An Improved Method for Estimating the Domain of Attraction of Passive Biped Walker

An indicator of a passive biped walker’s global stability is its domain of attraction, which is usually estimated by the simple cell mapping method. It needs to calculate a large number of cells’ Poincare mapping result in the estimating process. However, the Poincare mapping is usually computationally expensive and time-consuming due to the complex dynamical equation of the passive biped walker. How to estimate the domain of attraction efficiently and reliably is a problem to be solved. Based on the simple cell mapping method, an improved method is proposed to solve it. The proposed method uses the multiple iteration algorithm to calculate a stable domain of attraction and effectively decreases the total number of Poincare mappings. Through the simulation of the simplest passive biped walker, the improved method can obtain the same domain of attraction as that calculated using the simple cell mapping method and reduce calculation time significantly. Furthermore, this improved method not only proposes a way of rapid estimating the domain of attraction, but also provides a feasible tool for selecting the domain of interest and its discretization level.

Dynamic modeling of aircraft landing gear and multi-objective optimization with simple cell mapping method

To study the dynamic characteristics of aircraft landing gear and carry out successive optimizations, a mathematical model of flexible landing gear is established by the Hamiltonian principle. The dynamic model includes a tire force estimation derived from the impact model. Dynamic analysis with the flexible model is then conducted. Stress distribution is obtained from the dynamic analysis, which can be used for fatigue analysis, optimization design, etc. To achieve better dynamic characteristics in terms of vibration reduction, a multi-objective optimization problem is formulated and solved via a simple cell mapping algorithm. Optimal simulations indicate the quality of optimal structural designs. Compared with the baseline structure, candidate optimal designs can improve dynamic performance of fuselage vibration suppression, shock absorber efficiency, and stress settling time. The proposed multi-objective optimal parameter design provides a fast tuning procedure that saves considerable time compared to finite element method-based optimization. In addition, the optimal parameter set provides useful interface information for detailed landing gear structural modeling that serves other analysis purposes.

Multi-objective optimal design of sliding mode control with parallel simple cell mapping method

This paper presents a study of the multi-objective optimal design of a sliding mode control for an under-actuated nonlinear system with the parallel simple cell mapping method. The multi-objective optimal design of the sliding mode control involves six design parameters and five objective functions. The parallel simple cell mapping method finds the Pareto set and Pareto front efficiently. The parallel computing is done on a graphics processing unit. Numerical simulations and experiments are done on a rotary flexible arm system. The results show that the proposed multi-objective designs are quite effective.

Multi-Objective Optimal Design and Validation of Sliding Mode Control

This paper presents a study of multi-objective optimal design of a slide mode control for an under-actuated nonlinear system with the parallel simple cell mapping method. The multi-objective optimal design of the slide mode control involves 6 design parameters and 5 objective functions. The parallel simple cell mapping method finds the Pareto set and Pareto front efficiently. The parallel computing is done on a graphic processing unit (GPU). Numerical simulations and experiments are done on a rotary flexible arm system. The results show that the proposed multi-objective designs are quite effective.