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.

-- In this paper, we explore the space of running gaits for the bipedal robot Cassie. Our first contribution is to present an approach for optimizing gait efficiency across a spectrum of speeds with the aim of enabling extremely high-speed running on hardware. This raises the question of how the resulting gaits compare to human running mechanics, which are known to be highly efficient in comparison to quadrupeds. Our second contribution is to conduct this comparison based on established human biomechanical studies. We find that despite morphological differences between Cassie and humans, key properties of the gaits are highly similar across a wide range of speeds. Finally, our third contribution is to integrate the optimized running gaits into a full controller that satisfies the rules of the real-world task of the 100m dash, including starting and stopping from a standing position. We demonstrate this controller on hardware to establish the Guinness World Record for F astest 100m by a Bipedal Robot . I. INTRODUCTION In recent years, reinforcement learning (RL) has proven highly effective for sim-to-real training of bipedal locomotion [1-3].

Advances in wearable robotics challenge the traditional definition of human motor systems, as wearable robots redefine body structure, movement capability, and perception of their own bodies. While these devices can empower the wearer's motor performance, there is limited understanding of how wearer s update their perception of body images, especially images in dynamic movements, while learning to use these modern devices. This study aimed to fill the gap by examining the changes of body image as individuals learned to walk with a robotic prosthetic l eg over multi - day training. We measured gait performance and perceived body images via Selected Coefficient of Perceived Motion (SCoMo) after each training session. Based on human motor learning theory extended to wearer - robot systems, w e hypothesized that learning the perceived body image when walking with a robotic leg co - evolves with the actual gait improvement and becomes more certain and more accurate to the actual motion. Our result confirmed that motor learning improved both physical and perceived ga it pattern towards normal, indicating that via practice the wearers incorporated the robotic leg into their sensorimotor systems to enable wearer - robot movement coordination. However, a persistent discrepancy between perceived and actual motion remained, l ikely due to the absence of direct sensation and control of the prosthesis from wearers. Additionally, the perceptual overestimation at the later training sessions might limit further motor improvement. These findings suggest that enhancing the human sense of wearable robots and frequent calibrating perception of body image are essential for effective training with lower limb wearable robots and for developing more embodied assistive technologies.

Evolutionary methods have previously been shown to be an effective learning method for walking gaits on hexapod robots. However, the ability of these algorithms to evolve an effective policy rapidly degrades as the input space becomes more complex. This degradation is due to the exponential growth of the solution space, resulting from an increasing parameter count to handle a more complex input. In order to address this challenge, we introduce Sparse Cosine Optimized Policy Evolution (SCOPE). SCOPE utilizes the Discrete Cosine Transform (DCT) to learn directly from the feature coefficients of an input matrix. By truncating the coefficient matrix returned by the DCT, we can reduce the dimensionality of an input while retaining the highest energy features of the original input. We demonstrate the effectiveness of this method by using SCOPE to learn the gait of a hexapod robot. The hexapod controller is given a matrix input containing time-series information of previous poses, which are then transformed to gait parameters by an evolved policy. In this task, the addition of SCOPE to a reference algorithm achieves a 20% increase in efficacy. SCOPE achieves this result by reducing the total input size of the time-series pose data from 2700 to 54, a 98% decrease. Additionally, SCOPE is capable of compressing an input to any output shape, provided that each output dimension is no greater than the corresponding input dimension. This paper demonstrates that SCOPE is capable of significantly compressing the size of an input to an evolved controller, resulting in a statistically significant gain in efficacy.

Motion planning for locomotion systems typically requires translating high-level rigid-body tasks into low-level joint trajectories-a process that is straightforward for car-like robots with fixed, unbounded actuation inputs but more challenging for systems like snake robots, where the mapping depends on the current configuration and is constrained by joint limits. In this paper, we focus on generating continuous families of optimal gaits-collections of gaits parameterized by step size or steering rate-to enhance controllability and maneuverability. We uncover the underlying geometric structure of these optimal gait families and propose methods for constructing them using both global and local search strategies, where the local method and the global method compensate each other. The global search approach is robust to nonsmooth behavior, albeit yielding reduced-order solutions, while the local search provides higher accuracy but can be unstable near nonsmooth regions. To demonstrate our framework, we generate optimal gait families for viscous and perfect-fluid three-link swimmers. This work lays a foundation for integrating low-level joint controllers with higher-level motion planners in complex locomotion systems.

