A Singularity-Robust LQR Controller for Parallel Robots
Ricard Bordalba, Josep M. Porta, Lluis Ros
2018
2018 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)
Parallel robots exhibit the so-called forward singularities, which complicate substantially the planning and control of their motions. Often, such complications are circumvented by restricting the motions to singularity-free regions of the workspace. However, this comes at the expense of reducing the motion range of the robot substantially. It is for this reason that, recently, efforts are underway to control singularitycrossing trajectories. This paper proposes a reliable controller to
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... e such kind of trajectories. The controller is based on the classical theory of linear quadratic regulators, which we adapt appropriately to the case of parallel robots. As opposed to traditional computed-torque methods, the obtained controller does not rely on expensive inverse dynamics computations. Instead, it uses an optimal control law that is easy to evaluate, and does not generate instabilities at forward singularities. The performance of the controller is exemplified on a five-bar parallel robot accomplishing two tasks that require the traversal of singularities. I. I Parallel robots may be advantageous because of their stiffness, precision, and the efficiency of their movements [1] . These assets come at a high cost however: their workspace tends to be limited, and the planning and control of their motions are rather involved. Their closed kinematic chains and passive joints give rise to forward singularities [2], [3], in which the system becomes underactuated [4] . In such configurations, thus, the system will be unable to follow arbitrary accelerations. Actually, for some accelerations, the inverse dynamic problem will yield extremely large motor torques. It is important to note, however, that singularity-crossing motions can safely be executed if the kinodynamic constraints of the robot are respected [4], [5], [6], [7]. This is a key finding, because the motion capabilities of the robot can be greatly enlarged if such motions are allowed. A recent planner, in fact, is able to generate singularitycrossing motions [8], [9]. This planner relies only on forward dynamics, and thus obtains trajectories that fulfill all kinodynamic constraints, even at the forward singularities. These trajectories are "open loop" though, and thus they need to be stabilized a posteriori with a feedback controller. The purpose of this paper is to complete this task, in order to achieve stable trajectory trackings, even in the presence of disturbances or dynamic model inaccuracies. This work has been partially funded by the Spanish Ministry of Economy and Competitiveness under projects DPI2014-57220-C2-2-P and DPI2017-88282-P. Ricard Bordalba, Josep M. Porta, and Lluís Ros are with the In-
doi:10.1109/iros.2018.8594084
dblp:conf/iros/BordalbaPR18
fatcat:xcdgmvjvi5dazcxarnfye2hwve