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Locomotion on dynamic rigid surface (i.e., rigid surface accelerating in an inertial frame) presents complex challenges for controller design, which are essential to address for deploying humanoid robots in dynamic real-world environments such as moving trains, ships, and airplanes. This paper introduces a real-time, provably stabilizing control approach for humanoid walking on periodically swaying rigid surface. The first key contribution is an analytical extension of the classical angular momentum-based linear inverted pendulum model from static to swaying grounds whose motion period may be different than the robot’s gait period. This extension results in a time-varying, nonhomogeneous robot model, which is fundamentally different from the existing pendulum models. We synthesize a discrete footstep control law for the model and derive a new set of sufficient stability conditions that verify the controller’s stabilizing effect. Finally, experiments conducted on a Digit humanoid robot, both in simulations and on hardware, demonstrate the framework’s effectiveness in addressing bipedal locomotion on swaying ground, even under uncertain surface motions and unknown external pushes. 

Controller design for bipedal walking on dynamic rigid surfaces (DRSes), which are rigid surfaces moving in the inertial frame (e.g., ships and airplanes), remains largely underexplored. This paper introduces a hierarchical control approach that achieves stable underactuated bipedal walking on a horizontally oscillating DRS. The highest layer of our approach is a real-time motion planner that generates desired global behaviors (i.e., center of mass trajectories and footstep locations) by stabilizing a reduced-order robot model. One key novelty of this layer is the derivation of the reduced-order model by analytically extending the angular momentum based linear inverted pendulum (ALIP) model from stationary to horizontally moving surfaces. The other novelty is the development of a discrete-time foot-placement controller that exponentially stabilizes the hybrid, linear, time-varying ALIP. The middle layer translates the desired global behaviors into the robot’s full-body reference trajectories for all directly actuated degrees of freedom, while the lowest layer exponentially tracks those reference trajectories based on the full-order, hybrid, nonlinear robot model. Simulations confirm that the proposed framework ensures stable walking of a planar underactuated biped under different swaying DRS motions and gait types. 

Ultimately, feedback control is about making adjustments using current state information in order to meet an objective in the future. In the control of bipedal locomotion, linear velocity of the center of mass has been widely accepted as the primary variable around which feedback control objectives are formulated. In this paper, we argue that it is easier to predict the one-step ahead evolution of angular momentum about the contact point than it is to make a similar prediction for linear velocity, and hence it provides a superior quantity for feedback control. So as not to confuse the benefits of predicting angular momentum with any other control design decisions, we reformulate the standard LIP model in terms of angular momentum and show how to regulate swing foot touchdown position at the end of the current step so as to meet an angular momentum objective at the end of the next step. We implement the resulting feedback controller on the 20 degreeof- freedom bipedal robot, Cassie Blue, where each leg accounts for nearly one-third of the robot’s total mass of 32 Kg. Under this controller, the robot achieves fast walking, rapid turning while walking, large disturbance rejection, and locomotion on rough terrain. 

This paper reports on developing an integrated framework for safety-aware informative motion planning suitable for legged robots. The information-gathering planner takes a dense stochastic map of the environment into account, while safety constraints are enforced via Control Barrier Functions (CBFs). The planner is based on the Incrementally-exploring Information Gathering (IIG) algorithm and allows closed-loop kinodynamic node expansion using a Model Predictive Control (MPC) formalism. Robotic exploration and information gathering problems are inherently path-dependent problems. That is, the information collected along a path depends on the state and observation history. As such, motion planning solely based on a modular cost does not lead to suitable plans for exploration. We propose SAFE-IIG, an integrated informative motion planning algorithm that takes into account: 1) a robot’s perceptual field of view via a submodular information function computed over a stochastic map of the environment, 2) a robot’s dynamics and safety constraints via discrete-time CBFs and MPC for closedloop multi-horizon node expansions, and 3) an automatic stopping criterion via setting an information-theoretic planning horizon. The simulation results show that SAFE-IIG can plan a safe and dynamically feasible path while exploring a dense map. 

One of the big attractions of low-dimensional models for gait design has been the ability to compute solutions rapidly, whereas one of their drawbacks has been the difficulty in mapping the solutions back to the target robot. This paper presents a set of tools for rapidly determining solutions for “humanoids” without removing or lumping degrees of freedom. The main tools are: (1) C-FROST, an open-source C++ interface for FROST, a direct collocation optimization tool; and (2) multithreading. The results will be illustrated on a 20-DoF floatingbase model for a Cassie-series bipedal robot through numerical calculations and physical experiments. 

The Cassie bipedal robot designed by Agility Robotics is providing academics with 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. Software supporting the work in this paper is available on GitHub.