A robotic system can be viewed as a collection of lower-dimensional systems that are coupled via reaction forces (Lagrange multipliers) enforcing holonomic constraints. Inspired by this viewpoint, this paper presents a novel formulation for nonlinear control systems that are subject to coupling constraints via virtual "coupling" inputs that abstractly play the role of Lagrange multipliers. The main contribution of this paper is a process---mirroring solving for Lagrange multipliers in robotic systems---wherein we isolate subsystems free of coupling constraints that provably encode the full-order dynamics of the coupled control system from which it was derived. This dimension reduction is leveraged in the formulation of a nonlinear optimization problem for the isolated subsystem that yields periodic orbits for the full-order coupled system. We consider the application of these ideas to robotic systems, which can be decomposed into subsystems. Specifically, we view a quadruped as a coupled control system consisting of two bipedal robots, wherein applying the framework developed allows for gaits (periodic orbits) to be generated for the individual biped yielding a gait for the full-order quadruped. This is demonstrated through walking experiments of a quadrupedal robot in simulation and on rough terrains.
DreamWaQ++: Obstacle-Aware Quadrupedal Locomotion With Resilient Multi-Modal Reinforcement Learning
Urban Robotics Lab., School of Electrical Engineering, KAIST（韩国科学技术院电子工程系城市机器人实验室）；KRAFTON（KRAFTON公司）；URobotics（URobotics公司）；Laboratory for Information and Decision Systems (LIDS), MIT（麻省理工学院信息与决策系统实验室）
Learning Quadrupedal Locomotion over Challenging Terrain
Robotic Systems Lab, ETH Zurich（苏黎世联邦理工学院机器人系统实验室）；Robotics and Artificial Intelligence Lab, KAIST（韩国科学技术院机器人与人工智能实验室）；Intelligent Systems Lab, Intel（英特尔智能系统实验室）
SAC-Loco: Safe and Adjustable Compliant Quadrupedal Locomotion
Department of Electrical and Computer Engineering, National University of Singapore（新加坡国立大学电子与计算机工程系）；School of Computer Science and Engineering, Sun Yat-sen University（中山大学计算机科学与工程学院）
Effect of Gait Design on Proprioceptive Sensing of Terrain Properties in a Quadrupedal Robot
Department of Mechanical Engineering, Massachusetts Institute of Technology（机械工程系，麻省理工学院）；Ming Hsieh Department of Electrical and Computer Engineering, University of Southern California（Ming Hsieh 电子与计算机工程系，南加州大学）；Department of Earth and Environmental Science, University of Pennsylvania（地球与环境科学系，宾夕法尼亚大学）
本文对比四足机器人的Crawl N' Sense与Trot-Walk步态，证明慢速爬行步态能更稳定、准确地感知可变形地形强度及表面结壳破裂。
