Optimal Design and Control of Multibody Systems with Friction

In practical multibody systems, various factors such as friction, joint clearances, and external events play a significant role and can greatly influence the optimal design of the system and its controller. This research focuses on the use of gradient-based optimization methods for multibody dynamic systems with the incorporation of joint friction. The dynamic formulation has been derived in using two distinct techniques: Index-1 DAE and the tangent-space formulation in minimal coordinates. It employs a two different approaches for gradient computation: direct sensitivity approach and the adjoint sensitivity approach. After a comprehensive review of different friction models developed over time, the Brown McPhee model is selected as the most suitable due to its accuracy in dynamic simulations and its compatibility with sensitivity analysis. The proposed methodology supports the simultaneous optimization of both the system and its controller. Moreover, the sensitivities obtained using these formulations have been thoroughly validated for numerical accuracy and benchmarked against other friction models that are based on dynamic events for stiction to friction transition. The approach presented is particularly valuable in applications like robotics and servo-mechanical systems where the design and actuation are closely interconnected. To obtain numerical results, a new implementation of the MBSVT (Multi-Body Systems at Virginia Tech) software package, known as MBSVT 2.0, is reprogrammed in Julia and MATLAB to ensure ease of implementation while maintaining high computational efficiency. The research includes multiple case studies that illustrate the advantages of the concurrent optimization of design and control for specific applications. Efficient techniques for control signal parameterization are presented using linear basis functions. A special focus has been made on the computational efficiency of the formulation and various techniques like sparse-matrix algebra and Jacobian-free products have been employed in the implementation. The dissertation concludes with a summary of key results and contributions and the future scope for this research.