| 研究実績の概要 |
In the last year of this project, it was established that for the pure rolling (no twisting) motion mode the dynamic realizability condition always holds true for a pendulum-driven robot. As a result, motion planning can be decoupled into kinematic and dynamic levels. The former can be organized with the use of conventional planners, while the latter is represented by a reduced dynamic model (underactuated system featuring a nonholonomic constraint of second order). A rest-to-rest motion planning algorithm for the reduced model based on the idea of geometric phases was proposed. The algorithm employs the linearized solution of the optimal control problem with the minimum effort criterion. The applicability (the range of movements) of the algorithm and its feasibility were verified under simulations for tracing various spherical curves (geodesic lines, circles, Viviani curve and the Loxodrome). It was also shown how the resulting contact trajectories can be tracked by an adaptive (and asymptotically stable) feedback controller with the use of a function approximation technique in order to deal with uncertainties. On the practical side, two spherical robots (one driven by pendulum and one driven by dynamically symmetric rotors) were designed and prototyped.
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