Rigidity Theory for Multi-agent Systems Meets Parallel Robots: Towards the Discovery of Common Models and Methods
The goals of this workshop are to explore connections and encourage discussion between two historically distinct communities: the parallel robotics community and the multi-robot community (for what concerns, generally speaking, rigidity-based methods for distributed formation control and localization). Indeed, although these two areas may appear as quite distant, they actually share a strong common underline theme: understanding how pairwise geometrical constraints (e.g., relative distances or angles) can affect the mobility or state (pose) estimation for robotic systems. Moreover, there is a strong analogy between multi-agent systems and parallel robots: each robot of the system can be seen as a passive joint of a virtual mechanical (parallel) architecture and each measurement between two robots as a rigid connection between them, rigid connection whose dimension can vary thanks to a virtual actuator. So it is possible to find virtual parallel robot architectures associated with multi-agent systems.
Rigidity-based multi-robot control/estimation is typically concerned about topics such as: (i) understanding what is the minimum number of edges (of constraints) for ensuring rigidity in some configuration space, (ii) characterizing the (infinitesimal) motions of a formation that preserve desired shapes, (iii) stabilizing a rigid formation towards desired shapes, (iv) reconstruct the formation shape/pose from local pair-wise measurements, or (v) maintaining for- mation rigidity at runtime despite sensing/communication constraints. Parallel robotics is instead concerned about (i) finding the solutions of complex algebraic equations associated with the estimation of the configuration of the end-effector for a given set of active joint positions, and (ii) finding the singular configurations leading to a loss of controllability for the end-effector (loss of mechanical rigidity). These problems in both fields have some similarities that we propose to explore. The next two sections give a more detailed overview of both communities.
This workshop hopes to bring together, at the highest level, audiences from the robotics community and the controls community. We hope the workshop will be of particular interest to researchers and students focusing on formation control theory and parallel robotics. The expected learning outcome of this workshop is to provide every attendant with a clear picture of both communities (open problems, tools, methods, ideas) and of how the two worlds could benefit from each other.
Session 1 (8:00–10:00) - Rigidity Theory
3 invited talks of 35 minutes each focusing on rigidity theory. Talks will be a blend of both tutorial style and presentation of recent results in the field.