Modeling and control of tree-like structured vehicles and robots using Appell method

A vehicle may be considered as a multi-body system with the chassis, the six degrees of freedom moving ability relative to the inertial reference frame, and with the wheels as the end effectors. In this paper the geometry, kinematics and dynamics of the vehicle are modeled as a tree structured mechanical system using the modified Denavit-Hartenberg convention. Two type of techniques are considered to find the dynamic model: the mixed Newton-Euler formalism based on the inverse dynamic model and Appell´s method based on the Gibbs function (acceleration energy). Newton-Euler formalism needs a very large number of calls of the inverse dynamic function to find the total dynamic model. The novel Appell formalism eliminates this disadvantage. Two software systems were developed both for poor numerical and advanced symbolic computations taking into account the kinematic constraints at the wheel/ground contact points by applying Lagrange-multipliers. Simulation results illustrate the effectiveness of the method for a 16 DoF vehicle in the presence of active PID suspension control.