gait
Surrogate compliance modeling enables reinforcement learned locomotion gaits for soft robots
Wang, Jue, Jiang, Mingsong, Ramirez, Luis A., Yang, Bilige, Zhang, Mujun, Figueroa, Esteban, Yan, Wenzhong, Kramer-Bottiglio, Rebecca
Adaptive morphogenetic robots adapt their morphology and control policies to meet changing tasks and environmental conditions. Many such systems leverage soft components, which enable shape morphing but also introduce simulation and control challenges. Soft-body simulators remain limited in accuracy and computational tractability, while rigid-body simulators cannot capture soft-material dynamics. Here, we present a surrogate compliance modeling approach: rather than explicitly modeling soft-body physics, we introduce indirect variables representing soft-material deformation within a rigid-body simulator. We validate this approach using our amphibious robotic turtle, a quadruped with soft morphing limbs designed for multi-environment locomotion. By capturing deformation effects as changes in effective limb length and limb center of mass, and by applying reinforcement learning with extensive randomization of these indirect variables, we achieve reliable policy learning entirely in a rigid-body simulation. The resulting gaits transfer directly to hardware, demonstrating high-fidelity sim-to-real performance on hard, flat substrates and robust, though lower-fidelity, transfer on rheologically complex terrains. The learned closed-loop gaits exhibit unprecedented terrestrial maneuverability and achieve an order-of-magnitude reduction in cost of transport compared to open-loop baselines. Field experiments with the robot further demonstrate stable, multi-gait locomotion across diverse natural terrains, including gravel, grass, and mud.
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Coordinating Spinal and Limb Dynamics for Enhanced Sprawling Robot Mobility
Atasever, Merve, Okhovat, Ali, Nazaripouya, Azhang, Nisbet, John, Kurkutlu, Omer, Deshmukh, Jyotirmoy V., Aydin, Yasemin Ozkan
Sprawling locomotion in vertebrates, particularly salamanders, demonstrates how body undulation and spinal mobility enhance stability, maneuverability, and adaptability across complex terrains. While prior work has separately explored biologically inspired gait design or deep reinforcement learning (DRL), these approaches face inherent limitations: open-loop gait designs often lack adaptability to unforeseen terrain variations, whereas end-to-end DRL methods are data-hungry and prone to unstable behaviors when transferring from simulation to real robots. We propose a hybrid control framework that integrates Hildebrand's biologically grounded gait design with DRL, enabling a salamander-inspired quadruped robot to exploit active spinal joints for robust crawling motion. Our evaluation across multiple robot configurations in target-directed navigation tasks reveals that this hybrid approach systematically improves robustness under environmental uncertainties such as surface irregularities. By bridging structured gait design with learning-based methodology, our work highlights the promise of interdisciplinary control strategies for developing efficient, resilient, and biologically informed spinal actuation in robotic systems.
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Robust Dynamic Walking for a 3D Dual-SLIP Model under One-Step Unilateral Stiffness Perturbations: Towards Bipedal Locomotion over Compliant Terrain
Karakasis, Chrysostomos, Poulakakis, Ioannis, Artemiadis, Panagiotis
Bipedal walking is one of the most important hallmarks of human that robots have been trying to mimic for many decades. Although previous control methodologies have achieved robot walking on some terrains, there is a need for a framework allowing stable and robust locomotion over a wide range of compliant surfaces. This work proposes a novel biomechanics-inspired controller that adjusts the stiffness of the legs in support for robust and dynamic bipedal locomotion over compliant terrains. First, the 3D Dual-SLIP model is extended to support for the first time locomotion over compliant surfaces with variable stiffness and damping parameters. Then, the proposed controller is compared to a Linear-Quadratic Regulator (LQR) controller, in terms of robustness on stepping on soft terrain. The LQR controller is shown to be robust only up to a moderate ground stiffness level of 174 kN/m, while it fails in lower stiffness levels. On the contrary, the proposed controller can produce stable gait in stiffness levels as low as 30 kN/m, which results in a vertical ground penetration of the leg that is deeper than 10% of its rest length. The proposed framework could advance the field of bipedal walking, by generating stable walking trajectories for a wide range of compliant terrains useful for the control of bipeds and humanoids, as well as by improving controllers for prosthetic devices with tunable stiffness.
