Trajectory Optimization of Contact-Rich Motions Using Implicit Differential Dynamic Programming

This work presents a Differential Dynamic Programming (DDP) approach for systems characterized by implicit dynamics using sensitivity analysis, such as those modelled via inverse dynamics, variational, and integrators. It leads to more general formulation of DDP, enabling the use faster recursive Newton-Euler dynamics. We leverage precise exact contact modelling in where we focus on two contributions: (1) at acceleration level; (2) an invertible model forward pass closed-form solution backward improve numerical resolution contacts. The performance proposed framework is validated comparing versus explicit DDP swing-up double pendulum, planning motions tasks single leg making multi-body contacts with environment: standing up from ground, priori enumeration challenging, maintaining balance under external perturbation.