Abstract
The aim of the work presented is to develop a rider model for controlling a motorcycle during multibody simulations. In particular, it had to simulate human behavior during standard handling tests such as lane change, U-turn and slalom. The paper illustrates three main ideas: an algorithm for vehicle tracking and look-ahead, an architecture for the virtual rider, and a procedure for the optimization of control gains. The vehicle tracking algorithm is based on the description of the road and the vehicle position using Curvilinear coordinates: the advantage of this method is that the space covered along the road and the lateral deviation from the road center are included in the model variables, hence no additional tracking algorithms are needed. This technique is applied to a look-ahead point too.
The input of the rider model is the target path and roll angle. The output is the steering torque, whereas any torso movements of the rider are neglected. The proposed steering control is based on the classical PD architecture and consists in a look-ahead strategy on the lateral deviation from the desired path and the roll angle. Two additional terms, proportional respectively to the yaw and steering rates, are used to improve vehicle stability. The controller is completed with a low-pass filter whose aim is to replicate the limited ability of human riders in performing very fast maneuvers. All control parameters are adjustable as the speed, the acceleration and the roll angle varies. The rider model includes also a speed control, which is quite simple and is not described in the paper.
Since the tuning of control parameters is not easy, an automatic optimization procedure has been introduced. For any given set of control parameters, the performance index is defined as the rms error between the target and simulated motion. Unilateral constraints are also considered, such as vehicle stability, roll angle overshoot, maximum steering torque, maximum deviation from the desired path, etc. The best control gains are found by optimizing the performance index using a non-derivative algorithm. Since the exact evaluation of the performance index is computationally onerous, the performance is estimated by basing it on the linearized model of the vehicle. Time histories are obtained by using Laplace´s transform techniques, which make it possible to estimate the vehicle motion without integrating the equations of motion. The advantages of this approach are various: the (in)stability of the system is immediately recognizable, the method is much faster than time integration and is insensitive to the step-size.
This rider model has been implemented in a Fortran code and has been coupled to a complex, non-linear multibody model of the motorcycle. Examples of control optimization and nonlinear simulation will be illustrated for a lane change, a slalom and a severe cornering maneuvers. The proposed virtual rider reproduces the behavior of human riders very well. The extension of this method to more general maneuvers (e.g. the replication of a track lap) is under development.
Keywords:rider, motorcycle, control, multibody, dynamics