Adjoint sensitivity analysis method for dynamic optimization of multibody systems considering collision and friction

Collision and friction will cause the nonsmooth phenomenon of the state variables of mechanisms, and affect the stability and dynamic behavior of multibody systems. For the dynamic optimization of multibody systems, the optimization methods roughly include gradient-free methods and gradient methods. The gradient-free optimization methods need a lot of function evaluation, and the convergence speed is often quite slow. However, gradient optimization methods can obtain optimization results with less iterations. Among them, gradient, that is, dynamic sensitivity analysis, is inevitable and difficult, and there are few research reports. Taking contact and friction phenomena into consideration, an adjoint sensitivity analysis method for dynamic optimization of multibody systems is proposed in this paper. The calculation formulas of analytical and semi-analytical sensitivity analysis methods and optimization flow are given. In addition, the availability and engineering practicability of the proposed method are verified by the dynamic optimization examples of rigid five-bar mechanism and rigid-flexible tensegrity structure.