Stair Climbing using the Angular Momentum Linear Inverted Pendulum Model and Model Predictive Control

TL;DR

This paper explores a variation of the ALIP model that allows the length of the virtual pendulum formed by the robot's stance foot and center of mass to follow smooth trajectories during a step and couple this model with a control strategy constructed from a novel combination of virtual constraint-based control and a model predictive control algorithm to stabilize a stair climbing gait that does not soley rely on foot placement.

Abstract

A new control paradigm using angular momentum and foot placement as state variables in the linear inverted pendulum model has expanded the realm of possibilities for the control of bipedal robots. This new paradigm, known as the ALIP model, has shown effectiveness in cases where a robot's center of mass height can be assumed to be constant or near constant as well as in cases where there are no non-kinematic restrictions on foot placement. Walking up and down stairs violates both of these assumptions, where center of mass height varies significantly within a step and the geometry of the stairs restrict the effectiveness of foot placement. In this paper, we explore a variation of the ALIP model that allows the length of the virtual pendulum formed by the robot's stance foot and center of mass to follow smooth trajectories during a step. We couple this model with a control strategy constructed from a novel combination of virtual constraint-based control and a model predictive control algorithm to stabilize a stair climbing gait that does not soley rely on foot placement. Simulations on a 20-degree of freedom model of the Cassie biped in the SimMechanics simulation environment show that the controller is able to achieve periodic gait.

Figures (10)

• Figure 1: The underactuated Cassie biped walking up stairs in the SimMechanics Simulation environment.
• Figure 2: Schematic of an inverted pendulum to derive a variation on the ALIP model.
• Figure 3: 3D model of the Cassie robot in the SimMechanics simulation environment.
• Figure 4: Angular momentum and CoM angle during simulation where robot stands for two seconds, steps in place for the next four seconds, and then is commanded to walk forward at 0.5 m/s for the remainder of the simulation runtime. Fixed step gait is turned on at the 12 second mark. Two test results are shown, (a) not using ankle torque during fixed step, and (b) using ankle torque during fixed step.
• Figure 5: Angular momentum and CoM angle over time with and without ankle torque to stabilize marching in place with perturbations at $t=3$ sec (a) without ankle torque and (b) with ankle torque. Note, that only the relevant time portion of the plot is shown ($2 < t < 8$) to highlight the effects of the perturbation. In (a), there is no data after $\sim 3.8$ sec because the simulation fails at this time. Data continues until the end of the simulation for (b) because the robot is able to fully recover after the perturbation.