Morphing-Enabled Path Planning for Flying Tensegrity Robots as a Semidefinite Program

The development of deformable drones is of high importance but presents significant challenges. Such drones can be based on tensegrity structures, which leaves open the questions of configuration-space path planning for such robots. In this paper we propose a method that takes advantage of a simplified encoding of the drone's shape, allowing to turn the path planning into a sequence of semidefinite programs. The mapping from the simplified description and the actual tensegrity configuration is done via a data-driven method, using a pre-computed dataset of statically stable configurations and their outer Löwner-John ellipsoids, as well as eigendecompositions of the ellipsoid matrices. Together it allows rapid containment check, whose computational cost depends linearly on the number of dataset entries. Thus, the proposed method offloads computationally-intensive parts to the offline dataset generation procedure, speeding up the algorithm execution.