Cristian Mahulea

Path Planning of Cooperative Mobile Robots Using Discrete Event Models


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[81]. The control problem associated with a mobile robot can then be defined as a feedback control system. The idea is that the controller senses the position/pose of the robot, compares it against the desired reference, computes corrective actions based on a model of the robot and actuates the robot to effect the desired change. As highlighted in [9], the key issues in designing control logic are ensuring that the dynamics of the closed‐loop system are stable (bounded disturbances give bounded errors) and that they have additional desired behavior (good disturbance attenuation and fast responsiveness to changes in the operating point, among others).

      It is important to remark that mobile robotics comprises a challenging field from a control standpoint as there are some phenomena that influence robot's controllability, such as hard constraints fulfillment (e.g. physical limitations of actuators, narrow workspaces), and uncertainties (e.g. unmodelled dynamics, simplified models, noisy measurements). For that reason, in the past few years, many research efforts have been devoted to the application of different control strategies.

      The second major problem dealing with mobile robot control is the trajectory tracking problem. In this case, the robot must follow a “virtual robot” (position and orientation) at each sampling time [81, 163]. This problem has benefited from the application of advanced controllers that appeared in the field of state feedback control [9, 24, 202]. For example, in [24, 105], a linear feedback control strategy is used for controlling a non‐holonomic mobile robot where stability is ensured by tuning the feedback gains of the control strategy according to a Lyapunov function. This controller was extended in [80] for compensating for longitudinal slip in mobile robots operating in off‐road conditions.

      The problem of trajectory tracking in mobile robotics has also benefited from another broad body of research: Model Predictive Control (MPC). MPC is based on generating the control input to be applied to the robot by solving an optimization problem considering the robot constraints and the desired reference to be tracked [156, 177, 208]. For instance, in [137], the authors use an MPC controller to enable both anticipation of approaching curvature and to compensate from lateral slip phenomena for path tracking control of an agricultural vehicle. In [108], an MPC is applied to the trajectory tracking problem. The control law is analytically derived, which permits its application to a physical mobile robot. In order to avoid vehicle slip, velocity and acceleration are bounded. The work [77] presents a predictive strategy that permits the robot to avoid unexpected static obstacles in the robot environment. In this case, a neural network was trained to be able to run the MPC‐based controller in real‐time. A Smith‐predictor‐based generalized predictive controller is discussed in [161]. This control strategy permits dealing with dead‐time uncertainties related to a mobile robot control motion. Generally, the main issue of robust MPC strategies, which sometimes prevent its physical application, is related to the high computation burden [176]. Recently, an efficient theoretical concept, called a “tube‐based MPC”, has been applied to robustify MPC and has been applied to mobile robots operating in off‐road conditions [11, 80, 81].

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      One possible necessity of using high‐level specifications instead of standard navigation problem (reaching a final configuration) is in the factories of the future, where workers and robots will cooperate in fulfilling complex tasks, in order to obtain as soon as possible the products requested by the consumers [55, 179, 189]. The robots should automatically adapt and optimize the usage of these shared frameworks [50, 197], and one of the important aspects is to automatically compute collision‐free trajectories. Since the number of mobile robots could be high, it is important to have computationally attractive techniques to plan trajectories for teams of robots.

      Linear‐time temporal logic is a general‐purpose mathematical language for describing linear‐time problems, which was first pointed out by Amir Pnueli in 1977 [171]. In the specific context of mobile robotics, the set of mathematical operators defined by LTL can be used for encoding rules about the sequence of paths that a robot (or a team of robots) should follow. The success of LTL is that high‐level specifications defined in a natural human level can be easily translated into LTL statements. Although LTL formulation has demonstrated a significant contribution to the field of mobile robotics [13, 66, 111], it generally demands a high computation load.