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1. Quadrupedal Robotic Walking on Sloped Terrains via Exact Decomposition into Coupled Bipedal Robots

   https://doi.org/10.1109/IROS45743.2020.9341181  

   Ma, Wen-Loong ; Csomay-Shanklin, Noel ; Ames, Aaron D. ( October 2020 , IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS))

   null (Ed.)

   Can we design motion primitives for complex legged systems uniformly for different terrain types without neglecting modeling details? This paper presents a method for rapidly generating quadrupedal locomotion on sloped terrains-from modeling to gait generation, to hardware demonstration. At the core of this approach is the observation that a quadrupedal robot can be exactly decomposed into coupled bipedal robots. Formally, this is represented through the framework of coupled control systems, wherein isolated subsystems interact through coupling constraints. We demonstrate this concept in the context of quadrupeds and use it to reduce the gait planning problem for uneven terrains to bipedal walking generation via hybrid zero dynamics. This reduction method allows for the formulation of a nonlinear optimization problem that leverages low-dimensional bipedal representations to generate dynamic walking gaits on slopes for the full-order quadrupedal robot dynamics. The result is the ability to rapidly generate quadrupedal walking gaits on a variety of slopes. We demonstrate these walking behaviors on the Vision 60 quadrupedal robot; in simulation, via walking on a range of sloped terrains of 13°, 15°, 20°, 25°, and, experimentally, through the successful locomotion of 13° and 20° ~ 25° sloped outdoor grasslands. 

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2. Dynamic Walking: Toward Agile and Efficient Bipedal Robots

   https://doi.org/10.1146/annurev-control-071020-045021  

   Reher, Jenna ; Ames, Aaron D. ( May 2021 , Annual Review of Control, Robotics, and Autonomous Systems)

   null (Ed.)

   Dynamic walking on bipedal robots has evolved from an idea in science fiction to a practical reality. This is due to continued progress in three key areas: a mathematical understanding of locomotion, the computational ability to encode this mathematics through optimization, and the hardware capable of realizing this understanding in practice. In this context, this review outlines the end-to-end process of methods that have proven effective in the literature for achieving dynamic walking on bipedal robots. We begin by introducing mathematical models of locomotion, from reduced-order models that capture essential walking behaviors to hybrid dynamical systems that encode the full-order continuous dynamics along with discrete foot-strike dynamics. These models form the basis for gait generation via (nonlinear) optimization problems. Finally, models and their generated gaits merge in the context of real-time control, wherein walking behaviors are translated to hardware. The concepts presented are illustrated throughout in simulation, and experimental instantiations on multiple walking platforms are highlighted to demonstrate the ability to realize dynamic walking on bipedal robots that is both agile and efficient. 

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3. Autonomous navigation of underactuated bipedal robots in height-constrained environments

   https://doi.org/10.1177/02783649231187670  

   Li, Zhongyu ; Zeng, Jun ; Chen, Shuxiao ; Sreenath, Koushil ( July 2023 , The International Journal of Robotics Research)

   Navigating a large-scaled robot in unknown and cluttered height-constrained environments is challenging. Not only is a fast and reliable planning algorithm required to go around obstacles, the robot should also be able to change its intrinsic dimension by crouching in order to travel underneath height-constrained regions. There are few mobile robots that are capable of handling such a challenge, and bipedal robots provide a solution. However, as bipedal robots have nonlinear and hybrid dynamics, trajectory planning while ensuring dynamic feasibility and safety on these robots is challenging. This paper presents an end-to-end autonomous navigation framework which leverages three layers of planners and a variable walking height controller to enable bipedal robots to safely explore height-constrained environments. A vertically actuated spring-loaded inverted pendulum (vSLIP) model is introduced to capture the robot’s coupled dynamics of planar walking and vertical walking height. This reduced-order model is utilized to optimize for long-term and short-term safe trajectory plans. A variable walking height controller is leveraged to enable the bipedal robot to maintain stable periodic walking gaits while following the planned trajectory. The entire framework is tested and experimentally validated using a bipedal robot Cassie. This demonstrates reliable autonomy to drive the robot to safely avoid obstacles while walking to the goal location in various kinds of height-constrained cluttered environments.

    

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4. Optimizing Bipedal Maneuvers of Single Rigid-Body Models for Reinforcement Learning

   https://doi.org/10.1109/Humanoids53995.2022.9999741  

   Batke, Ryan ; Yu, Fangzhou ; Dao, Jeremy ; Hurst, Jonathan ; Hatton, Ross L. ; Fern, Alan ; Green, Kevin ( November 2022 , 2022 IEEE-RAS 21st International Conference on Humanoid Robots (Humanoids))

   In this work, we propose a method to generate reduced-order model reference trajectories for general classes of highly dynamic maneuvers for bipedal robots for use in sim-to-real reinforcement learning. Our approach is to utilize a single rigid-body model (SRBM) to optimize libraries of trajectories offline to be used as expert references that guide learning by regularizing behaviors when incorporated in the reward function of a learned policy. This method translates the model's dynamically rich rotational and translational behavior to a full-order robot model and successfully transfers to real hardware. The SRBM's simplicity allows for fast iteration and refinement of behaviors, while the robustness of learning-based controllers allows for highly dynamic motions to be transferred to hardware. Within this work we introduce a set of transferability constraints that amend the SRBM dynamics to actual bipedal robot hardware, our framework for creating optimal trajectories for a variety of highly dynamic maneuvers as well as our approach to integrating reference trajectories for a high-speed running reinforcement learning policy. We validate our methods on the bipedal robot Cassie on which we were successfully able to demonstrate highly dynamic grounded running gaits up to 3.0 m/s. 

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5. Bipedal Model and Hybrid Zero Dynamics of Human Walking With Foot Slip

   https://doi.org/10.1115/1.4043360  

   Trkov, Mitja ; Chen, Kuo ; Yi, Jingang ( October 2019 , Journal of Computational and Nonlinear Dynamics)

   null (Ed.)

   Abstract Foot slip is one of the major causes of falls in human locomotion. Analytical bipedal models provide an insight into the complex slip dynamics and reactive control strategies for slip-induced fall prevention. Most of the existing bipedal dynamics models are built on no foot slip assumption and cannot be used directly for such analysis. We relax the no-slip assumption and present a new bipedal model to capture and predict human walking locomotion under slip. We first validate the proposed slip walking dynamic model by tuning and optimizing the model parameters to match the experimental results. The results demonstrate that the model successfully predicts both the human walking and recovery gaits with slip. Then, we extend the hybrid zero dynamics (HZD) model and properties to capture human walking with slip. We present the closed-form of the HZD for human walking and discuss the transition between the nonslip and slip states through slip recovery control design. The analysis and design are illustrated through human walking experiments. The models and analysis can be further used to design and control wearable robotic assistive devices to prevent slip-and-fall. 

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