Controlling Shapes of Ensembles of Robots of Finite Size with Nonholonomic Constraints

Abstract

Abstract-In this paper we focus on the construction of distributed formation control laws that permit the control of individual mobile ground robots in a formation to a desired distribution with minimal knowledge of the global state. As in previous work, we consider an abstraction of the team that is derived from a shape descriptor of the ensemble and the position and orientation of the ensemble. We consider the control of the abstract state with decentralized control laws which are independent of the number of agents. However, we incorporate an important departure from previous work by explicitly modeling the shape of the robot, the geometric, non-interpenetration constraints and nonholonomic, kinematic constraints. Further, we propose a motion planning technique to plan motions for ensembles of robots and a technique for the splitting and merging of groups and subgroups. We demonstrate the effectiveness of the algorithms on a team of differential drive robots in simulation and on real hardware.

Decentralized feedback controllers for multi-agent teams in environments with obstacles

“…, u| v D + 1 } are the inputs evaluated at the vertices. The linear program (10) generates the inputs at the vertices of each simplex, which must be interpolated within the simplex (for more detail see [20]). Every point in a simplex is described by a unique convex combination of the vertices.…”

Autonomous navigation with teams of aerial robots

“…This paper is most closely related to the above work and builds on previous results for planar robots. 20,22 Specifically we develop a framework and controllers for a team of aerial robots that requires only partial state feedback. The robots maintain a three-dimensional formation and navigate while avoiding collisions.…”

Motion planning under bounded uncertainty using ensemble control

“…The more recent work of Brockett, Khaneja, and Li has found primary application so far to quantum systems, for example manipulating nuclear spins in Nuclear Magnetic Resonance (NMR) spectroscopy [1]- [7]. Robotics researchers are also beginning to adopt the term "ensemble," for example in the context of multi-robot formations [10], but the formal methodology of ensemble control has yet to be applied. We should also note that other approaches to dealing with infinite-dimensional systems (such as taking advantage of differential flatness) have been developed in parallel, as in [11].…”