This brief presents the design of a controller that allows an underactuated vessel to track a reference trajectory in the x − y plane. A trajectory tracking controller designed originally for robotic systems is applied for underactuated surface ships. Such a model is represented by numerical methods and, from this approach, the control actions for an optimal operation of the system are obtained. Its main advantage is that the condition for the tracking error tends to zero, and the calculation of control actions are obtained solving a system of linear equations. The proofs of convergence to zero of the tracking error are presented here and complete the previous work of the authors. Simulation results show the good performance of the proposed control system.

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A major issue in the automatic guidance of vehicles is the design of control laws dedicated to the specific mobile platform used. Thus, if the model associated with the mobile platform or its constraints change, a new control law must be designed. In this paper, the problem of designing trajectory tracking controllers for unmanned vehicles is addressed. The methodology proposed here is an algebraic approach for obtaining optimum and stable trajectory tracking controllers for nonholonomic vehicles. Such an algebraic formulation makes the proposal suitable for embedded applications. The stability and optimality of the proposed controllers design method is theoretically proven for both bicycle‐type and unicycle‐type mobile robots, although the methodology can be extended to other types of unmanned vehicles. Four tests were carried out in this work in order to show the advantages of the proposal: the step discontinuity test, the curvature test, the real world test, and navigation under disturbances in the control actions. The results obtained were compared with four trajectory tracking controllers previously published in the literature. Additionally, an agricultural application is included in order to show the performance of the proposed controller when applied to a service unit within an agricultural environment. Field experiments demonstrating the capabilities of our proposal are also reported and discussed.

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SUMMARYThis paper presents the design of four controllers for a mobile robot such that the system may follow a preestablished trajectory. To reach this aim, the kinematic model of a mobile robot is approximated using numerical methods. Then, from such approximation, the control actions to get a minimal tracking error are calculated. Both simulation and experimental results on a PIONEER 2DX mobile robot are presented, showing a good performance of the four proposed mobile robot controllers. Also, an application of the proposed controllers to a leader robot following problem is shown; in it, the relative position between robots is obtained through a laser.