Jessy Grizzle

Yuxiao Chen, Ayonga Hereid, Huei Peng et al.

Correct-by-construction techniques, such as control barrier functions (CBFs), can be used to guarantee closed-loop safety by acting as a supervisor of an existing or legacy controller. However, supervisory-control intervention typically compromises the performance of the closed-loop system. On the other hand, machine learning has been used to synthesize controllers that inherit good properties from a training dataset, though safety is typically not guaranteed due to the difficulty of analyzing the associated neural network. In this paper, supervised learning is combined with CBFs to synthesize controllers that enjoy good performance with provable safety. A training set is generated by trajectory optimization that incorporates the CBF constraint for an interesting range of initial conditions of the truck model. A control policy is obtained via supervised learning that maps a feature representing the initial conditions to a parameterized desired trajectory. The learning-based controller is used as the performance controller and a CBF-based supervisory controller guarantees safety. A case study of lane keeping for articulated trucks shows that the controller trained by supervised learning inherits the good performance of the training set and rarely requires intervention by the CBF supervisor

Odest Chadwicke Jenkins, Jessy Grizzle, Ella Atkins et al.

The Robotics Major at the University of Michigan was successfully launched in the 2022-23 academic year as an innovative step forward to better serve students, our communities, and our society. Building on our guiding principle of "Robotics with Respect" and our larger Robotics Pathways model, the Michigan Robotics Major was designed to define robotics as a true academic discipline with both equity and excellence as our highest priorities. Understanding that talent is equally distributed but opportunity is not, the Michigan Robotics Major has embraced an adaptable curriculum that is accessible through a diversity of student pathways and enables successful and sustained career-long participation in robotics, AI, and automation professions. The results after our planning efforts (2019-22) and first academic year (2022-23) have been highly encouraging: more than 100 students declared Robotics as their major, completion of the Robotics major by our first two graduates, soaring enrollments in our Robotics classes, thriving partnerships with Historically Black Colleges and Universities. This document provides our original curricular proposal for the Robotics Undergraduate Program at the University of Michigan, submitted to the Michigan Association of State Universities in April 2022 and approved in June 2022. The dissemination of our program design is in the spirit of continued growth for higher education towards realizing equity and excellence. The most recent version of this document is also available on Google Docs through this link: https://ocj.me/robotics_major

Yukai Gong, Ross Hartley, Xingye Da et al.

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.

Grant Gibson, Oluwami Dosunmu-Ogunbi, Yukai Gong et al.

This paper presents a gait controller for bipedal robots to achieve highly agile walking over various terrains given local slope and friction cone information. Without these considerations, untimely impacts can cause a robot to trip and inadequate tangential reaction forces at the stance foot can cause slippages. We address these challenges by combining, in a novel manner, a model based on an Angular Momentum Linear Inverted Pendulum (ALIP) and a Model Predictive Control (MPC) foot placement planner that is executed by the method of virtual constraints. The process starts with abstracting from the full dynamics of a Cassie 3D bipedal robot, an exact low-dimensional representation of its center of mass dynamics, parameterized by angular momentum. Under a piecewise planar terrain assumption and the elimination of terms for the angular momentum about the robot's center of mass, the centroidal dynamics about the contact point become linear and have dimension four. Importantly, we include the intra-step dynamics at uniformly-spaced intervals in the MPC formulation so that realistic workspace constraints on the robot's evolution can be imposed from step-to-step. The output of the low-dimensional MPC controller is directly implemented on a high-dimensional Cassie robot through the method of virtual constraints. In experiments, we validate the performance of our control strategy for the robot on a variety of surfaces with varied inclinations and textures.

Yukai Gong, Jessy Grizzle

Low-dimensional models are ubiquitous in the bipedal robotics literature. On the one hand is the community of researchers that bases feedback control design on pendulum models selected to capture the center of mass dynamics of the robot during walking. On the other hand is the community that bases feedback control design on virtual constraints, which induce an exact low-dimensional model in the closed-loop system. In the first case, the low-dimensional model is valued for its physical insight and analytical tractability. In the second case, the low-dimensional model is integral to a rigorous analysis of the stability of walking gaits in the full-dimensional model of the robot. This paper seeks to clarify the commonalities and differences in the two perspectives for using low-dimensional models. In the process of doing so, we argue that angular momentum about the contact point is a better indicator of robot state than linear velocity. Concretely, we show that an approximate (pendulum and zero dynamics) model parameterized by angular momentum provides better predictions for foot placement on a physical robot (e.g., legs with mass) than does a related approximate model parameterized in terms of linear velocity. We implement an associated angular-momentum-based controller on Cassie, a 3D robot, and demonstrate high agility and robustness in experiments.

Yukai Gong, Jessy Grizzle

In the control of bipedal locomotion, linear velocity of the center of mass has been widely accepted as a primary variable for summarizing a robot's state vector. The ubiquitous massless-legged linear inverted pendulum (LIP) model is based on it. In this paper, we argue that angular momentum about the contact point has several properties that make it superior to linear velocity for feedback control. So as not to confuse the benefits of angular momentum with any other control design decisions, we first reformulate the standard LIP controller in terms of angular momentum. We then implement the resulting feedback controller on the 20 degree-of-freedom bipedal robot, Cassie Blue, where each leg accounts for nearly one-third of the robot's total mass of 35~Kg. Under this controller, the robot achieves fast walking, rapid turning while walking, large disturbance rejection, and locomotion on rough terrain. The reasoning developed in the paper is applicable to other control design philosophies, whether they be Hybrid Zero Dynamics or Reinforcement Learning.

Omar Harib, Ayonga Hereid, Ayush Agrawal et al.

This manuscript presents control of a high-DOF fully actuated lower-limb exoskeleton for paraplegic individuals. The key novelty is the ability for the user to walk without the use of crutches or other external means of stabilization. We harness the power of modern optimization techniques and supervised machine learning to develop a smooth feedback control policy that provides robust velocity regulation and perturbation rejection. Preliminary evaluation of the stability and robustness of the proposed approach is demonstrated through the Gazebo simulation environment. In addition, preliminary experimental results with (complete) paraplegic individuals are included for the previous version of the controller.

Christine Chevallereau, Hamed Razavi, Damien Six et al.

This paper seeks insight into stabilization mechanisms for periodic walking gaits in 3D bipedal robots. Based on this insight, a control strategy based on virtual constraints, which imposes coordination between joints rather than a temporal evolution, will be proposed for achieving asymptotic convergence toward a periodic motion. For planar bipeds with one degree of underactuation, it is known that a vertical displacement of the center of mass---with downward velocity at the step transition---induces stability of a walking gait. This paper concerns the qualitative extension of this type of property to 3D walking with two degrees of underactuation. It is shown that a condition on the position of the center of mass in the horizontal plane at the transition between steps induces synchronization between the motions in the sagittal and frontal planes. A combination of the conditions for self-synchronization and vertical oscillations leads to stable gaits. The algorithm for self-stabilization of 3D walking gaits is first developed for a simplified model of a walking robot (an inverted pendulum with variable length legs), and then it is extended to a complex model of the humanoid robot Romeo using the notion of Hybrid Zero Dynamics. Simulations of the model of the robot illustrate the efficacy of the method and its robustness.