Vision-aided Dynamic Quadrupedal Locomotion on Discrete Terrain using Motion Libraries

In this paper, we present a framework rooted in control and planning that enables quadrupedal robots to traverse challenging terrains with discrete footholds using visual feedback. Navigating discrete terrain is challenging for quadrupeds because the motion of the robot can be aperiodic, highly dynamic, and blind for the hind legs of the robot. Additionally, the robot needs to reason over both the feasible footholds as well as robot velocity by speeding up and slowing down at different parts of the terrain. We build an offline library of periodic gaits which span two trotting steps on the robot, and switch between different motion primitives to achieve aperiodic motions of different step lengths on an A1 robot. The motion library is used to provide targets to a geometric model predictive controller which controls stance. To incorporate visual feedback, we use terrain mapping tools to build a local height map of the terrain around the robot using RGB and depth cameras, and extract feasible foothold locations around both the front and hind legs of the robot. Our experiments show a Unitree A1 robot navigating multiple unknown, challenging and discrete terrains in the real world.

[1]  R. Siegwart,et al.  ROBOT-CENTRIC ELEVATION MAPPING WITH UNCERTAINTY ESTIMATES , 2014 .

[2]  Aaron Ames,et al.  Bipedal Walking on Constrained Footholds: Momentum Regulation via Vertical COM Control , 2021, 2022 International Conference on Robotics and Automation (ICRA).

[3]  Maani Ghaffari,et al.  Contact-aided invariant extended Kalman filtering for robot state estimation , 2020, Int. J. Robotics Res..

[4]  Jerry Pratt,et al.  Velocity-Based Stability Margins for Fast Bipedal Walking , 2006 .

[5]  Koushil Sreenath,et al.  Safety-Critical Control for Dynamical Bipedal Walking with Precise Footstep Placement , 2015, ADHS.

[6]  Xingye Da,et al.  GLiDE: Generalizable Quadrupedal Locomotion in Diverse Environments with a Centroidal Model , 2021, ArXiv.

[7]  Koushil Sreenath,et al.  Dynamic bipedal locomotion over stochastic discrete terrain , 2018, Int. J. Robotics Res..

[8]  Koushil Sreenath,et al.  Dynamic Walking on Randomly-Varying Discrete Terrain with One-step Preview , 2017, Robotics: Science and Systems.

[9]  Koushil Sreenath,et al.  Dynamic Walking on Stepping Stones with Gait Library and Control Barrier Functions , 2016, WAFR.

[10]  Ayush Agrawal,et al.  Bipedal Robotic Running on Stochastic Discrete Terrain , 2019, 2019 18th European Control Conference (ECC).

[11]  A. D. Lewis,et al.  Geometric control of mechanical systems : modeling, analysis, and design for simple mechanical control systems , 2005 .

[12]  Sangbae Kim,et al.  Dynamic Locomotion in the MIT Cheetah 3 Through Convex Model-Predictive Control , 2018, 2018 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS).

[13]  Joonho Lee,et al.  DeepGait: Planning and Control of Quadrupedal Gaits Using Deep Reinforcement Learning , 2020, IEEE Robotics and Automation Letters.

[14]  Aaron D. Ames,et al.  3D dynamic walking with underactuated humanoid robots: A direct collocation framework for optimizing hybrid zero dynamics , 2016, 2016 IEEE International Conference on Robotics and Automation (ICRA).

[15]  Michiel van de Panne,et al.  ALLSTEPS: Curriculum‐driven Learning of Stepping Stone Skills , 2020, Comput. Graph. Forum.

[16]  Koushil Sreenath,et al.  3D dynamic walking on stepping stones with control barrier functions , 2016, 2016 IEEE 55th Conference on Decision and Control (CDC).

[17]  Richard M. Murray,et al.  A Mathematical Introduction to Robotic Manipulation , 1994 .

[18]  Koushil Sreenath,et al.  The Reaction Mass Biped: Geometric Mechanics and Control , 2018, J. Intell. Robotic Syst..

[19]  Taeyoung Lee,et al.  Control of Complex Maneuvers for a Quadrotor UAV using Geometric Methods on SE(3) , 2010, ArXiv.

[20]  Guofan Wu,et al.  Variation-Based Linearization of Nonlinear Systems Evolving on SO(3) and 𝕊2 , 2015, IEEE Access.

[21]  Claudio Semini,et al.  MPC-based Controller with Terrain Insight for Dynamic Legged Locomotion , 2020, 2020 IEEE International Conference on Robotics and Automation (ICRA).

[22]  Patrick M. Wensing,et al.  Variational-Based Optimal Control of Underactuated Balancing for Dynamic Quadrupeds , 2020, IEEE Access.

[23]  Jessy W. Grizzle,et al.  Rapid Trajectory optimization Using C-FROST with Illustration on a Cassie-Series Dynamic Walking Biped , 2018, 2019 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS).

[24]  Koushil Sreenath,et al.  Deep visual perception for dynamic walking on discrete terrain , 2017, 2017 IEEE-RAS 17th International Conference on Humanoid Robotics (Humanoids).

[25]  Kazuhito Yokoi,et al.  Biped walking pattern generation by using preview control of zero-moment point , 2003, 2003 IEEE International Conference on Robotics and Automation (Cat. No.03CH37422).

[26]  Stephen P. Boyd,et al.  OSQP: an operator splitting solver for quadratic programs , 2017, 2018 UKACC 12th International Conference on Control (CONTROL).

[27]  Marco Hutter,et al.  Probabilistic Terrain Mapping for Mobile Robots With Uncertain Localization , 2018, IEEE Robotics and Automation Letters.

[28]  Aaron D. Ames,et al.  Multi-Layered Safety for Legged Robots via Control Barrier Functions and Model Predictive Control , 2020, 2021 IEEE International Conference on Robotics and Automation (ICRA).

[29]  Seungwoo Hong,et al.  Real-Time Constrained Nonlinear Model Predictive Control on SO(3) for Dynamic Legged Locomotion* , 2020, 2020 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS).