Search for: All records

This paper introduces an analytically tractable and computationally efficient model for legged robot dynamics during locomotion on a dynamic rigid surface (DRS), along with an approximate analytical solution and a real-time walking pattern generator synthesized based on the model and solution. By relaxing the static-surface assumption, we extend the classical, time-invariant linear inverted pendulum (LIP) model for legged locomotion on a static surface to dynamic-surface locomotion, resulting in a time-varying LIP model termed as “DRS-LIP”. Sufficient and necessary stability conditions of the time-varying DRS-LIP model are obtained based on the Floquet theory. This model is also transformed into Mathieu’s equation to derive an approximate analytical solution that provides reasonable accuracy with a relatively low computational cost. Using the extended model and its solution, a walking pattern generator is developed to efficiently plan physically feasible trajectories for quadrupedal walking on a vertically oscillating surface. Finally, simulations and hardware experiments from a Laikago quadrupedal robot walking on a pitching treadmill (with a maximum vertical acceleration of 1 m/s ) confirm the accuracy and efficiency of the proposed analytical solution, as well as the efficiency, feasibility, and robustness of the pattern generator, under various surface motions and gait parameters. 

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. 

Abstract A safety-critical measure of legged locomotion performance is a robot's ability to track its desired time-varying position trajectory in an environment, which is herein termed as “global-position tracking.” This paper introduces a nonlinear control approach that achieves asymptotic global-position tracking for three-dimensional (3D) bipedal robots. Designing a global-position tracking controller presents a challenging problem due to the complex hybrid robot model and the time-varying desired global-position trajectory. Toward tackling this problem, the first main contribution is the construction of impact invariance to ensure all desired trajectories respect the foot-landing impact dynamics, which is a necessary condition for realizing asymptotic tracking of hybrid walking systems. Thanks to their independence of the desired global position, these conditions can be exploited to decouple the higher-level planning of the global position and the lower-level planning of the remaining trajectories, thereby greatly alleviating the computational burden of motion planning. The second main contribution is the Lyapunov-based stability analysis of the hybrid closed-loop system, which produces sufficient conditions to guide the controller design for achieving asymptotic global-position tracking during fully actuated walking. Simulations and experiments on a 3D bipedal robot with twenty revolute joints confirm the validity of the proposed control approach in guaranteeing accurate tracking. 

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. 

Abstract This paper introduces an adaptive robust trajectory tracking controller design to provably realize stable bipedal robotic walking under parametric and unmodeled uncertainties. Deriving such a controller is challenging mainly because of the highly complex bipedal walking dynamics that are hybrid and involve nonlinear, uncontrolled state-triggered jumps. The main contribution of the study is the synthesis of a continuous-phase adaptive robust tracking control law for hybrid models of bipedal robotic walking by incorporating the construction of multiple Lyapunov functions into the control Lyapunov function. The evolution of the Lyapunov function across the state-triggered jumps is explicitly analyzed to construct sufficient conditions that guide the proposed control design for provably guaranteeing the stability and tracking the performance of the hybrid system in the presence of uncertainties. Simulation results on fully actuated bipedal robotic walking validate the effectiveness of the proposed approach in walking stabilization under uncertainties.