Akihiro Morinaga

On the dynamic model and motion planning for a spherical rolling robot actuated by orthogonal internal rotors

The paper deals with the dynamics of a spherical rolling robot actuated by internal rotors that are placed on orthogonal axes. The driving principle for such a robot exploits nonholonomic constraints to propel the rolling carrier. A full mathematical model as well as its reduced version are derived, and the inverse dynamics are 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 rotors the conditions of controllability and dynamic realizability 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 implication of this fact to motion planning is explored under a case study. It is shown there that in maneuvering the robot by tracing circles on the sphere the dynamically realizable trajectories are essentially different from those resulted from kinematic models. The dynamic motion planning problem is then formulated in the optimal control settings, and properties of the optimal trajectories are illustrated under simulation.

A Motion Planning Strategy for a Spherical Rolling Robot Driven by Two Internal Rotors

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.

On the dynamic model and motion planning for a class of spherical rolling robots

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.

On the motion planning problem for a spherical rolling robot driven by two rotors

The paper deals with the motion planning for a spherical rolling robot actuated by two internal rotors that are placed on orthogonal axes. The condition of controllability is derived and it is shown that the robot is controllable unless the contact trajectory goes along the equatorial line in the plane of the two rotors. The dynamic motion planning problem is then formulated, and an approach based on the nilpotentization of the originally non-nilpotent robot dynamics and on the three step motion panning strategy is explored. A nilpotent approximation is constructed and used for iterative steering of the rolling robot. The initial simulations show the feasibility of this approach.

An analysis of the motion planning problem for a spherical rolling robot driven by internal rotors

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.

On the iterative steering of a rolling robot actuated by internal rotors

This chapter deals with a motion planning problem for a spherical rolling robot actuated by two internal rotors that are placed on orthogonal axes. The mathematical model of the robot, represented by a driftless control system, contains a physical singularity corresponding to the motion of the contact point along the equatorial line in the plane of the two rotors. It is shown that steering through the singularity by finding a globally regular valid basis is not applicable to the system under consideration. The solution of the motion planning problem employs the nilpotent approximation of the originally non-nilpotent robot dynamics, and is based on an iterative steering algorithm. At each iteration, the control inputs are constructed with the use of geometric phases. To solve the state-to-state transfer problem, a globally convergent steering algorithm with adjustable step size is implemented and tested under simulation. It is shown that its steering efficiency is not superior to the algorithm with constant iteration step size.

Motion planning of drifting vehicle with friction model considering nonholonomic constraint

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.

Modeling of tire friction force of vehicle considering nonholonomic constraints

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.

A dynamically realizable reconfiguration strategy for steering a spherical rolling with two internal rotors

The paper addresses the problem of reconfiguring a spherical rolling robot actuated by two internal rotors that are placed on orthogonal axes. The problem is stated in dynamic formulation. 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. A working model for solving the motion planning problem is obtained by modifying the contact kinematic equations by the condition of dynamic realizability which constrains the component of the angular velocity of the rolling carrier and depends on the mass distribution. By using a motion planning strategy based on tracing a figure eight on the sphere, an exact and dynamically realizable motion planning algorithm is fabricated and verified under simulation. It is shown that the dynamically realizable contact paths are shorter and essentially different than those resulted from the kinematic model of pure rolling.

Motion analysis and feedforward control of a tail-slide vehicle

Conventional motion planners for wheeled vehicles often attempt to prevent wheel slipping or even assume no-slipping condition. However, in some practical situations slipping can be useful. The purpose of this work is construct a motion planning strategy for tail-slide vehicles where the rear wheel is slipping. First we develop a dynamic model of a four-wheeled vehicle by combining an extended 2D-model of the Coulomb friction and the nonholonomic rolling constraints. We then show that, compare to model ignoring sliding, the turning radius of the vehicle can be made smaller by using the tail-slide. After revealing the realizability condition of the tail-slide, we construct a motion planning strategy for steady-state cornering by combining the tail-slide and nonholonomic motion maneuvers. The feasibility of the motion planning strategy is tested under simulation.