Rotation and translation selective Pareto optimal solution to the box-pushing problem by mobile robots using NSGA-II

Abstract

The paper proposes a novel formulation of the classical box-pushing problem by mobile robots as a multiobjective optimization problem, and presents Pareto optimal solution to the problem using Non-dominated Sorting Genetic Algorithm-II (NSGA-II). The proposed method adopts local planning scheme, and allows both turning and translation of the box in the robots' workspace in order to minimize the consumption of both energy and time. The planning scheme introduced here determines the magnitude of the forces applied by two mobile robots at specific location on the box in order to align and translate it along the time-and energy-optimal trajectory in each distinct step of motion of the box. The merit of the proposed work lies in autonomous selection of translation distance and other important parameters of the robot motion model using NSGA-II. The suggested scheme, to the best of the authors' knowledge, is a first successful realization of a communication-free, centralized cooperation between two robots used in box shifting problem satisfying both time and energy minimization objectives simultaneously, presuming no additional user-defined constraint on the selection of linear distance traversal.

A Comparison of Various Approaches to Reinforcement Learning Algorithms for Multi-robot Box Pushing

“…Of the non-machine learning solutions, there have been several attempts to perform box pushing. Genetic algorithms (GA) have been applied to attempt a Pareto optimal solution that minimizes time taken and energy expended to push a box [1]. GA-based methods did not attempt to include obstacles in the environment and are not necessarily suitable for obstacle ridden environments.…”

Multi-robot cooperative box-pushing problem using multi-objective Particle Swarm Optimization technique

“…A specific version of the Box-pushing problem, where two similar robots have to plan the trajectory of motion of the box from a pre-defined starting position to a fixed goal position in a given environment, containing a static number of obstacles is considered in this work [6]. The robots are capable of shifting a large box from initial position to the final goal position.…”

Multi-robot box-pushing in presence of measurement noise

“…The entire procedure is executed for k= [1, N] and i= [1,NP]. IQR is capable to capture the true spread of samples in the noisy environment better than the variance (as in (19)) as the measurement of IQR eliminates the impact of the extreme values of the noisy fitness samples.…”

“…In this paper, the energy consumed by the robots and the time required to execute the box-pushing task are considered as two conflicting primary objective functions [19 . The time and energy objectives need to be optimized here before each step of local movement of the box (for local planning) to select the optimum next position among many alternatives.…”