Ritsumeikan University, Japan
Professor, Department of Mechanical Engineering, Kyushu University
Bai Y., Svinin M., Yamamoto M.
Dynamics-Based Motion Planning for a Pendulum-Actuated Spherical Rolling Robot
2018, vol. 23, no. 4, pp. 372-388
This paper deals with the dynamics and motion planning for a spherical rolling robot with a pendulum actuated by two motors. First, kinematic and dynamic models for the rolling robot are introduced. In general, not all feasible kinematic trajectories of the rolling carrier are dynamically realizable. A notable exception is when the contact trajectories on the sphere and on the plane are geodesic lines. Based on this consideration, a motion planning strategy for complete reconfiguration of the rolling robot is proposed. The strategy consists of two trivial movements and a nontrivial maneuver that is based on tracing multiple spherical triangles. To compute the sizes and the number of triangles, a reachability diagram is constructed. To define the control torques realizing the rest-to-rest motion along the geodesic lines, a geometric phase-based approach has been employed and tested under simulation. Compared with the minimum effort optimal control, the proposed technique is less computationally expensive while providing similar system performance, and thus it is more suitable for real-time applications.
Svinin M., Morinaga A., Yamamoto M.
On the Dynamic Model and Motion Planning for a Spherical Rolling Robot Actuated by Orthogonal Internal Rotors
2013, vol. 18, no. 1-2, pp. 126-143
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.