Moving past point-contacts: Extending the ALIP model to humanoids with non-trivial feet using hierarchical, full-body momentum control

TL;DR

Problem: ALIP assumes point-contact feet and negligible centroidal momentum, limiting applicability to general humanoids with complex feet and distributed limb masses. Approach: develop a task-space, full-body hierarchical momentum controller that enforces ALIP-like behavior by regulating centroidal momentum and projecting dynamics to a user-defined contact frame, while a sagittal/frontal ALIP planner computes foot placements to realize the template. Contributions: (i) conditions under which full humanoid dynamics can be captured by ALIP, (ii) a HQP-based controller that enforces these conditions, and (iii) extension of the ALIP planner to non-point-contact feet with large, offset feet and non-centralized arms, demonstrated in MuJoCo on the Guardian XO. Findings: the controller tracks the ALIP references, minimizes centroidal angular momentum, maintains constant CoM height, and achieves stable forward and lateral gaits up to 0.45 m/s forward and 0.225 m/s lateral. Significance: broadens ALIP applicability to industrial humanoids and exoskeleton hybrids, enabling robust, real-time locomotion on robots with nontrivial feet and inertia.

Abstract

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.

Figures (9)

• Figure 1: During the single support phase, the bipedal robot will experience a resolved contact wrench $\vec{\lambda}_{\space c}=[\vec{\tau}_{\space c}^\top~\vec{f}_{c}^{\space\top}]^\top$ at the reference contact frame $\{c\}$ (assuming that the no-slip contact constraint is maintained).
• Figure 2: Representation of the ALIP model walking with positive velocity in the sagittal and frontal planes for two consecutive steps delimited by the impacts $\{k-1, k, k+1\}$ with the states before (-) and after the impact (+). Ideally the states converge such that $\vec{x}_k^{\space-} = \vec{x}_{k+1}^{\space-}$ and $\vec{y}_k^{\space-} = \vec{y}_{k+1}^{\space-}$.
• Figure 3: Phase portrait for the sagittal and frontal plane of motion. The ALIP template produces stable hybrid orbits represented by the thick grey lines for the continuous part of the dynamics and the dashed lines for the instantaneous impact. Note that the contact angular momentum is impact invariant. The blue lines show the effect of using the feedback regulation $(u_x, u_y)$ to drive an initial state (here $x_{test}$ and $y_{test}$) to a desired orbit.
• Figure 4: Sarcos© Guardian® XO® is a 150 kg full-body hybrid humanoid/exoskeleton robot with non-point-contact feet. We observe a rendered version on the left and the right, the MuJoCo model used in the simulation.
• Figure 5: Comparing the desired CoM trajectories (red) prescribed by the ALIP planner with the measured CoM values produced by the centroidal momentum controller (blue).