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Discovering Optimal Natural Gaits of Dissipative Systems via Virtual Energy Injection
Griesbauer, Korbinian, Calzolari, Davide, Raff, Maximilian, Remy, C. David, Albu-Schäffer, Alin
Legged robots offer several advantages when navigating unstructured environments, but they often fall short of the efficiency achieved by wheeled robots. One promising strategy to improve their energy economy is to leverage their natural (unactuated) dynamics using elastic elements. This work explores that concept by designing energy-optimal control inputs through a unified, multi-stage framework. It starts with a novel energy injection technique to identify passive motion patterns by harnessing the system's natural dynamics. This enables the discovery of passive solutions even in systems with energy dissipation caused by factors such as friction or plastic collisions. Building on these passive solutions, we then employ a continuation approach to derive energy-optimal control inputs for the fully actuated, dissipative robotic system. The method is tested on simulated models to demonstrate its applicability in both single- and multi-legged robotic systems. This analysis provides valuable insights into the design and operation of elastic legged robots, offering pathways to improve their efficiency and adaptability by exploiting the natural system dynamics.
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Toward the smooth mesh climbing of a miniature robot using bioinspired soft and expandable claws
Wang, Hong, Liu, Peng, Ngoc, Phuoc Thanh Tran, Li, Bing, Li, Yao, Sato, Hirotaka
--While most micro -robots face difficulty traveling on rugged and uneven terrain, b eetles can walk smoothly on the complex substrate without slipping or getting stuck o n the surface due to their stiffness-variable tarsi and expandable hooks on the tip of tarsi. In this study, we found that beetles actively bent and expand ed their claws regularly to crawl freely on mesh surfaces. Inspired by the crawling mechanism of the beetles, we designed an 8 -cm miniature climbing robot equipping artificial claw s to open and bend in the same cyclic manner as natural beetles. The robot can climb freely with a controllable gait on the mesh surface, steep incline of the angle of 60, and even transition surface. To our best knowledge, this is the first micro -scale robot that can climb both the mesh surface and cliffy incline. Their small size, lightweight, and strong navigation capabilities allow them to be deployed in complicated environments quickly. Numerous insect -scale robots have been developed with diversiform locomotion modes, including crawling [1-3], rolling [4-6], jumping[7-9], gliding [10, 11], and flying [12-14]. The actuators are diverse from traditional motor s [15] and pneumatic [16] to shape memory alloy [17], piezoelectric ceramics [18], and dielectric elastomer [19]. However, they can only locomote on a nearly level surface, which makes them unable to overcome barriers several times larger than their body size.
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Learning Omnidirectional Locomotion for a Salamander-Like Quadruped Robot
Liu, Zhiang, Liu, Yang, Fang, Yongchun, Guo, Xian
Salamander-like quadruped robots are designed inspired by the skeletal structure of their biological counterparts. However, existing controllers cannot fully exploit these morphological features and largely rely on predefined gait patterns or joint trajectories, which prevents the generation of diverse and flexible locomotion and limits their applicability in real-world scenarios. In this paper, we propose a learning framework that enables the robot to acquire a diverse repertoire of omnidirectional gaits without reference motions. Each body part is controlled by a phase variable capable of forward and backward evolution, with a phase coverage reward to promote the exploration of the leg phase space. Additionally, morphological symmetry of the robot is incorporated via data augmentation, improving sample efficiency and enforcing both motion-level and task-level symmetry in learned behaviors. Extensive experiments show that the robot successfully acquires 22 omnidirectional gaits exhibiting both dynamic and symmetric movements, demonstrating the effectiveness of the proposed learning framework.
