Optimal stabilization and path-following controls for a bicycle

The article is about stabilizing and path-tracking control of a bicycle by a rider. It is based on previously published work, in which it has been shown how a driver's or rider's preview of the roadway can be combined with the linear dynamics of an appropriate vehicle to yield a problem of discrete-time optimal-linear-control-theory form. In the previous work, it was shown how an optimal ‘driver’ converts path preview sample values, modelled as deriving from a Gaussian white-noise process, into steering control inputs to cause the vehicle to follow the previewed path. The control compromises between precision and ease, to an extent that is controllable through choice of weights in the optimal control calculations. Research into the dynamics of bicycles has yielded a benchmark model, with equations of motion firmly established by extensive cross-checking. Model predictions have been verified for modest speeds by experimental testing. The established optimal linear preview stabilizing and tracking control theory is now brought together with the benchmark bicycle description to yield optimal controls for the bicycle for variations in speed and performance objectives. The resulting controls are installed in the bicycle, giving a virtual rider-controlled system, and frequency responses of the rider-controlled system are calculated to demonstrate tracking capability. Then path-tracking simulations are used to illustrate the behaviour of the controlled system. Tight and loose controls, representing different balances between tracking accuracy and control effort, are calculated and illustrated through the simulations.