A <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mi>d</mml:mi><mml:mi>ϕ</mml:mi></mml:math>-Strategy: Facilitating Dual-Formation Control of a Virtually Connected Team

Abstract

This paper describes the design of new centralized acceleration-based controllers for the multitask problem of motion planning and control of a coordinated lead-carrier team fixed in a dual-formation within an obstacle-ridden environment. A <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mi>d</mml:mi><mml:mi>ϕ</mml:mi></mml:math>-strategy, where <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M3"><mml:mrow><mml:mi>d</mml:mi></mml:mrow></mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M4"><mml:mrow><mml:mi>ϕ</mml:mi></mml:mrow></mml:math> are Euclidean measures with respect to the lead robot, is developed to ensure virtual connectivity of the carrier robots to the lead robot. This connectivity, built into the system itself, inherently ensures globally rigid formation between each lead-carrier pair of the team. Moreover, a combination of target configuration, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M5"><mml:mi>d</mml:mi><mml:mi>ϕ</mml:mi></mml:math>-strategy, orientation consensus, and avoidance of end-effector of robots results in a second, locally rigid formation (not infinitesimally rigid). Therefore, for the first time, a dual-formation control problem of a lead-carrier team of mobile manipulators is considered. This and other kinodynamic constraints have been treated simultaneously via the overarching Lyapunov-based control scheme, essentially a potential field method favored in the field of robotics. The formulation of this new scheme, demonstrated effectively via computer simulations, is timely, given that the current proposed engineering solutions, allowing autonomous vehicles on public roads, include the development of special lanes imbued with special sensors and wireless technologies.