On discrete-valued modeling of nonholonomic mobile robot systems

In this paper, we pursuit possibility of discrete-valued version of nonholonomic mobile robot systems. Instead of the special Euclidean space SE(2), we suppose the hexagonal cellular space as the field of planar locomotion. We then consider discrete equivalent of wheeled mobile robot governed by nonholonomic kinematic constraints, which is defined by discrete-valued difference equations rather than continuous-valued differential equations. We also propose a model of discrete-valued trailer system, which undergoes both nonholonomic constraints of wheels and nonholonomic constraints of rigid linkage, followed by its extension to snake robot systems with passive wheels and active joints. Finally, we examine the reachability of system states in the discrete settings, and discuss the minimal number of steps required to cover the entire neiborhood of the initial state.