Structured contact force optimization for kino-dynamic motion generation

Optimal control approaches in combination with trajectory optimization have recently proven to be a promising control strategy for legged robots. Computationally efficient and robust algorithms were derived using simplified models of the contact interaction between robot and environment such as the linear inverted pendulum model (LIPM). However, as humanoid robots enter more complex environments, less restrictive models become increasingly important. As we leave the regime of linear models, we need to build dedicated solvers that can compute interaction forces together with consistent kinematic plans for the whole-body. In this paper, we address the problem of planning robot motion and interaction forces for legged robots given predefined contact surfaces. The motion generation process is decomposed into two alternating parts computing force and motion plans in coherence. We focus on the properties of the momentum computation leading to sparse optimal control formulations to be exploited by a dedicated solver. In our experiments, we demonstrate that our motion generation algorithm computes consistent contact forces and joint trajectories for our humanoid robot. We also demonstrate the favorable time complexity due to our formulation and composition of the momentum equations.

Authors

• Alexander Herzog
• Stefan Schaal
• Ludovic Righetti

Keywords

• Mathematical model
• Optimal control
• Force
• Computational modeling
• Dynamics
• Legged locomotion
• Contact Force
• Motion Generation
• Linear Model
• Efficient Algorithm
• Contact Surface
• Path Planning
• Optimal Formulation
• Momentum Equation
• Trajectory Optimization
• Contact Interaction
• Humanoid Robot
• Joint Trajectories
• Inverted Pendulum
• Legged Robots
• Optimal Control Approach
• Optimization Problem
• Objective Function
• Optimization Algorithm
• Force Profile
• Angular Momentum
• Optimal Control Problem
• Linear Momentum
• End-effector
• Change In Momentum
• Interior Point Method
• Tridiagonal Matrix
• Constraint In Eq