Proportional Control for Stochastic Regulation on Allocation of Multi-Robots

TL;DR

This paper presents a stochastic control approach using proportional control to manage uncertainties in multi-robot task allocation, enabling precise distribution despite environmental and robot-level variabilities.

Contribution

It introduces a structured stochastic jump process model and a gain design method to control mean and variance in robot ensemble task allocation.

Findings

Successful regulation of ensemble behavior demonstrated through simulations.

Ability to reduce variance and improve task allocation accuracy.

Flexible adjustment of allocation distribution via control parameters.

Abstract

Any strategy used to distribute a robot ensemble over a set of sequential tasks is subject to inaccuracy due to robot-level uncertainties and environmental influences on the robots' behavior. We approach the problem of inaccuracy during task allocation by modeling and controlling the overall ensemble behavior. Our model represents the allocation problem as a stochastic jump process and we regulate the mean and variance of such a process. The main contributions of this paper are: Establishing a structure for the transition rates of the equivalent stochastic jump process and formally showing that this approach leads to decoupled parameters that allow us to adjust the first- and second-order moments of the ensemble distribution over tasks, which gives the flexibility to decrease the variance in the desired final distribution. This allows us to directly shape the impact of uncertainties on the group allocation over tasks. We introduce a detailed procedure to design the gains to achieve the desired mean and show how the additional parameters impact the covariance matrix, which is directly associated with the degree of task allocation precision. Our simulation and experimental results illustrate the successful control of several robot ensembles during task allocation.