Stable and Robust SLIP Model Control via Energy Conservation-Based Feedback Cancellation for Quadrupedal Applications
Hassan, Muhammad Saud Ul, Vasquez, Derek, Asif, Hamza, Hubicki, Christian
In this paper, we present an energy-conservation based control architecture for stable dynamic motion in quadruped robots. We model the robot as a Spring-loaded Inverted Pendulum (SLIP), a model well-suited to represent the bouncing motion characteristic of running gaits observed in various biological quadrupeds and bio-inspired robotic systems. The model permits leg-orientation control during flight and leg-length control during stance, a design choice inspired by natural quadruped behaviors and prevalent in robotic quadruped systems. Our control algorithm uses the reduced-order SLIP dynamics of the quadruped to track a stable parabolic spline during stance, which is calculated using the principle of energy conservation. Through simulations based on the design specifications of an actual quadruped robot, Ghost Robotics Minitaur, we demonstrate that our control algorithm generates stable bouncing gaits. Additionally, we illustrate the robustness of our controller by showcasing its ability to maintain stable bouncing even when faced with up to a 10% error in sensor measurements.
Learning Natural and Robust Hexapod Locomotion over Complex Terrains via Motion Priors based on Deep Reinforcement Learning
Liu, Xin, Wu, Jinze, Li, Yinghui, Qi, Chenkun, Xue, Yufei, Gao, Feng
Abstract-- Multi-legged robots offer enhanced stability to navigate complex terrains with their multiple legs interacting with the environment. However, how to effectively coordinate the multiple legs in a larger action exploration space to generate natural and robust movements is a key issue. In this paper, we introduce a motion prior-based approach, successfully applying deep reinforcement learning algorithms to a real hexapod robot. We generate a dataset of optimized motion priors, and train an adversarial discriminator based on the priors to guide the hexapod robot to learn natural gaits. The learned policy is then successfully transferred to a real hexapod robot, and demonstrate natural gait patterns and remarkable robustness without visual information in complex terrains. This is the first time that a reinforcement learning controller has been used to achieve complex terrain walking on a real hexapod robot.
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Wearable Sensor-Based IoT XAI Framework for Predicting Freezing of Gait in Parkinsons Disease
This research discusses the critical need for early detection and treatment for early prediction of Freezing of Gaits (FOG) utilizing a wearable sensor technology powered with LoRa communication. The system consisted of an Esp-32 microcontroller, in which the trained model is utilized utilizing the Micromlgen Python library. The research investigates accurate FOG classification based on pertinent clinical data by utilizing machine learning (ML) algorithms like Catboost, XGBoost, and Extra Tree classifiers. The XGBoost could classify with approximately 97% accuracy, along with 96% for the catboost and 90% for the Extra Trees Classifier model. The SHAP analysis interpretability shows that GYR SI degree is the most affecting factor in the prediction of the diseases. These results show the possibility of monitoring and identifying the affected person with tracking location on GPS and providing aid as an assistive technology for aiding the affected. The developed sensor-based technology has great potential for real-world problem solving in the field of healthcare and biomedical technology enhancements.
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Inverse Optimal Control of Muscle Force Sharing During Pathological Gait
Bečanović, Filip, Bonnet, Vincent, Jovanović, Kosta, Mohammed, Samer, Dumas, Raphaël
Muscle force sharing is typically resolved by minimizing a specific objective function to approximate neural control strategies. An inverse optimal control approach was applied to identify the "best" objective function, among a positive linear combination of basis objective functions, associated with the gait of two post-stroke males, one high-functioning (subject S1) and one low-functioning (subject S2). It was found that the "best" objective function is subject- and leg-specific. No single function works universally well, yet the best options are usually differently weighted combinations of muscle activation- and power-minimization. Subject-specific inverse optimal control models performed best on their respective limbs (\textbf{RMSE 178/213 N, CC 0.71/0.61} for non-paretic and paretic legs of S1; \textbf{RMSE 205/165 N, CC 0.88/0.85} for respective legs of S2), but cross-subject generalization was poor, particularly for paretic legs. Moreover, minimizing the root mean square of muscle power emerged as important for paretic limbs, while minimizing activation-based functions dominated for non-paretic limbs. This may suggest different neural control strategies between affected and unaffected sides, possibly altered by the presence of spasticity. Among the 15 considered objective functions commonly used in inverse dynamics-based computations, the root mean square of muscle power was the only one explicitly incorporating muscle velocity, leading to a possible model for spasticity in the paretic limbs. Although this objective function has been rarely used, it may be relevant for modeling pathological gait, such as post-stroke gait.
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