Contact-Implicit Trajectory Optimization Using an Analytically Solvable Contact Model for Locomotion on Variable Ground

Abstract

This paper presents a novel contact-implicit trajectory optimization method using an analytically solvable contact model to enable planning of interactions with hard, soft, and slippery environments. Specifically, we propose a novel contact model that can be computed in closed-form, satisfies friction cone constraints and can be embedded into direct trajectory optimization frameworks without complementarity constraints. The closed-form solution decouples the computation of the contact forces from other actuation forces and this property is used to formulate a minimal direct optimization problem expressed with configuration variables only. Our simulation study demonstrates the advantages over the rigid contact model and a trajectory optimization approach based on complementarity constraints. The proposed model enables physics-based optimization for a wide range of interactions with hard, slippery, and soft grounds in a unified manner expressed by two parameters only. By computing trotting and jumping motions for a quadruped robot, the proposed optimization demonstrates the versatility for multi-contact motion planning on surfaces with different physical properties.

Lifted contact dynamics for efficient optimal control of rigid body systems with contacts

“…The simplest approach is to approximate the contact forces using spring-damper systems [1]; however, it lacks accuracy and involves stiff optimization problems. The same problem typically occurs in other smooth soft-contact models such as in [2].…”

HapFIC: An Adaptive Force/Position Controller for Safe Environment Interaction in Articulated Systems

“…Examples include activities that involve interacting with soft objects, handling fluids, or walking in a crowded room. If we look at these tasks in the context of robotics, they all continue to be open research questions [1]- [8]. The methods currently deployed rely on accurate environmental interaction models that might require tracking non-accessible environmental states.…”

“…The methods currently deployed rely on accurate environmental interaction models that might require tracking non-accessible environmental states. Notwithstanding the modelling challenge, the curseof-dimensionality makes them computationally intensive for higher-dimensional systems [1], [3], [9], [10]. The feasibility of available architectures so far has focused on small scale scenarios with controlled interaction conditions (e.g.…”

“…known contact dynamics). These optimisation algorithms and controllers also exhibited a lack of robustness, which is connected to the need for accurate task models to guarantee interaction stability [1]- [3], [6]. Improving both interaction robustness and haptics is of interest for robotics at large.…”

Meta-Learning for Fast Adaptive Locomotion with Uncertainties in Environments and Robot Dynamics

“…These changes and unexpected situations can be intrinsic or extrinsic, such as robot damage, motor failures, changing friction, and external force disturbances. For robot locomotion, traditional approaches of planning and control require expert knowledge and accurate dynamics models and constraints of both the robot and the environment [1], [2], which are all subject to unforeseeable changes that are difficult to know beforehand. Moreover, even using dataefficient learning techniques such as Bayesian optimization to tune decision variables and control parameters, it can only achieve adaptation on a trial-by-trial basis [3] and also require extensive computation [4] which is not able to respond to changes on the fly.…”