Dynamics and Motion Control of Wheeled Robotic Systems

Mobile robotic systems, which include a mobile platform with one or more manipulators, mounted at specific locations on the mobile base, are of great interest in a number of applications. In this paper, after thorough kinematic studies on the platform and manipulator motions, a systematic methodology will be presented to obtain the dynamic equations for such systems without violating the base nonholonomic constraints. Combining the kinematic model with the initial dynamic equations and eliminating Lagrange multiplier with natural orthogonal complement technique lead to the comprehensive dynamic model. The variables of this model include the path of a reference point of the base and the position and orientation of the end-effector. The proposed approach will be applied on a car-like platform and a manipulator with 5 degrees-of freedom. The calculations for deriving such a model will be implemented by a program in Maple which can be used for control design and simulation purposes. The validity of the methodology is demonstrated using a second model and comparing the elements of these two models with each other. With trajectory generation for platform and manipulator generalized coordinates separately, set points for control system design will be provided. Motion generation for the platform, which due to the nonholonomic constraint has more sensitivity, will be dealt with by two motion modes. Inverting the model in terms of joint space variables, strict control of the work space variables is accomplished. Introducing state space variables and inverting the system into first order equations, the necessary preliminaries for control system design will be provided. Based on two simulation programs in Matlab, two controllers are designed with model-based algorithm (MBA) and Transposed Jacobian (TJ) control. Simulating different external conditions such as parameter perturbation, disturbances and noise, the robotic system behavior in the vicinity of real conditions will be examined. The results obtained show the merits of the TJ algorithm in controlling highly nonlinear and complex systems with multiple degrees- of freedom (DOF), without requiring a priori knowledge of plant dynamics, and with reduced computational burden which motivates further work on this algorithm