Search results

Various parameter values are provided in the form of data tables, where data keys are ordered and unevenly spaced in general, for real‐time simulation of dynamic systems. However, most parameter values required for simulation do not explicitly exist in data tables. Thus, unit intervals, including parameter values, are searched rather than the data keys. Since real‐time constraint enforces use of a fixed step size in integration of system differential equations because of the inherent nature of input from and output to real hardware, the worst case of iterated probes in searching algorithms is the core measure for comparison. The worst case is expressed as Big O. In this study, conventional bisection, interpolation, and fast searches are analyzed and compared in Big O as well as the newly developed searching algorithms: modified fast search and modified regular falsi search. If the criterion is actual execution time required for searching, most numerical tests in this paper show that bisection search is superior to the others. Interpolation search and its variations show better performance in the case of linear or near linear data distribution than bisection search. The numerical tests show that modified regular falsi search is faster than the other interpolation searches in either expected time or worst cases. Given parameter tables should be carefully examined for their data distribution in order to determine the most appropriate searching algorithm for the application.

For realistic simulation of off‐road vehicles terrain surfaces have to be modeled in detail, and wheel‐surface contacting geometry must be well defined in order to obtain proper ground‐reaction and friction forces. Delaunay triangulation is one of the most widely used methods in modeling 3D terrain surfaces, and triangle‐search (T‐search) is a relevant algorithm for searching resultant triangular polygons. The T‐search method searches polygons in successive order and may not allow real‐time computation of off‐road vehicle dynamics if the terrain is modeled with many polygons, depending on the computer performance used in the simulation. Dynamic T‐search, which is proposed in this paper, combines conventional T‐search and the concept of a dynamic window, which is a moving subset of the database and where an actual search is made at each frame, by taking advantage of the information regarding dynamic characteristics of a simulated vehicle. Numerical tests show improvement of searching speeds by about 5 percent for randomly distributed triangles. For continuous searches along a vehicle path, which actually occur in a vehicle simulation, the searching speed of the new method becomes four times faster than the conventional one.

Optimal switching angles are investigated for minimizing accumulated numerical errors when the dual‐Euler method is used in the simulation of angular rotation.

First, round‐off errors are theoretically modeled with a simplified mathematical representation of rotation. Round‐off errors take critical roles in the vicinity of indefinite points because they cause major numerical inaccuracy in very large numerical values represented with limited binary numbers. Optimal switching angles of (±π/4, ±3π/4) are derived and numerically examined. With a more practical and severe rotational model, the switching angles are numerically tested.

In conclusion, switching pitch angles of (±π/4, ±3π/4) yield near minimum numerical errors in angular parameters of pitch, yaw, and roll if truncation errors are not dominant by using high‐order integration algorithms and small step sizes. It is also noticed that accumulated numerical errors increase dramatically if pitch and roll angles are switched beyond the optimal angles with a little margin.

Optimal switching angles in the dual‐Euler method are identified based on the truncation error analysis. The mechanism of accumulated numerical errors in the dual‐Euler method, which depends on switching angles, is also revealed.