Complementarity Constraint

Complementarity constraints model systems with interacting, discontinuous dynamics, such as those involving contact in robotics or switching behaviors in other domains. Current research focuses on developing efficient algorithms, often based on optimization techniques like linear or nonlinear programming, to solve problems incorporating these constraints, particularly within model predictive control and trajectory optimization frameworks. This work is crucial for advancing the control and planning of complex systems, enabling more robust and efficient solutions in areas like robotic manipulation, locomotion, and aerospace engineering. The development of differentiable solvers and improved learning methods for these systems is a significant area of ongoing progress.