On Time Optimization of Centroidal Momentum Dynamics

Abstract

Recently, the centroidal momentum dynamics has received substantial attention to plan dynamically consistent motions for robots with arms and legs in multi-contact scenarios. However, it is also non convex which renders any optimization approach difficult and timing is usually kept fixed in most trajectory optimization techniques to not introduce additional non convexities to the problem. But this can limit the versatility of the algorithms. In our previous work, we proposed a convex relaxation of the problem that allowed to efficiently compute momentum trajectories and contact forces. However, our approach could not minimize a desired angular momentum objective which seriously limited its applicability. Noticing that the non-convexity introduced by the time variables is of similar nature as the centroidal dynamics one, we propose two convex relaxations to the problem based on trust regions and soft constraints. The resulting approaches can compute time-optimized dynamically consistent trajectories sufficiently fast to make the approach realtime capable. The performance of the algorithm is demonstrated in several multi-contact scenarios for a humanoid robot. In particular, we show that the proposed convex relaxation of the original problem finds solutions that are consistent with the original non-convex problem and illustrate how timing optimization allows to find motion plans that would be difficult to plan with fixed timing † .

An Open Torque-Controlled Modular Robot Architecture for Legged Locomotion Research

“…In these experiments, we demonstrate the dexterity and capabilities of the quadruped robot. Moreover, we present First Impact First Stance Second Impact Second Stance the first real robot experiments using motions computed with a centroidal dynamics-based kino-dynamic planner [9], [24]. a) Kino-dynamic motion optimizer and controller: The motions are planned using the full body kino-dynamic optimizer proposed in [9].…”

“…In our experiments, consensus was typically achieved after two iterations. The centroidal dynamics optimization problem is solved using the algorithm proposed in [24].…”

“…Low-weight, inexpensive yet robust robots are particularly relevant when testing advanced algorithms for dynamic locomotion [4], [23], [24]. Indeed, simple robot operation and collaborative development through open-source initiatives can accelerate testing cycles.…”

“…Towards these goals, we present a novel, fully opensource, modular force-controlled leg architecture for dynamic legged robot research. This paper presents five main contributions: 1) a novel light-weight, low-complexity, torque-controlled actuator module suitable for impedance and force control, 2) a foot contact sensor suitable for legged robots withstanding hard impacts, 3) a complete characterization of the achieved impedance with one leg constructed with the actuator modules and foot sensor, demonstrating effective dimensionless impedance within the range of human running, 4) a 2.2 kg quadruped robot, Solo, assembled from 4 legs, with a very large range of motion and which is, to the best of our knowledge, the lightest forcecontrolled quadruped and 5) a torque-controller tracking fullbody motions computed with a kino-dynamic motion optimizer [9], [24], demonstrating for the first time that motions computed with this motion optimizer can be executed on real robots under moderate environmental uncertainty. The complete design requires mostly 3D printed parts and offthe-shelf components, except for three small machined parts, and is fully open-sourced, including mechanical drawings, electronic circuits and control software [1].…”

Learning to Explore in Motion and Interaction Tasks

“…We start by collecting trajectories {(s 1:T , a 1:T ) i } from all the available policies. We note here that we only need trajectories and not the full policies for training the model, so our approach could work even if that is all we have access to (for example as a result of doing trajectory optimization [15], [16] or learning by demonstration [17]).…”