Multirobot Control Using Time-Varying Density Functions

Abstract

This paper presents an approach to externally influencing a team of robots by means of time-varying density functions. These density functions represent rough references for where the robots should be located. To this end, a continuous-time algorithm is proposed that moves the robots so as to provide optimal coverage given the density functions as they evolve over time. The developed algorithm represents an extension to previous coverage algorithms in that time-varying densities are explicitly taken into account in a provable manner. A distributed approximation to this algorithm is moreover proposed whereby the robots only need to access information from adjacent robots. Simulations and robotic experiments show that the proposed algorithms do indeed exhibit the desired behaviors in practice as well as in theory.

Multi-Robot Control Using Coverage Over Time-Varying Domains: Extended Abstract

“…In [5], a control law was proposed which was later shown in [6] to achieve exponential converge to a CVT in the case of time-varying densities. This control law was called TVD-C for time-varying densities, centralized case, given byṗ…”

“…The ∂c ∂t term improves the error performance by 54.97% in this scenario with a large group of agents. The error is not exactly zero because the distributed form of the control law (5) was used, which does not perform feedforward on every agent in the team. Thus, the agents on the boundary can immediately follow the motion of subdomain as they have direct access to the boundary conditions (i.e., whose Voronoi cell boundaries have overlapped edges with subdomain's boundaries), but the agents on the interior must wait for the boundary conditions to propagate through feedback.…”

“…In this paper, the coverage control algorithm [5] is taken as a mechanism to affect the behavior of a big multi-robot team by involving time-varying domains. We define a time-varying subdomain in the workspace, and command the robots to optimally distribute in the time-varying subdomain.…”

Coordinated Control of Multi-Robot Systems: A Survey

“…Consider the scenario where the function ϕ measuring the relative importance of points in the environment changes with time [20], [57], e.g., according to the preferences specified by a human operator. Formally, we have ϕ : D × R → R, (p, t) → ϕ(p, t).…”

“…The matrix is sparse, but its inversion is not. One can tackle this, for instance, by approximating the inverse matrix with the Taylor series expansion which, as the matrix sparse, is amenable to distributed implementation [57]. An example of this approach is shown in Fig.…”