Contact-Implicit Whole-Body Trajectory Optimization for Humanoid Robots on Parameterizable Uneven Terrain

This paper proposes a contact-implicit whole-body optimization framework for humanoid robots to generate dynamic motion trajectories on parameterizable complex terrains such as steps and ramps, without requiring a predefined contact sequence. The method approximates ground geometry with smooth surfaces and extends rigid-body interaction from planar surfaces to arbitrary smooth surfaces through new contact constraints, using nonlinear programming to plan motions across various terrain topologies. The authors conducted preliminary feasibility tests on non-coplanar terrains in simulation and on the real robot ErgoCub.