Convex Properties of Center-of-Mass Trajectories for Locomotion Based on Divergent Component of Motion

Abstract

This letter presents an in-depth analysis of the convex properties of center-of-mass (CoM) trajectories for legged robot locomotion based on the concept of Divergent Component of Motion (DCM). In particular, we show that the union of all possible trajectories forms a bounded convex set under appropriate boundary conditions. Additionally, we describe in detail our approach of generating closed-form CoM trajectories through piecewise interpolation over a sequence of waypoints and show how to compute the CoM trajectory efficiently through equations given in a matrix form. Applying the convex properties to our trajectory-generation approach, we present an algorithm for computing convex overapproximations of the CoM waypoints. Finally, we provide an example of usage in placing waypoints that lead to feasible CoM trajectories with respect to kinematic and dynamic constraints. The approach is validated with a multi-contact scenario in simulation with the humanoid robot TORO.

Humanoid Robots in Aircraft Manufacturing: The Airbus Use Cases

“…• normal, upright walking, with knees slightly bent • crouched walking, required to move within the mockup and prevent collisions with the head due to the low height of the ceiling. Based on the DCM formulation, CoM trajectories (position, velocity and acceleration) are generated using a piecewise interpolation over a sequence of waypoints [27], while the trajectories of the feet are generated as fifth-order polynomials. These reference trajectories are tracked by a passivity-based whole-body controller.…”

DCM-Based Gait Generation for Walking on Moving Support Surfaces

“…For each single transition phase, the reference eCMP e(t) is constructed via i.e., via linear interpolation between a preceding eCMP support point e A (t) and a leading eCMP support point e B (t) using a temporal interpolation function f (t). Furthermore, if 0 f (t) 1 ∀t ∈ [0, T ] (T denoting the duration of the interpolation), (14) forms a convex interpolation between the two points [14]. Inserting (14) into (5) we find…”

“…In [12], we extended the DCM model to 3D, while Hopkins et al [13] extended it to varying virtual pendulum heights (time-varying DCM). In [14], Mesesan et al analyze the convex properties of CoM trajectories based on DCM and perform multi-contact locomotion in simulation. While robotic walking over flat or uneven stationary grounds has been successfully addressed, robotic walking across moving ground surfaces, as presented by Unhelkar et al [15] for a wheeled mobile platform, is not covered by the state of the art.…”

“…This paper presents an awesome gait generator that extends our DCM-based planning and control framework [14], [16]- [18] to allow the traversal of moving support surfaces such as moving plates, conveyor belts and escalators. While in case of walking on stationary ground, one may argue about the number of previewed steps, a multi-step preview German Aerospace Center (DLR), Institute of Robotics and Mechatronics, 82234 Wessling, Germany.…”

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

“…The works that are the closest to the present paper propose a convex relaxation of the CoM constraints [19], [20]. The method proposed in this paper is conservative rather than approximate while being more computationally efficient.…”