The Cassie bipedal robot designed by Agility Robotics is providing academics a common platform for sharing and comparing algorithms for locomotion, perception, and navigation. This paper focuses on feedback control for standing and walking using the methods of virtual constraints and gait libraries. The designed controller was implemented six weeks after the robot arrived at the University of Michigan and allowed it to stand in place as well as walk over sidewalks, grass, snow, sand, and burning brush. The controller for standing also enables the robot to ride a Segway. A model of the Cassie robot has been placed on GitHub and the controller will also be made open source if the paper is accepted.

reflects the opinions and conclusions of its authors and not the funding entities. Dr. M Ghaffari offered advice during the course of this project. The first author thanks Wonhui Kim for useful conversations and Ray Zhang for generating the semantic image.

The factor graph framework is a convenient modeling technique for robotic state estimation where states are represented as nodes, and measurements are modeled as factors. When designing a sensor fusion framework for legged robots, one often has access to visual, inertial, joint encoder, and contact sensors. While visual-inertial odometry has been studied extensively in this framework, the addition of a preintegrated contact factor for legged robots has been only recently proposed. This allowed for integration of encoder and contact measurements into existing factor graphs, however, new nodes had to be added to the graph every time contact was made or broken. In this work, to cope with the problem of switching contact frames, we propose a hybrid contact preintegration theory that allows contact information to be integrated through an arbitrary number of contact switches. The proposed hybrid modeling approach reduces the number of required variables in the nonlinear optimization problem by only requiring new states to be added alongside camera or selected keyframes. This method is evaluated using real experimental data collected from a Cassie-series robot where the trajectory of the robot produced by a motion capture system is used as a proxy for ground truth. The evaluation shows that inclusion of the proposed preintegrated hybrid contact factor alongside visual-inertial navigation systems improves estimation accuracy as well as robustness to vision failure, while its generalization makes it more accessible for legged platforms.

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We propose and experimentally demonstrate a reactive planning system for bipedal robots on unexplored, challenging terrains. The system consists of a low-frequency planning thread (5 Hz) to find an asymptotically optimal path and a high-frequency reactive thread (300 Hz) to accommodate robot deviation. The planning thread includes: a multi-layer local map to compute traversability for the robot on the terrain; an anytime omnidirectional Control Lyapunov Function (CLF) for use with a Rapidly Exploring Random Tree Star (RRT*) that generates a vector field for specifying motion between nodes; a sub-goal finder when the final goal is outside of the current map; and a finite-state machine to handle high-level mission decisions. The system also includes a reactive thread to obviate the non-smooth motions that arise with traditional RRT* algorithms when performing path following. The reactive thread copes with robot deviation while eliminating non-smooth motions via a vector field (defined by a closed-loop feedback policy) that provides real-time control commands to the robot's gait controller as a function of instantaneous robot pose. The system is evaluated on various challenging outdoor terrains and cluttered indoor scenes in both simulation and experiment on Cassie Blue, a bipedal robot with 20 degrees of freedom. All implementations are coded in C++ with the Robot Operating System (ROS) and are available at https://github.com/UMich-BipedLab/CLF_reactive_planning_system.