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1. Informed Sampling-Based Planning to Enable Legged Robots to Safely Negotiate Permeable Obstacles

   https://doi.org/10.1115/1.4055625  

   Chen, Yiyu; Lian, Lingchen; Hsieh, Yu-Hsiu; Nguyen, Quan; Gupta, Satyandra K. (October 2023, Journal of Mechanisms and Robotics)

   Abstract Legged robots have a unique capability of traversing rough terrains and negotiating cluttered environments. Recent control development of legged robots has enabled robust locomotion on rough terrains. However, such approaches mainly focus on maintaining balance for the robot body. In this work, we are interested in leveraging the whole body of the robot to pass through a permeable obstacle (e.g., a small confined opening) with height, width, and terrain constraints. This paper presents a planning framework for legged robots manipulating their body and legs to perform collision-free locomotion through a permeable obstacle. The planner incorporates quadrupedal gait constraint, biasing scheme, and safety margin for the simultaneous body and foothold motion planning. We perform informed sampling for the body poses and swing foot position based on the gait constraint while ensuring stability and collision avoidance. The footholds are planned based on the terrain and the contact constraint. We also integrate the planner with robot control to execute the planned trajectory successfully. We validated our approach in high-fidelity simulation and hardware experiments on the Unitree A1 robot navigating through different representative permeable obstacles. 

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2. Robust Multilegged Walking Robots for Interactions With Different Terrains

   https://doi.org/10.1115/1.4062303  

   Robson, Nina; Audrey, Vanessa; Dwivedi, Ashutosh; Kunzmann, Dylan (January 2024, Journal of Mechanisms and Robotics)

   Abstract This paper explores the kinematic synthesis, design, and pilot experimental testing of a six-legged walking robotic platform able to traverse through different terrains. We aim to develop a structured approach to designing the limb morphology using a relaxed kinematic task with incorporated conditions on foot-environments interaction, specifically contact force direction and curvature constraints, related to maintaining contact. The design approach builds up incrementally starting with studying the basic human leg walking trajectory and then defining a “relaxed” kinematic task. The “relaxed” kinematic task consists only of two contact locations (toe-off and heel-strike) with higher-order motion task specifications compatible with foot-terrain(s) contact and curvature constraints in the vicinity of the two contacts. As the next step, an eight-bar leg image is created based on the “relaxed” kinematic task and incorporated within a six-legged walking robot. Pilot experimental tests explore if the proposed approach results in an adaptable behavior which allows the platform to incorporate different walking foot trajectories and gait styles coupled to each environment. The results suggest that the proposed “relaxed” higher-order motion task combined with the leg morphological properties and feet material allowed the platform to walk stably on the different terrains. Here we would like to note that one of the main advantages of the proposed method in comparison with other existing walking platforms is that the proposed robotic platform has carefully designed limb morphology with incorporated conditions on foot-environment interaction. Additionally, while most of the existing multilegged platforms incorporate one actuator per leg, or per joint, our goal is to explore the possibility of using a single actuator to drive all six legs of the platform. This is a critical step which opens the door for the development of future transformative technology that is largely independent of human control and able to learn about the environment through their own sensory systems. 

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3. Contributions of spatial and temporal control of step length symmetry in the transfer of locomotor adaptation from a motorized to a non-motorized split-belt treadmill

   https://doi.org/10.1098/rsos.202084  

   Gregory, Daniel L.; Sup, Frank C.; Choi, Julia T. (February 2021, Royal Society Open Science)

   null (Ed.)

   Walking requires control of where and when to step for stable interlimb coordination. Motorized split-belt treadmills which constrain each leg to move at different speeds lead to adaptive changes to limb coordination that result in after-effects (e.g. gait asymmetry) on return to normal treadmill walking. These after-effects indicate an underlying neural adaptation. Here, we assessed the transfer of motorized split-belt treadmill adaptations with a custom non-motorized split-belt treadmill where each belt can be self-propelled at different speeds. Transfer was indicated by the presence of after-effects in step length, foot placement and step timing differences. Ten healthy participants adapted on a motorized split-belt treadmill (2 : 1 speed ratio) and were then assessed for after-effects during subsequent non-motorized treadmill and motorized tied-belt treadmill walking. We found that after-effects in step length difference during transfer to non-motorized split-belt walking were primarily associated with step time differences. Conversely, residual after-effects during motorized tied-belt walking following transfer were associated with foot placement differences. Our data demonstrate decoupling of adapted spatial and temporal locomotor control during transfer to a novel context, suggesting that foot placement and step timing control can be independently modulated during walking. 

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4. Human locomotor control timescales depend on the environmental context and sensory input modality

   Wang, W_C; De_Comite, A; Voloshina, A; Daley, M; Seethapathi, N (August 2025, arxiv.org)

   Everyday locomotion is a complex sensorimotor process that can unfold over multiple timescales, from long-term path planning to rapid, reactive adjustments. However, we lack an understanding of how factors such as environmental demands, or the available sensory information simultaneously influence these control timescales. To address this, we present a unified data-driven framework to quantify the control timescales by identifying how early we can predict future actions from past inputs. We apply this framework across tasks including walking and running, environmental contexts including treadmill, overground, and varied terrains, and sensory input modalities including gaze fixations and body states. We find that deep neural network architectures that effectively handle long-range dependencies, specifically Gated Recurrent Units and Transformers, outperform other architectures and widely used linear models when predicting future actions. Our framework reveals the factors that influence locomotor foot placement control timescales. Across environmental contexts, we discover that humans rely more on fast timescale control in more complex terrain. Across input modalities, we find a hierarchy of control timescales where gaze predicts foot placement before full-body states, which predict before center-of-mass states. Our model also identifies mid-swing as a critical phase when the swing foot's state predicts its future placement, with this timescale adapting across environments. Overall, this work offers data-driven insights into locomotor control in everyday settings, offering models that can be integrated with rehabilitation technologies and movement simulations to improve their applicability in everyday settings. 

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5. Reinforcement Learning for Safety-Critical Control under Model Uncertainty, using Control Lyapunov Functions and Control Barrier Functions

   Choi, Jason; Castañeda, Fernando; Tomlin, Claire J.; Sreenath, Koushil (July 2020, Robotics: Science and Systems (RSS))

   In this paper, the issue of model uncertainty in safety-critical control is addressed with a data-driven approach. For this purpose, we utilize the structure of an input-output linearization controller based on a nominal model along with a Control Barrier Function and Control Lyapunov Function based Quadratic Program (CBF-CLF-QP). Specifically, we propose a novel reinforcement learning framework which learns the model uncertainty present in the CBF and CLF constraints, as well as other control-affine dynamic constraints in the quadratic program. The trained policy is combined with the nominal model based CBF-CLF-QP, resulting in the Reinforcement Learning based CBF-CLF-QP (RL-CBF-CLF-QP), which addresses the problem of model uncertainty in the safety constraints. The performance of the proposed method is validated by testing it on an underactuated nonlinear bipedal robot walking on randomly spaced stepping stones with one step preview, obtaining stable and safe walking under model uncertainty. 

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