In robotics simulation and game engines, rigid-body dynamics are commonly represented using two coordinate parameterizations: maximal coordinates and reduced coordinates. Maximal coordinates model each rigid body directly with six degrees of freedom (DoF), allowing joints, contacts, and frictions to be handled uniformly as constraints. This makes them particularly suitable for scenarios involving frequent, complex contacts or rapidly changing topology. However, they require numerical stabilization of joint constraints, are more sensitive to large mass ratios, and exhibit significantly increased computational cost as the number of constraints grows.
In contrast, reduced coordinates represent the system state by the base pose plus the DoFs of each joint, inherently satisfying joint constraints (eliminating joint drift), reducing the number of variables, and providing greater robustness under large mass ratios. Motivated by these trade-offs, this thesis proposes a hybrid formulation: using reduced coordinates to solve articulated joint constraints for efficiency and stability, while leveraging maximal coordinates for complex contact handling, thereby combining the strengths of both approaches.
The objective of this thesis is to integrate the proposed hybrid formulation into a multibody dynamics simulation framework to enable efficient simulation of articulated mechanisms. The work will proceed as follows: (1) conduct a literature review to examine existing hybrid formulations that combine maximal and reduced coordinates, (2) implement the method within a C++ simulation platform, and (3) evaluate its performance on benchmark cases, comparing it against conventional maximal-coordinate approaches.
Keywords: Robotics Simulation, Hybrid Coordinate Formulation, Contact Handling
Requirements:
- You are studying Electrical Engineering, Automation, or Robotics Systems Engineering.
- You are interested in robot simulation or game physics engines; ideally, you have studied multibody dynamics or robotics dynamics.
- Ideally, you have programming skills in C++.
Relevant Literature:
- Wang, Y., Weidner, N.J., Baxter, M.A., Hwang, Y., Kaufman, D.M. and Sueda, S., 2019. REDMAX: Efficient & flexible approach for articulated dynamics. ACM Transactions on Graphics (TOG), 38(4), pp.1-10.
Betreuer: Shao, Email:
