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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. 

Complex robotic systems require whole-body controllers to handle contact interactions, handle closed kinematic chains, and track task-space control objectives. However, for many applications, safety-critical controllers are essential to steer away from undesired robot configurations and prevent unsafe behaviors. A prime example is legged robotics, where we can have tasks such as balance control, regulation of torso orientation, and, most importantly, walking. As the coordination of multi-body systems is non-trivial, following a combination of those tasks might lead to configurations that are deemed dangerous, such as stepping on its support foot during walking, leaning the torso excessively, or producing excessive centroidal momentum, resulting in non-human-like walking. To address these challenges, we propose a formulation of an inverse dynamics control enhanced with control barrier functions that allow general higher-order relative degree safe sets for robotic systems with numerous degrees of freedom. Our approach utilizes a quadratic program that respects closed kinematic chains, minimizes the control objectives, and imposes desired constraints on the Zero Moment Point, friction cone, and torque. More importantly, it also ensures the forward invariance of a general user-defined high Relative-Degree safety set. We demonstrate the effectiveness of our method by applying it to the 3D biped robot Digit, both in simulation and with hardware experiments. 

The Angular-Momentum Linear Inverted Pendulum (ALIP) model is a promising motion planner for bipedal robots. However, it relies on two assumptions: (1) the robot has point-contact feet or passive ankles, and (2) the angular momentum around the center of mass, known as centroidal angular momentum, is negligible. This paper addresses the question of whether the ALIP paradigm can be applied to more general bipedal systems with complex foot geometry (e.g., flat feet) and nontrivial torso/limb inertia and mass distribution (e.g., non-centralized arms). In such systems, the dynamics introduce non-negligible centroidal momentum and contact wrenches at the feet, rendering the assumptions of the ALIP model invalid. This paper presents the ALIP planner for general bipedal robots with non-point-contact feet through the use of a task-space whole-body controller that regulates centroidal momentum, thereby ensuring that the robot's behavior aligns with the desired template dynamics. To demonstrate the effectiveness of our proposed approach, we conduct simulations using the Sarcos©Guardian® XO®robot, which is a hybrid humanoid/exoskeleton with large, offset feet. The results demonstrate the practicality and effectiveness of our approach in achieving stable and versatile bipedal locomotion. 

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. 

We present a framework to generate periodic trajectory references for a 3D under-actuated bipedal robot, using a linear inverted pendulum (LIP) based controller with adaptive neural regulation. We use the LIP template model to estimate the robot's center of mass (CoM) position and velocity at the end of the current step, and formulate a discrete controller that determines the next footstep location to achieve a desired walking profile. This controller is equipped on the frontal plane with a Neural-Network-based adaptive term that reduces the model mismatch between the template and physical robot that particularly affects the lateral motion. Then, the foot placement location computed for the LIP model is used to generate task space trajectories (CoM and swing foot trajectories) for the actual robot to realize stable walking. We use a fast, real-time QP-based inverse kinematics algorithm that produces joint references from the task space trajectories, which makes the formulation independent of the knowledge of the robot dynamics. Finally, we implemented and evaluated the proposed approach in simulation and hardware experiments with a Digit robot obtaining stable periodic locomotion for both cases. 

Controlling a bipedal robot that walks on a dynamic rigid surface (DRS) is a challenging task due to the complexity of the associated robot dynamics. We introduce a hybrid linear inverted pendulum (LIP) model for underactuated bipedal walking on a DRS. We also propose a discrete-time stepping controller to provably stabilize the periodic gait of the hybrid LIP.