The Analytical Formulations for Vehicle Motion Planning

We are now just entering the age of intelligent electro-mechanical systems. In this case, a multi-wheeled vehicle is to be modernized by opening up the architecture (it is fully modular and can be assembled on demand). In particular, the mobile platform can have any body geometry for N wheels (supported by articulated suspensions of 2 to 3 DOF), all acting in parallel. Given the motion specifications of each wheel/suspension leads to a programming and mathematical nightmare which rapidly loses all physical meaning. Here, we decide to specify the motion of the platform up to, say, the 4 th order, algebraically compute the required input parameters at each of the N wheels (up to the 4 th order) and then evaluate the actuator and traction resources to see if those input commands are satisfied and with what margins (positive means success, negative means failure). The ultimate goal is to balance all the margins in real time to ensure system success and how marginal that success is even in poor weather, rough terrain, emergency maneuvers, etc. This, then, leads to a 5 to10 milli-sec. decision making problem which must be made in terms of physically meaningful criteria, which is the basis for the formulation presented in this paper