Abstract
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.
Highlights
The last 2 decades have seen steady progress in the theory of tensegrity structures and their applications in Robotics
We propose a method for finding sequences of configurations of deformable tensegrity drones as a sequence of deformations of the original shape, with the space of deformations being equivalent to the space of positive-definite matrices
For fixed rest lengths of the elastic elements that form tensegrity structure, the static equilibrium problem can be solved by minimizing potential energy of the structure, or equivalently, by solving a feasibility problem, given force equilibrium equations and force limits arising from the physical properties of the elements of which the structure consists: the cables can only experience tensile forces, while the struts are designed to experience compressive forces
Summary
The last 2 decades have seen steady progress in the theory of tensegrity structures and their applications in Robotics. From tensegrity planetary landers [see Sabelhaus et al (2015a); Vespignani et al (2018)] to tensegrity spines for quadruped robots [Mirletz et al (2014); Sabelhaus et al (2015b); Zappetti et al (2020)], the properties of these structures have provided new ways to design mobile objects performing difficult tasks These properties include low weight, resistance to damage from collisions, the ability to control the stiffness of the structures, and the ability to control the deformation of the robot [see Liu et al (2022) for a review of other properties of the tensegrity structures]. We propose a method for finding sequences of configurations of deformable tensegrity drones as a sequence of deformations of the original shape, with the space of deformations being equivalent to the space of positive-definite matrices This limits the possible shapes the structure can assume, but at the same time, it allows to cast the problem as a semidefinite program (SDP), taking advantage of the widely used solvers with well-understood properties.
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