Force/motion control of constrained mobile manipulators including actuator dynamics

No-Overturn Conditions for Omnivehicle Motion

“…In the papers covering omnivehicle motion and control, the model with the bilateral constraints between the wheels and the surface is widespread [2,[6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25]. The majority of these papers can be divided into two vast groups: those considering motion with friction between the wheels and the surface [13,19,[23][24][25] and those dealing with motion on a perfectly rough plane [2, 6-12, 17, 18, 20-22]. In the first group of papers, in the majority of works reactions are examined…”

Dynamics-Based Piecewise Constant Control of an Omnivehicle

“…The majority of papers investigating omnivehicles can be divided into two vast groups: those concerning the assembly of real prototypes and enhancement of their maneuverability (for example, [7][8][9][10], see also [3]) and those studying the ways of control on the prescribed trajectories (for example, [11][12][13][14][15][16]). The analysis of their dynamics helps enhance the properties of the prototypes and the controllers.…”

“…The simplest dynamical model of the omnivehicle is based on the no-slip constraints of wheels: the omniwheel is modeled as a rigid disk which does not slip in the direction of the contact roller axis (so the dynamics of the rollers is neglected). Different methods are used to derive equations that govern the dynamics of the vehicle (for example, analysis of the reaction force [11,17], Lagrange's multipliers method [6,12,14], Chaplygin's equations [18], Ferrers' equations [19], the Appel -Gibbs method [15,20,21], and Tatarinov's laconic equations [22,23]). All of them give three ordinary differential equations that determine the change of the center of mass velocity and angular velocity due to controls.…”