Zero Step Capturability for Legged Robots in Multicontact

Abstract

The ability to anticipate a fall is fundamental for any robot that has to balance. Currently, fast fall-prediction algorithms only exist for simple models, such as the Linear Inverted Pendulum Model (LIPM), whose validity breaks down in multi-contact scenarios (i.e. when contacts are not limited to a flat ground). This paper presents a fast fall-prediction algorithm based on the point-mass model, which remains valid in multicontact scenarios. The key assumption of our algorithm is that, in order to come to a stop without changing its contacts, a robot only needs to accelerate its center of mass in the direction opposite to its velocity. This assumption allows us to predict the fall by means of a convex optimal control problem, which we solve with a fast custom algorithm (less than 11 ms of computation time). We validated the approach through extensive simulations with the humanoid robot HRP-2 in randomly-sampled scenarios. Comparisons with standard LIPM-based methods demonstrate the superiority of our algorithm in predicting the fall of the robot, when controlled with a state-of-the-art balance controller. This work lays the foundations for the solution of the challenging problem of push recovery in multi-contact scenarios.

C-CROC: Continuous and Convex Resolution of Centroidal Dynamic Trajectories for Legged Robots in Multicontact Scenarios

“…For future work we would like to empirically determine the accuracy of our method with respect to this problem, using a framework similar to [14].…”

“…If not, we can then proceed to evaluate the next candidate until we find a relevant contact. The transition feasibility problem also addresses the N-step capturability problem [12]- [14]: given the current state of the robot, determine whether it will be able to come to a stop without falling in at most N steps (N ≥ 0). This issue is very important to guarantee the safety of the robot and its surroundings.…”

Robust Humanoid Contact Planning With Learned Zero- and One-Step Capturability Prediction

“…[32] further extends it to consider 3D movements, and develops an analytical tool to determine capturability in the VHIP model. [9] proposes an efficient analytical tool to compute zero-step capturability for multi-contact configuration using a centroidal dynamics model. However, it has strong assumptions on using zero angular momentum, and cannot generalize to use additional steps.…”

“…In particular, we consider zero-step and one-step capture motion using either foot or palm contacts. Previous approaches [9], [10] demonstrated the use of kino-dynamic optimization to compute multi-contact capture motions. However, they are either limited to special cases or computationally prohibitive to be used in a planner.…”

Safe 3D Bipedal Walking through Linear MPC with 3D Capturability

“…We establish this capturability constraint based on a comparison between CoM and CoP trajectories involving exponentials as in [9] instead of polynomials as in [12]. This capturability constraint involves stopping along a segment of line as in [16], but considering only planar contact with the ground during the stopping motion to obtain a formulation which depends linearly on foot placement and CoM motion. Stopping along curves has already been approached, but with ad-hoc numerical schemes that can't be integrated in a linear MPC scheme as done here [17], [18].…”