, we find that considering different co-dependent metrics such as mean base angular velocity and joint acceleration result in different 'optimal' gaits than those that minimize COT. We deploy our controller in various hardware experiments, focusing on 9 quadruped animal gaits, and demonstrate generalizability to novel and unseen gaits during training, and robustness to leg failures.

We present a framework for learning visually-guided quadruped locomotion by integrating exteroceptive sensing and central pattern generators (CPGs), i.e. systems of coupled oscillators, into the deep reinforcement learning (DRL) framework. Through both exteroceptive and proprioceptive sensing, the agent learns to coordinate rhythmic behavior among different oscillators to track velocity commands, while at the same time override these commands to avoid collisions with the environment. We investigate several open robotics and neuroscience questions: 1) What is the role of explicit interoscillator couplings between oscillators, and can such coupling improve sim-to-real transfer for navigation robustness? 2) What are the effects of using a memory-enabled vs. a memory-free policy network with respect to robustness, energy-efficiency, and tracking performance in sim-to-real navigation tasks? 3) How do animals manage to tolerate high sensorimotor delays, yet still produce smooth and robust gaits? To answer these questions, we train our perceptive locomotion policies in simulation and perform sim-to-real transfers to the Unitree Go1 quadruped, where we observe robust navigation in a variety of scenarios. Our results show that the CPG, explicit interoscillator couplings, and memory-enabled policy representations are all beneficial for energy efficiency, robustness to noise and sensory delays of 90 ms, and tracking performance for successful sim-to-real transfer for navigation tasks.

Balance loss is a significant challenge in lower-limb exoskeleton applications, as it can lead to potential falls, thereby impacting user safety and confidence. We introduce a control framework for omnidirectional recovery step planning by online optimization of step duration and position in response to external forces. We map the step duration and position to a human-like foot trajectory, which is then translated into joint trajectories using inverse kinematics. These trajectories are executed via an impedance controller, promoting cooperation between the exoskeleton and the user. Moreover, our framework is based on the concept of the divergent component of motion, also known as the Extrapolated Center of Mass, which has been established as a consistent dynamic for describing human movement. This real-time online optimization framework enhances the adaptability of exoskeleton users under unforeseen forces thereby improving the overall user stability and safety. To validate the effectiveness of our approach, simulations, and experiments were conducted. Our push recovery experiments employing the exoskeleton in zero-torque mode (without assistance) exhibit an alignment with the exoskeleton’s recovery assistance mode, that shows the consistency of the control framework with human intention. To the best of our knowledge, this is the first cooperative push recovery framework for the lower-limb human exoskeleton that relies on the simultaneous adaptation of intra-stride parameters in both frontal and sagittal directions. The proposed control scheme has been validated with human subject experiments.

Learning a locomotion policy for quadruped robots has traditionally been constrained to a specific robot morphology, mass, and size. The learning process must usually be repeated for every new robot, where hyperparameters and reward function weights must be re-tuned to maximize performance for each new system. Alternatively, attempting to train a single policy to accommodate different robot sizes, while maintaining the same degrees of freedom (DoF) and morphology, requires either complex learning frameworks, or mass, inertia, and dimension randomization, which leads to prolonged training periods. In our study, we show that drawing inspiration from animal motor control allows us to effectively train a single locomotion policy capable of controlling a diverse range of quadruped robots. The robot differences encompass: a variable number of DoFs, (i.e. 12 or 16 joints), three distinct morphologies, a broad mass range spanning from 2 kg to 200 kg, and nominal standing heights ranging from 18 cm to 100 cm. Our policy modulates a representation of the Central Pattern Generator (CPG) in the spinal cord, effectively coordinating both frequencies and amplitudes of the CPG to produce rhythmic output (Rhythm Generation), which is then mapped to a Pattern Formation (PF) layer. Across different robots, the only varying component is the PF layer, which adjusts the scaling parameters for the stride height and length. Subsequently, we evaluate the sim-to-real transfer by testing the single policy on both the Unitree Go1 and A1 robots. Remarkably, we observe robust performance, even when adding a 15 kg load, equivalent to 125% of the A1 robot’s nominal mass.

