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

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.Comment: in IEEE Robotics and Automation Letter

Whole-body trajectory optimization for non-periodic dynamic motions on quadrupedal systems

Autonomous legged robots will be required to handle a wide range of tasks in complex environments. While a lot of research has focused on developing their abilities for periodic locomotion tasks, less effort has been invested in devising generalized strategies for dynamic, non-periodic movements. Motion design approaches are frequently enlisted in the form of teleoperation or predefined heuristics in such scenarios. We employ a realistic simulation of the hydraulically actuated HyQ2Max quadrupedal system for investigations on two distinctive tasks: rearing and posture recovery. We present a whole-body optimization methodology for non-periodic tasks on quadrupedal systems. This approach delivers solutions involving multiple contacts without the need for predefined feet placements. The results obtained show the potential of optimization approaches for motion synthesis in the context of complex tasks