Contact-implicit optimization

Letting contact timing emerge#

A conventional plan may specify exactly when each foot touches and leaves the ground. Contact-implicit methods instead optimize motion and contact forces together. Posa, Cantu, and Tedrake developed a direct method for rigid-body trajectories with inelastic impacts and Coulomb friction that removes the need to prescribe the mode ordering in advance.

A common formulation uses complementarity: a contact gap is nonnegative, the normal force is nonnegative, and their product is zero. A positive gap therefore excludes a contact force; a positive force requires closed contact. Other formulations use smooth contact approximations.

Uses in locomotion and manipulation#

The optimizer can search for useful stepping or pushing behavior as part of a trajectory-optimization problem. This is helpful when the contact sequence is itself an important design choice, rather than something already known.

Search freedom increases numerical difficulty#

Complementarity creates a difficult nonconvex problem. The optimization survey by Wensing and colleagues discusses poor numerical conditioning and dependence on good initial guesses. Relaxed constraints may permit unphysical intermediate solutions while the solver searches. A final trajectory therefore needs checks against the intended contact model and constraints; finding a local solution does not establish that it is the best possible contact strategy.