Animals possess a remarkable ability to navigate challenging terrains, achieved through the interplay of various pathways between the brain, central pattern generators (CPGs) in the spinal cord, and musculoskeletal system. Traditional bioinspired control frameworks often rely on a singular control policy that models both higher (supraspinal) and spinal cord functions. In this work, we build upon our previous research by introducing two distinct neural networks: one tasked with modulating the frequency and amplitude of CPGs to generate the basic locomotor rhythm (referred to as the spinal policy), and the other responsible for receiving environmental perception data and directly modulating the rhythmic output from the spinal policy to execute precise movements on challenging terrains (referred to as the descending modulation policy). This division of labor more closely mimics the hierarchical locomotor control systems observed in legged animals, thereby enhancing the robot’s ability to navigate various uneven surfaces, including steps, high obstacles, and terrains with gaps. Additionally, we investigate the impact of sensorimotor delays within our framework, validating several biological assumptions about animal locomotion systems. Specifically, we demonstrate that spinal circuits play a crucial role in generating the basic locomotor rhythm, while descending pathways are essential for enabling appropriate gait modifications to accommodate uneven terrain. Notably, our findings also reveal that the multi-layered control inherent in animals exhibits remarkable robustness against sensorimotor delays. These findings advance our understanding of the fundamental principles governing the interplay between spinal and supraspinal mechanisms in biological locomotion. Moreover, they inform the design of bioinspired locomotion controllers that emulate these biological structures, facilitating natural movement in complex and realistic environments.

Typical legged locomotion controllers are designed or trained offline. This is in contrast to many animals, which are able to locomote at birth, and rapidly improve their locomotion skills with few real-world interactions. Such motor control is possible through oscillatory neural networks located in the spinal cord of vertebrates, known as Central Pattern Generators (CPGs). Models of the CPG have been widely used to generate locomotion skills in robotics, but can require extensive hand-tuning or offline optimization of inter-connected parameters with genetic algorithms. In this paper, we present a framework for the online optimization of the CPG parameters through Bayesian Optimization. We show that our framework can rapidly optimize and adapt to varying velocity commands and changes in the terrain, for example to varying coefficients of friction, terrain slope angles, and added mass payloads placed on the robot. We study the effects of sensory feedback on the CPG, and find that both force feedback in the phase equations, as well as posture control (Virtual Model Control) are both beneficial for robot stability and energy efficiency. In hardware experiments on the Unitree Go1, we show rapid optimization (in under 3 minutes) and adaptation of energy-efficient gaits to varying target velocities in a variety of scenarios: varying coefficients of friction, added payloads up to 15 kg, and variable slopes up to 10 degrees.

Quadruped animal locomotion emerges from the interactions between the spinal central pattern generator (CPG), sensory feedback, and supraspinal drive signals from the brain. Computational models of CPGs have been widely used for investigating the spinal cord contribution to animal locomotion control in computational neuroscience and in bio-inspired robotics. However, the contribution of supraspinal drive to anticipatory behavior, i.e. motor behavior that involves planning ahead of time (e.g. of footstep placements), is not yet properly understood. In particular, it is not clear whether the brain modulates CPG activity and/or directly modulates muscle activity (hence bypassing the CPG) for accurate foot placements. In this paper, we investigate the interaction of supraspinal drive and a CPG in an anticipatory locomotion scenario that involves stepping over gaps. By employing deep reinforcement learning (DRL), we train a neural network policy that replicates the supraspinal drive behavior. This policy can either modulate the CPG dynamics, or directly change actuation signals to bypass the CPG dynamics. Our results indicate that the direct supraspinal contribution to the actuation signal is a key component for a high gap crossing success rate. However, the CPG dynamics in the spinal cord are beneficial for gait smoothness and energy efficiency. Moreover, our investigation shows that sensing the front feet distances to the gap is the most important and sufficient sensory information for learning gap crossing. Our results support the biological hypothesis that cats and horses mainly control the front legs for obstacle avoidance, and that hind limbs follow an internal memory based on the front limbs' information. Our method enables the quadruped robot to cross gaps of up to 20 cm (50% of body-length) without any explicit dynamics modeling or Model Predictive Control (MPC).