Conventional motion planners for wheeled vehicles often assume no-slipping and no-skidding conditions and construct motion trajectories in the context of nonholonomic motion planning. However, in some practical situations slipping and skidding cannot be ignored or can even be useful. To take them into account in the construction of planning algorithms, it is important to model the friction force between the tire and the contact plane. In this paper, we first construct a model of the friction force as an extension of the two-dimensional Coulomb model, considering both the slipping conditions and the nonholonomic constraints. Next, we formulate the motion planning problem as a drift parking problem and propose a motion planning strategy combining the nonholonomic planner and the control in the slipping mode. The feasibility and the performance of the proposed strategy are tested under simulation.

Most motion planners for a vehicle often assume no-slipping and no-skidding in the context of nonholonomic motion planning. However, there actually exist slipping and skidding in practical situations and it is important to know the force between the tire and the contact plane considering slipping and skidding in the planning problem. In this paper, a Coulomb friction model of the tire friction force of vehicle is extended to nonholonomic constraints. In the modeling, the longitudinal and lateral tire friction forces are modeled corresponding to no slipping and no skidding constraints, respectively. A two directional model based on the maximum dissipation principle is also developed. Some typical movements of vehicles with the proposed friction force model are illustrated by simulations.

This paper deals with a motion planning problem for a spherical rolling robot actuated by two internal rotors that are placed on orthogonal axes. The key feature of the problem is that it can be stated only in dynamic formulation. In addition, the problem features a singularity when the contact trajectory goes along the equatorial line in the plane of the two rotors. A motion planning strategy composed of two trivial and one nontrivial maneuver is devised. The trivial maneuvers implement motion along the geodesic line perpendicular to the singularity line. The construction of the nontrivial maneuver employs the nilpotent approximation of the originally nonnilpotent robot dynamics, and is based on an iterative steering algorithm. At each iteration, the control inputs are constructed with the use of geometric phases. The motion planning strategy thus constructed is verified under simulation.

The paper deals with the problem of motion planning for a spherical rolling robot actuated by two internal rotors that are placed on orthogonal axes. To solve the problem, we employ the so-called geometric phase approach based on the fact that tracing a closed path in the space of input variables results in a non-closed path in the space of output variables. To set up the governing equations, the contact kinematic equations are modified by the condition of dynamic realizability, which constrains the component of the angular velocity of the rolling carrier and depends on the mass distribution, and parameterized. By using a motion planning strategy based on tracing two circles on the spherical surface, an exact and dynamically realizable motion planning algorithm is fabricated and verified under simulation.

The paper deals with the dynamics and motion planning for a spherical rolling robot actuated by internal rotors that are placed on orthogonal axes. The driving principle for such a robot exploits non-holonomic constraints to propel the rolling carrier. The full mathematical model as well as its reduced version are derived, and the inverse dynamics is addressed. It is shown that if the rotors are mounted on three orthogonal axes, any feasible kinematic trajectory of the rolling robot is dynamically realizable. For the case of only two orthogonal axes of the actuation the condition of dynamic realizability of a feasible kinematic trajectory is established. The implication of this condition to motion planning in dynamic formulation is explored under a case study. It is shown there that in maneuvering the robot by tracing circles on the sphere surface the dynamically realizable trajectories are essentially different from those resulted from kinematic models.

The paper deals with the motion planning for a spherical rolling robot actuated by internal rotors that are placed on orthogonal axes. It is shown that if the robot is actuated by three rotors, any feasible kinematic trajectory is dynamically realizable. For the case of two rotors the conditions of controllability and dynamic realizability of a feasible kinematic trajectory are established. It is shown that in moving the robot by tracing straight lines and circles in the contact plane the dynamically realizable trajectories are not represented by the circles on the sphere, which is a feature of the kinematic model of pure rolling. The dynamic motion planning problem is then formulated in the optimal control settings, and the properties of the optimal trajectories are illustrated under simulation.