ARTIGO TÉCNICO Rui Soares1, Estela Bicho2* 1Esc. Sup. Tec. e Gestão de Felgueiras, Instituto Politécnico do Porto, rsoares@estgf.ipp.pt 2Dep. Electrónica Industrial, Universidade do Minho, estela.bicho@dei.uminho.pt *Corresponding author
COORDINATED TRANSPORTATION OF A LARGE OBJECT BY A TEAM OF TWO ROBOTS ABSTRACT In this paper dynamical systems theory is used as a theoretical language and tool to design a distributed control architecture for a team of two robots that must transport a large object and simultaneously avoid collisions with obstacles (either static or dynamic). This work extends the previous work with two robots (see [1] and [5]). However here we demonstrate that it’s possible to simplify the architecture presented in [1] and [5] and reach an equally stable global behavior. The robots have no prior knowledge of the environment. The dynamics of behavior is defined over a state space of behavior variables, heading direction and path velocity. Task constrains are modeled as attractors (i.e. asymptotic stable states) of a behavioral dynamics. For each robot, these attractors are combined into a vector field that governs the behavior. By design the parameters are tuned so that the behavioral variables are always very close to the corresponding attractors. Thus the behavior of each robot is controlled by a time series of asymptotic stable states. Computer simulations support the validity of the dynamical model architecture.
1. INTRODUCTION The motivation for the development of autonomous robots that are able to transport large objects arises from the potential applicability of these systems in industrials and civilian environments. There has been some research concerning this issue (e.g. [6, 7, 8, 9, 10, 12]). One of the most and fundamental problems in controlling multiple robots carrying an object together is the maintenance of a geometric fixed configuration during the movement. This paper attempts to simplify the previous work reported in [1] and [5]. In our previous works we used the dynamical systems theory as theoretical framework to design and implement a distributed control architecture for a team of two mobile robots that had to transport a long object in cluttered environments. As in previous work reported in [1] and [5] we assume that: (a) the robots have no prior knowledge of the environment and no path is given; (b) it is used a leader-helper decentralized motion control strategy, where the leader robot drives from an initial position to a final target destination (see for example [8]); (c) the helper robot (H1) takes the leader as a reference point and must maintain at all times a correct distance and orientation that permits to it to help the leader robot in the transportation task (see Figure1).
Figure 1 . Coordinated object transportation by two robots in an unknown environment. By default the robots must transport the object keeping a line forward/line backward formation (LF/LB). When due to encountered obstacles that is not possible robot H must drive in transition or column information. 1
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One difference with respect to our previous work is the used support base. In the work present here, the support base gives displacements of the bar in two directions while the support base used in our previous work only gave displacements of the bar in the direction of the robot leader with respect to the robot H1. The control architecture of each robot is structured in terms of elementary behaviors. The individual behaviors and their integration are generated by non-linear dynamical system. For each behavior, desired values for the controlled behavioral variables are identified and made attractor solutions of the dynamical systems that generates the robot’s motion. The rest of the paper is structured as follows: next section presents the robot team, their tasks and the basic assumptions in this work. Next is defined and described the behavioral dynamics for the robot helper (H1). Results obtained from computer simulations are presented in next section. The paper ends with a brief discussion, conclusions and an outlook of future work.
2. ROBOT TEAM AND TASK CONSTRAINS The simulated robots are based on the physical mobile robots used in [2], [5] and [11]. There is a difference in the support base used here with respect to the support base used in [5]. In [5] the displacement of the bar was measured only in the direction of the robot leader with respect to the robot follower. Now the support base gives displacements of the bar in two directions Δx and Δy (see Figure 2). The control and coordination are based on the main ideas presented on the previous work, but here an attempt is made to simplify the overall control architecture: (a) the behavior of each robot is controlled independently; (b) the leader robot knows the target position, and its task consists in moving from an initial position to a final target destination; (c) robot H1 must maintain at all times a correct orientation and distance with respect to the leader robot; (d) by default the H1 robot must move in an LF/LB formation, however if obstacles don’t allow it, robot H1 must drive in transition or column formation; (e) the leader robot communicates to robot H1 its path velocity; (f) robot H1 is able to measure the direction at witch the leader robot lies from its current position with respect to an external reference axis, ψH1,leader (see