In recent years, reinforcement learning (RL) based quadrupedal locomotion control has emerged as an extensively researched field, driven by the potential advantages of autonomous learning and adaptation compared to traditional control methods. This paper provides a comprehensive study of the latest research in applying RL techniques to develop locomotion controllers for quadrupedal robots. We present a detailed overview of the core concepts, methodologies, and key advancements in RL-based locomotion controllers, including learning algorithms, training curricula, reward formulations, and simulation-to-real transfer techniques. The study covers both gait-bound and gait-free approaches, highlighting their respective strengths and limitations. Additionally, we discuss the integration of these controllers with robotic hardware and the role of sensor feedback in enabling adaptive behavior. The paper also outlines future research directions, such as incorporating exteroceptive sensing, combining model-based and model-free techniques, and developing online learning capabilities. Our study aims to provide researchers and practitioners with a comprehensive understanding of the state-of-the-art in RL-based locomotion controllers, enabling them to build upon existing work and explore novel solutions for enhancing the mobility and adaptability of quadrupedal robots in real-world environments.

We present CROSS-GAiT, a novel algorithm for quadruped robots that uses Cross Attention to fuse terrain representations derived from visual and time-series inputs, including linear accelerations, angular velocities, and joint efforts. These fused representations are used to adjust the robot's step height and hip splay, enabling adaptive gaits that respond dynamically to varying terrain conditions. We generate these terrain representations by processing visual inputs through a masked Vision Transformer (ViT) encoder and time-series data through a dilated causal convolutional encoder. The cross-attention mechanism then selects and integrates the most relevant features from each modality, combining terrain characteristics with robot dynamics for better-informed gait adjustments. CROSS-GAiT uses the combined representation to dynamically adjust gait parameters in response to varying and unpredictable terrains. We train CROSS-GAiT on data from diverse terrains, including asphalt, concrete, brick pavements, grass, dense vegetation, pebbles, gravel, and sand. Our algorithm generalizes well and adapts to unseen environmental conditions, enhancing real-time navigation performance. CROSS-GAiT was implemented on a Ghost Robotics Vision 60 robot and extensively tested in complex terrains with high vegetation density, uneven/unstable surfaces, sand banks, deformable substrates, etc. We observe at least a 7.04% reduction in IMU energy density and a 27.3% reduction in total joint effort, which directly correlates with increased stability and reduced energy usage when compared to state-of-the-art methods. Furthermore, CROSS-GAiT demonstrates at least a 64.5% increase in success rate and a 4.91% reduction in time to reach the goal in four complex scenarios. Additionally, the learned representations perform 4.48% better than the state-of-the-art on a terrain classification task.

Gait benchmark empowers uncounted encouraging research fields such as gait recognition, humanoid locomotion, etc. Despite the growing focus on gait analysis, the research community is hindered by the limitations of the currently available databases, which mostly consist of videos or images with limited labeling. In this paper, we introduce GaitMotion, a multitask dataset leveraging wearable sensors to capture the patients' real-time movement with pathological gait. This dataset offers extensive ground-truth labeling for multiple tasks, including step/stride segmentation and step/stride length prediction, empowers researchers with a more holistic understanding of gait disturbances linked to neurological impairments. The wearable gait analysis suit captures the gait cycle, pattern, and parameters for both normal and pathological subjects. This data may prove beneficial for healthcare products focused on patient progress monitoring and post-disease recovery, as well as for forensics technologies aimed at person reidentification, and biomechanics research to aid in the development of humanoid robotics. Moreover, the analysis has considered the drift in data distribution across individual subjects. This drift can be attributed to each participant's unique behavioral habits or potential displacement of the sensor. Stride length variance for normal, Parkinson's, and stroke patients are compared to recognize the pathological walking pattern. As the baseline and benchmark, we provide an error of 14.1, 13.3, and 12.2 centimeters of stride length prediction for normal, Parkinson's, and Stroke gaits separately. We also analyzed the gait characteristics for normal and pathological gaits in terms of the gait cycle and gait parameters.

