C3: Consensus Complementarity Control

Making and breaking contact with the environment is one of the hardest problems in robotics. The moment a finger touches a box, a foot hits the ground, or a tool grips a surface, the system dynamics become nonsmooth: the physics jumps discontinuously. Traditional MPC and sampling-based controllers struggle here because they cannot reason across these contact transitions.

C3 (Consensus Complementarity Control) is a contact-implicit MPC framework, originally published by researchers at the DAIRLab, that solves this problem by reformulating contact as a complementarity constraint and using ADMM to decompose the resulting mixed-integer-like problem into parallel subproblems. The result is a controller that can plan through contact, deciding when and how to make or break contact as part of the trajectory optimization.

Plate balancing via contact control

Multi-object pushing from first sight

The algorithm was conceived and published by the DAIRLab research team (see publication below). My role is as lead developer and maintainer of the open-source reference implementation, responsible for turning the research prototype into a production-quality, contributor-ready codebase:

• Full codebase refactor: restructured the repository for modularity and long-term maintainability, separating simulation, hardware, and algorithm layers cleanly.
• CI/CD pipelines: built automated testing and integration workflows so every commit is validated against a suite of unit and integration tests.
• Example suite: created comprehensive, runnable examples (cartpole, plate balancing, cube pivoting, pushing) that both validate the algorithm and serve as onboarding for new contributors.
• Documentation and contributor guidelines: wrote guides and code structure documentation to enable the broader lab to build on top of C3.

Current and upcoming work focuses on extending C3 to new hardware platforms and pushing toward a journal publication.