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Section: New Results
Multi-robot and Crowd Motion Control
Rigidity-based Methods for Formation Control
Participants : Fabrizio Schiano, Paolo Robuffo Giordano.
Most multi-robot applications must rely on relative sensing among the robot pairs (rather than absolute/external sensing such as, e.g., GPS). For these systems, the concept of rigidity provides the correct framework for defining an appropriate sensing and communication topology architecture. Rigidity is a combinatorial theory for characterizing the “stiffness” or “flexibility” of structures formed by rigid bodies connected by flexible linkages or hinges. In a broader context, rigidity turns out to be an important architectural property of many multi-agent systems when a common inertial reference frame is unavailable. Applications that rely on sensor fusion for localization, exploration, mapping and cooperative tracking of a target, all can benefit from notions in rigidity theory. The concept of rigidity, therefore, provides the theoretical foundation for approaching decentralized solutions to the aforementioned problems using distance measurement sensors, and thus establishing an appropriate framework for relating system level architectural requirements to the sensing and communication capabilities of the system.
In our previous works we have addressed the problem of coordinating a team of quadrotor UAVs equipped with onboard cameras from which one could extract “relative bearings” (unit vectors in 3D) w.r.t. the neighboring UAVs in visibility. This problem is known as bearing-based formation control and localization. The basic assumption, however, was to always have a bearing rigid graph which may easily conflict with any sensing/communication constraint (measurements/edges can be lost whenever, e.g., a UAV leaves the camera fov, or it is occluded by another UAV/obstacle). In [62] we have then tackled the problem of “bearing rigidity maintenance” by studying how to formalize the problem of maintaining bearing rigidity over time despite possible sensing/communication constraints (min/max range, limited camera fov and occlusions in the reported work). Thanks to a suitable weighing machinery, we could define a “bearing rigidity eigenvalue” as a suitable metric for quantifying the degree of rigidity in the interaction graph, and then we could propose a gradient-based controller able to maintain the rigidity eigenvalue always positive (and, thus, guarantee bearing rigidity maintenance). The approach has been validated by experiments run on 5 quadrotor UAVs.
Cooperative Localization using Interval Analysis
Participants : Ide Flore Kenmogne Fokam, Vincent Drevelle.
In the context of multi-robot fleets, cooperative localization consists in gaining better position estimate through measurements and data exchange with neighboring robots. Positioning integrity (i.e., providing reliable position uncertainty information) is also a key point for mission-critical tasks, like collision avoidance. The goal of this work is to compute position uncertainty volumes for each robot of the fleet, using a decentralized method (i.e., using only local communication with the neighbors). The problem is addressed in a bounded-error framework, with interval analysis and constraint propagation methods. These methods enable to provide guaranteed position error bounds, assuming bounded-error measurements. They are not affected by over-convergence due to data incest, which makes them a well sound framework for decentralized estimation. Results have been obtained for image-based localization of a single UAV, enabling to characterize the pose uncertainty domain from measurements uncertainties [50], and also fusion with onboard proprioceptive sensors [49]. Extension to cooperative localization in a multi-UAV fleet has been studied in the two-robot case and continues as an ongoing work.