Lumbar disc herniation (LDH) is a prevalent orthopedic condition in clinical practice. Inertial measurement unit sensors (IMUs) are an effective tool for monitoring and assessing gait impairment in patients with lumbar disc herniation (LDH). However, the current gait assessment of LDH focuses solely on single-source acceleration signal data, without considering the diversity of sensor data. It also overlooks the individual differences in motor function deterioration between the healthy and affected lower limbs in patients with LDH. To address this issue, we developed an LDH gait feature model that relies on multi-source adaptive Kalman data fusion of acceleration and angular velocity. We utilized an adaptive Kalman data fusion algorithm for acceleration and angular velocity to estimate the attitude angle and segment the gait phase. Two Inertial Measurement Units (IMUs) were used to analyze the gait characteristics of patients with lumbar disc issues and healthy individuals. This analysis included 12 gait characteristics, such as gait spatiotemporal parameters, kinematic parameters, and expansibility index numbers. Statistical methods were employed to analyze the characteristic model and confirm the biological differences between the healthy affected side of LDH and healthy subjects. Finally, a classifier based on feature engineering was utilized to classify the gait patterns of the affected side of patients with lumbar disc disease and healthy subjects. This approach achieved a classification accuracy of 95.50%, enhancing the recognition of LDH and healthy gait patterns. It also provided effective gait feature sets and methods for assessing LDH clinically.

Abstract--Quadruped locomotion is rapidly maturing to a degree where robots are able to realise highly dynamic manoeuvres. However, current planners are unable to vary key gait parameters of the in-swing feet midair. In this work we address this limitation and show that it is pivotal in increasing controller robustness by learning a latent space capturing the key stance phases constituting a particular gait. This is achieved via a generative model trained on a single trot style, which encourages disentanglement such that application of a drive signal to a single dimension of the latent state induces holistic plans synthesising a continuous variety of trot styles. We demonstrate that specific properties of the drive signal map directly to gait parameters such as cadence, footstep height and full stance duration. Due to the nature of our approach these synthesised gaits are continuously variable online during robot operation. The use of a generative model facilitates the detection and mitigation of disturbances to provide a versatile and robust planning framework. We evaluate our approach on two versions of the real ANYmal quadruped robots and demonstrate that our method achieves a continuous blend of dynamic trot styles whilst being robust and reactive to external perturbations. Figure 1: Using a variational auto-encoder (VAE), our approach learns a structured latent space capturing key stance phases constituting a particular gait. The space is disentangled to I. I This approach by advances in optimisation-based [1]-[5] and reinforcement allows for precise base twist control and readily transfers from learning-based methods [6]-[8], quadrupeds are now able to ANYmal B to ANYmal C, a dynamically dissimilar robot, robustly plan and perform dynamic manoeuvres, making them without retraining. Additionally, we measure disturbances as an increasingly popular and reliable choice for tasks such out of distribution seen during training and adjust cadence as as inspection, monitoring, search and rescue or goods delivery a rudimentary, but effective response. However, despite recent advances, important limitations remain. Due to the complexity of the system, models used for gait planning and control are often overly contact schedules [1], [9]. Mathieu Geisert is with Agility Robotics, U.S.A. Work done while at Martin Engelcke is with DeepMind Technologies Ltd., London, U.K. Work done while at Oxford. Personal use of this material is permitted. These are often characterise and react to external perturbations. A large impulse computationally expensive [3], [4] meaning that varying the applied to the robot's base triggers a spike in the gait parameters is not achievable in real time. A limitation Evidence Lower Bound (ELBO) which clearly identifies the of all these methods is that they are unable to adjust key disturbance as out of the distribution seen during training.