Online Optimization of Central Pattern Generators for Quadruped Locomotion

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 \textit{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. See demo at: https://youtu.be/4qq5leCI2AI

Learning-based Hierarchical Control: Emulating the Central Nervous System for Bio-Inspired Legged Robot Locomotion

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, SCP), and the other responsible for receiving environmental perception data and directly modulating the rhythmic output from the SCP 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 time delays. Through these investigations, this paper contributes to a deeper understanding of the fundamental principles of interplay between spinal and supraspinal mechanisms in biological locomotion. It also supports the development of locomotion controllers in parallel to biological structures which are ...

Quadruped-Frog: Rapid Online Optimization of Continuous Quadruped Jumping

Legged robots are becoming increasingly agile in exhibiting dynamic behaviors such as running and jumping. Usually, such behaviors are either optimized and engineered offline (i.e. the behavior is designed for before it is needed), either through model-based trajectory optimization, or through deep learning-based methods involving millions of timesteps of simulation interactions. Notably, such offline-designed locomotion controllers cannot perfectly model the true dynamics of the system, such as the motor dynamics. In contrast, in this paper, we consider a quadruped jumping task that we rapidly optimize online. We design foot force profiles parameterized by only a few parameters which we optimize for directly on hardware with Bayesian Optimization. The force profiles are tracked at the joint level, and added to Cartesian PD impedance control and Virtual Model Control to stabilize the jumping motions. After optimization, which takes only a handful of jumps, we show that this control architecture is capable of diverse and omnidirectional jumps including forward, lateral, and twist (turning) jumps, even on uneven terrain, enabling the Unitree Go1 quadruped to jump 0.5 m high, 0.5 m forward, and jump-turn over 2 rad. Video results can be found at https://youtu.be/SvfVNQ90k_w.

ExoRecovery: Push Recovery with a Lower-Limb Exoskeleton based on Stepping Strategy

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.

ManyQuadrupeds: Learning a Single Locomotion Policy for Diverse Quadruped Robots

Learning a locomotion policy for quadruped robots has traditionally been constrained to 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. These 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 16 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.

Identifying Important Sensory Feedback for Learning Locomotion Skills

Robot motor skills can be learned through deep reinforcement learning (DRL) by neural networks as state-action mappings. While the selection of state observations is crucial, there has been a lack of quantitative analysis to date. Here, we present a systematic saliency analysis that quantitatively evaluates the relative importance of different feedback states for motor skills learned through DRL. Our approach can identify the most essential feedback states for locomotion skills, including balance recovery, trotting, bounding, pacing and galloping. By using only key states including joint positions, gravity vector, base linear and angular velocities, we demonstrate that a simulated quadruped robot can achieve robust performance in various test scenarios across these distinct skills. The benchmarks using task performance metrics show that locomotion skills learned with key states can achieve comparable performance to those with all states, and the task performance or learning success rate will drop significantly if key states are missing. This work provides quantitative insights into the relationship between state observations and specific types of motor skills, serving as a guideline for robot motor learning. The proposed method is applicable to differentiable state-action mapping, such as neural network based control policies, enabling the learning of a wide range of motor skills with minimal sensing dependencies.

DeepTransition: Viability Leads to the Emergence of Gait Transitions in Learning Anticipatory Quadrupedal Locomotion Skills

Quadruped animals seamlessly transition between gaits as they change locomotion speeds. While the most widely accepted explanation for gait transitions is energy efficiency, there is no clear consensus on the determining factor, nor on the potential effects from terrain properties. In this article, we propose that viability, i.e. the avoidance of falls, represents an important criterion for gait transitions. We investigate the emergence of gait transitions through the interaction between supraspinal drive (brain), the central pattern generator in the spinal cord, the body, and exteroceptive sensing by leveraging deep reinforcement learning and robotics tools. Consistent with quadruped animal data, we show that the walk-trot gait transition for quadruped robots on flat terrain improves both viability and energy efficiency. Furthermore, we investigate the effects of discrete terrain (i.e. crossing successive gaps) on imposing gait transitions, and find the emergence of trot-pronk transitions to avoid non-viable states. Compared with other potential criteria such as peak forces and energy efficiency, viability is the only improved factor after gait transitions on both flat and discrete gap terrains, suggesting that viability could be a primary and universal objective of gait transitions, while other criteria are secondary objectives and/or a consequence of viability. Moreover, we deploy our learned controller in sim-to-real hardware experiments and demonstrate state-of-the-art quadruped agility in challenging scenarios, where the Unitree A1 quadruped autonomously transitions gaits between trot and pronk to cross consecutive gaps of up to 30 cm (83.3 % of the body-length) at over 1.3 m/s.

Puppeteer and Marionette: Learning Anticipatory Quadrupedal Locomotion Based on Interactions of a Central Pattern Generator and Supraspinal Drive

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).

Online Bipedal Locomotion Adaptation for Stepping on Obstacles Using a Novel Foot Sensor

In this paper, we present a novel control architecture for the online adaptation of bipedal locomotion on inclined obstacles. In particular, we introduce a novel, cost-effective, and versatile foot sensor to detect the proximity of the robot's feet to the ground (bump sensor). By employing this sensor, feedback controllers are implemented to reduce the impact forces during the transition of the swing to stance phase or steeping on inclined unseen obstacles. Compared to conventional sensors based on contact reaction force, this sensor detects the distance to the ground or obstacles before the foot touches the obstacle and therefore provides predictive information to anticipate the obstacles. The controller of the proposed bump sensor interacts with another admittance controller to adjust leg length. The walking experiments show successful locomotion on the unseen inclined obstacle without reducing the locomotion speed with a slope angle of 12. Foot position error causes a hard impact with the ground as a consequence of accumulative error caused by links and connections' deflection (which is manufactured by university tools). The proposed framework drastically reduces the feet' impact with the ground.

Online DCM Trajectory Generation for Push Recovery of Torque-Controlled Humanoid Robots

We present a computationally efficient method for online planning of bipedal walking trajectories with push recovery. In particular, the proposed methodology fits control architectures where the Divergent-Component-of-Motion (DCM) is planned beforehand, and adds a step adapter to adjust the planned trajectories and achieve push recovery. Assuming that the robot is in a single support state, the step adapter generates new positions and timings for the next step. The step adapter is active in single support phases only, but the proposed torque-control architecture considers double support phases too. The key idea for the design of the step adapter is to impose both initial and final DCM step values using an exponential interpolation of the time varying ZMP trajectory.This allows us to cast the push recovery problem as a Quadratic Programming (QP) one, and to solve it online with state-of-the-art optimisers. The overall approach is validated with simulations of the torque-controlled 33 kg humanoid robot iCub. Results show that the proposed strategy prevents the humanoid robot from falling while walking at 0.28 m/s and pushed with external forces up to 150 Newton for 0.05 seconds.