Modeling and Control Design Using the Boltzmann-Hamel Equations: A Roller-Racer Example

Quasi-coordinates based dynamics modeling and control design for nonholonomic systems

“…at the step of a controller design. In [3] we use a partial feedback linearizing controller and design a composite computed torque controller that can track a desired motion. The sample motion, which is a circular trajectory as presented in [3] is illustrated in Fig.…”

“…The selection of the quasi-coordinates for the roller-racer modeling is due to its design and the way of propulsion [3,9]. Firstly, this is the underactuated system for which control has to be executed at the dynamics level.…”

“…For instance, some of them may be controlled at the kinematic level and the other may be controlled at the dynamic level only [3,6,9,16]. Their control properties depend upon the way they are designed and propelled, i.e.…”

Stabilizability and Motion Tracking Conditions for Mechanical Nonholonomic Control Systems

“…There is a subgroup of the wheeled systems for which their wheels are not powered. These are a snakeboard [24,25], a roller-racer [26,27], a roller-blader [28], a roller-walker [29], or snake-like robots [30,31]. All these systems can move their bodies due to the relative motion of their joints.…”

“…The same holds for motion tracking [6]. For some vehicles with idle wheels subjected to the constraints (2.1) no kinematic control models can be developed [26,27]. Kinematic control models of systems with the constraints (2.2) and (4) may have the formẋ…”