Читать книгу Path Planning of Cooperative Mobile Robots Using Discrete Event Models - Cristian Mahulea - Страница 17

The key goal of a mobile robot is to follow the route generated by the path planner, and this goal is responsible for the motion controller. More specifically, robot control deals with the problem of determining the forces (or velocities) that must be developed by the robotic actuators in order for the robot to go to a desired position, track a desired trajectory, and, in general, perform some tasks with desired performance requirements [202].

The control problem can be classified depending on how the reference path is defined: a single target point , a set of waypoints , or a set of poses , where is the time. The time in the previous variables represents a situation where those variables may change along the robot operation. In this sense, the control strategy can be understood as the problem of moving to a point, path following, and trajectory tracking, see Figure 1.5. Notice that, in the trajectory tracking problem the robot orientation must also be controlled, unlike in the other two cases where the final robot orientation depends on the starting position.

Essentially the control problem must ensure

(1.1)

Figure 1.5 Motion control methods. Main categories for motion control in mobile robotics and an example of some well‐known methods for each of them.

where is the error between the actual position of the robot and the desired target position. Notice that Eq. (1.1) defines a quasi‐zero error because in some situations, for instance considering uncertainty, an exact error equal to zero cannot be achieved [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.

One of the first path following approaches was proposed by R. Craig Coulter in the early 1980s for the Terregator robot [45]. The name “pure pursuit” comes from the analogy for the way humans drive. We tend to look some distance in front of the car and head toward that spot. This lookahead distance changes as we drive to reflect the twist of the road and vision occlusions. In the pure pursuit algorithm, this lookahead distance plays a key role between accuracy following the desired route and aggressiveness of the control actions [79]. A similar algorithm to pure pursuit is called “carrot heading”. Here, the algorithm determines the next point to be followed by calculating the intersection of a circle centered on the rover frame origin with the desired path [94]. These two well‐known approaches belong to the category of path followers, that is, the robot follows a desired path with no concern about the orientation.

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].