Autonomous robots that locomote and manipulate objects could replace humans in challenging/hazardous environments, e.g., nuclear waste handling/disposal, surgeries, and assembly/repair/maintenance of space structures. In these safety-critical settings, hardware experiments to understand contact behavior are challenging as errors could be catastrophic. While lab-based hardware experiments are an option, they are time-consuming to setup and expensive. These hardware-based challenges has inspired computer scientists, roboticists, and multibody dynamics experts to collectively work on high-fidelity computer simulators that are cheaper and faster for repetitive testing and insight generation. The main objectives are to gain a better understanding of multibody dynamics of systems (like robots) as they interact with objects and/or their surroundings which can be used to optimize robot designs in software or enhance real robots’ abilities to react to changes in real-time. A multibody contact simulator’s trade-offs are between accuracy and speed- design engineers desire more accurate models that help optimize a robot prior to deployment whereas hardware robotics engineers desire faster models so their robots can autonomously react to changes in real-time in the real-world. Methods for simulating multibody contact dynamics fall into two categories: penalty-based and complementarity methods. The former calculate penetration depths at every time step and compute restoring forces to repair penetrations, while the latter assume that the bodies are truly rigid and compute contact forces that prevent penetration from occurring at all. Thus, complementarity methods are more physically realistic. In this project, the hybrid contact dynamics of multibody systems will be formulated as a complementarity problem using Kane's method and a minimal coordinate formulation. The hypothesis here is that this should lead to faster simulations as Kane’s method is computationally more efficient for computational modelling/simulation of contact-free systems compared to classical approaches (e.g., Newton’s Law). Minimal coordinate formulations with these classical techniques result in smaller-sized complementarity problems that also lead to lower faster simulations. The work developed here will be benchmarked against state-of-the-art contact simulators to learn their merits, demerits, and limitations.  The model’s accuracy will then be verified via experiments on a lab-based space-relevant robotic testbed leading to the full life development of a novel, fast, and accurate contact dynamics solver. # Next notes 1. [[5a complementarity techniques]] 2. [[5b penalty-based methods]] 3. [[5c Gantt chart for a PhD on contact dynamics]] 4. [[5d Robotics simulation framework]] 5. [[5e multibody systems are classified by topology]] 6. [[5f Types of Contacts]] 7. [[5g Reinforcement Learning for Space Robotics]] 8. [[5h Nonlinear Relative Spacecraft Dynamics are simplified to derive Clohessy-Wiltshire Equations]] 9. [[5i Fiber Optical Strain Sensors for Contact]]