Path planning for active tensegrity structures

This paper presents a path planning method for actuated tensegrity structures with quasi-static motion. The valid configurations for such structures lay on an equilibrium manifold, which is implicitly defined by a set of kinematic and static constraints. The exploration of this manifold is difficult with standard methods due to the lack of a global parameterization. Thus, this paper proposes the use of techniques with roots in differential geometry to define an atlas, i.e., a set of coordinated local parameterizations of the equilibrium manifold. This atlas is exploited to define a rapidly-exploring random tree, which efficiently finds valid paths between configurations. However, these paths are typically long and jerky and, therefore, this paper also introduces a procedure to reduce their control effort. A variety of test cases are presented to empirically evaluate the proposed method.