Dynamic Complementarity Conditions and Whole-Body Trajectory Optimization for Humanoid Robot Locomotion

Overview

This journal paper presents a whole-body trajectory optimization framework for humanoid locomotion built around dynamic complementarity conditions. Rather than requiring a predefined contact sequence, the optimizer treats contacts implicitly: complementarity constraints couple contact forces and contact distances, so the solver can decide when and where contacts occur together with the robot motion.

Method

• Complementarity formulation. Contact activation is expressed through complementarity conditions, removing the need to hand-specify a gait or contact schedule.
• Whole-body model. The optimization considers the full-body dynamics, producing physically consistent, dynamically feasible trajectories.
• Planning as optimization. Foot placement, timing, and whole-body motion emerge jointly from a single nonlinear program.

Results

The framework generates a range of humanoid locomotion behaviors from high-level goals, demonstrating that complementarity-based whole-body trajectory optimization can autonomously synthesize contact-rich motions.