Sampling-Based Trajectory (re)planning for Differentially Flat Systems: Application to a 3D Gantry Crane

In this paper, a sampling-based trajectory planning algorithm for a laboratory-scale 3D gantry crane in an environment with static obstacles and subject to bounds on the velocity and acceleration of the gantry crane system is presented. The focus is on developing a fast motion planning algorithm for differentially flat systems, where intermediate results can be stored and reused for further tasks, such as replanning. The proposed approach is based on the informed optimal rapidly exploring random tree algorithm (informed RRT*), which is utilized to build trajectory trees that are reused for replanning when the start and/or target states change. In contrast to state-of-the-art approaches, the proposed motion planning algorithm incorporates a linear quadratic minimum time (LQTM) local planner. Thus, dynamic properties such as time optimality and the smoothness of the trajectory are directly considered in the proposed algorithm. Moreover, by integrating the branch-and-bound method to perform the pruning process on the trajectory tree, the proposed algorithm can eliminate points in the tree that do not contribute to finding better solutions. This helps to curb memory consumption and reduce the computational complexity during motion (re)planning. Simulation results for a validated mathematical model of a 3D gantry crane show the feasibility of the proposed approach.Comment: Published at IFAC-PapersOnLine (13th IFAC Symposium on Robot Control

Path planning and path following control for mechanical systems

Zusammenfassung in deutscher SpracheZiel dieser Arbeit ist die methodische Behandlung einer Pfadplanung und die anschließende Pfadfolgeregelung für mechanische Systeme. Der vorliegende Text ist in zwei Teile gegliedert, die jeweils einem dieser Probleme gewidmet sind. Im ersten Teil wird mittels der so genannten Rapidly Exploring Random Trees (schnell erkundende zufällige Bäume) ein allgemeines Pfadplanungsproblem gelöst. Dieses besteht aus der Forderung einen Pfad zwischen zwei definierten Punkten eines Raumes zu finden, der durch Hindernisse beschränkt ist. Mittels einer Erweiterung des Algorithmus können optimale Pfade, im Sinne eines spezifizierten Kriteriums, gefunden werden. Durch geeignete Annahmen lässt sich dieses Problem auf eine weite Klasse mechanischer Systeme anwenden. Der so gewonnene Pfad soll weiters durch ein mechanisches System gefolgt werden. Zu diesem Zweck wurde ein neuer Ansatz für eine Pfadfolgeregelung entwickelt. Hierbei ist nicht nur die Verfolgung des Pfades, sondern auch eine unabhängige Spezifikation der Reaktion auf Abweichungen möglich. Alle beschriebenen Methoden werden anhand geeigneter Simulationen analysiert und ausgewertet. Diesbezüglich wurden mechanische Systeme mit unterschiedlichen Charakteristika herangezogen, um die gewählten Ansätze zu illustrieren. Die Validierung der beschriebenen Methoden mithilfe eines drei-achsigen Parallelroboters untermauert deren praktische Anwendbarkeit.The goal of this thesis is to provide systematic means to plan and follow a path for mechanical systems. Therefore, this thesis is divided into two main parts, one for each of these problems. Firstly, the path planning problem is introduced and then solved by using the so-called Rapidly Exploring Random Tree algorithm. To improve the so-found paths, a modification is introduced which renders the solutions optimal with respect to a specific criterion. To avoid high computation times, the algorithm was simplified by consistent assumptions on the mechanical system. Secondly, a path following controller is derived to follow the calculated path in presence of disturbances and to account for modelling errors. Using this controller, it is possible to control the velocity along the path with one control law and a second control law is defined to account for deviations from the path. To the best of the authors knowledge, this controller, unlike for any other approach, can be specified in fixed coordinates. This particularly simple approach is applicable to a wide variety of systems, in particular mechanical systems. In simulation the proposed concepts were tested for a number of mechanical systems. To underline its practical feasibility the path following approach was validated using a parallel kinematic robot.4

Adaptive Two-Degrees-of-Freedom Current Control for Solenoids: Theoretical Investigation and Practical Application

In this paper, an adaptive two-degrees-offreedom current control algorithm for solenoids is presented comprising an adaptive pole placement controller in combination with a regularized least-squares parameter estimation law. An additional adaptive feedforward controller takes advantage of the estimated plant parameters to further enhance the tracking performance. The stability of the overall closed-loop system is rigorously proven. The proposed solution differs from existing approaches by the adaptive feedforward controller and the way the parameter estimation is performed. The control concept is applied with the same controller parametrization to three solenoids from different applications, with substantially differing parameters. The experimental results show high tracking performance and fast parameter convergence even with poor initial estimates and despite the nonlinear dependence of the inductance on the current and position. The experimental results are also compared to two benchmark control design paradigms known from the literature, i.e. a second-order sliding mode controller and a nonlinear model reference adaptive control solution, which are both outperformed by the proposed controller