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

Abstract

Synthesizing legged locomotion requires planning one or several steps ahead (literally): when and where, and with which effector should the next contact(s) be created between the robot and the environment? Validating a contact candidate implies a minima the resolution of a slow, non-linear optimization problem, to demonstrate that a Center Of Mass (CoM) trajectory, compatible with the contact transition constraints, exists.We propose a conservative reformulation of this trajectory generation problem as a convex 3D linear program, CROC (Convex Resolution Of Centroidal dynamic trajectories). It results from the observation that if the CoM trajectory is a polynomial with only one free variable coefficient, the non-linearity of the problem disappears. This has two consequences. On the positive side, in terms of computation times CROC outperforms the state of the art by at least one order of magnitude, and allows to consider interactive applications (with a planning time roughly equal to the motion time). On the negative side, in our experiments our approach finds a majority of the feasible trajectories found by a non-linear solver, but not all of them. Still, we demonstrate that the solution space covered by CROC is large enough to achieve the automated planning of a large variety of locomotion tasks for different robots, demonstrated in simulation and on the real HRP-2 robot, several of which were rarely seen before.Another significant contribution is the introduction of a Bezier curve representation of the problem, which guarantees that the constraints of the CoM trajectory are verified continuously, and not only at discrete points as traditionally done. This formulation is lossless, and results in more robust trajectories. It is not restricted to CROC, but could rather be integrated with any method from the state of the art.

The Pinocchio C++ library : A fast and flexible implementation of rigid body dynamics algorithms and their analytical derivatives

“…It is also used to perform manipulation planning in the Humanoid Path Planner (HPP) software [36] on various robots: UR5, PR-2, and Romeo. It has also been recently used inside the HPP framework to plan dynamically feasible contact sequences on HRP-2 [37], [38].…”

Recent Progress in Legged Robots Locomotion Control

“…This way, the motion of the robot can be approached without having to specify the exact contact sequence in the first hand, which reduces dramatically the complexity of the motion planning problem, enabling fast online replanning to adapt to changing environments in a fraction of a second. The exact contact sequence is recovered in a second stage using a variety of heuristics such as maximizing robust quasi-static balance, accounting for kinematic and even dynamic feasibility constraints on uneven terrain [15,[43][44][45]. This multistage approach can be very efficient but the reliance on heuristics can be a source of failure.…”

“…1-2 have emerged as a solution to compute a feasible CoM trajectory, angular momentum and corresponding contact Fig. 2 Typical control architecture, composed of three main stages: contact planning, centroidal dynamics resolution, and whole-body control (adapted from [15]) forces in generic contact configurations. Contact sequences can even be optimized simultaneously [51].…”

Motion Planning with Multi-Contact and Visual Servoing on Humanoid Robots

“…The complete architecture of the multi-contact planner presented in [13] is shown in figure 3. The following paragraphs describe briefly each method of the architecture and refer the interested reader to the papers introducing this methods.…”