Abstract:

This paper presents a didactic graphical user interface for simulating the state-space control of a five-bar planar parallel robot and studying how its controllability is affected by singularities. Parallel robots consist of two or more serial kinematic chains connected in parallel between the fixed base of the robot and its gripper, forming closed kinematic chains. Such closed chains provide parallel robots with higher stiffness, payload-to-weight ratio, and dynamic capabilities, but also originate singular configurations (typically called type 2 or parallel singularities, to distinguish them from other types of singularities) at which the robot is not fully controllable. Usually, this loss of controllability is studied from a velocity point of view, which reveals that these singularities allow the gripper of the robot to adopt velocities in some directions even if all actuators are perfectly locked. In this work, we propose a simulation tool to study this loss of controllability from a state-space point of view. The proposed tool is a Javascript web-based graphical user interface that allows students to simulate the kinematics and dynamics of a five-bar planar parallel robot. When simulating the dynamics of this robot using the proposed tool, the students can decide to simulate its open-loop dynamics (where actuation torques are directly specified by the student) or its closed-loop control. When simulating the closed-loop control, the student can choose between a classical decoupled Proportional-Integral-Derivative controller that can be independently designed for each degree of freedom of the robot, or a more sophisticated state-feedback controller, which is more suitable for parallel robots since these are MIMO (Multiple-Input Multiple-Output) dynamical systems in which all degrees of freedom are coupled. After reading the matrices of the linearized state-space model of the robot from the simulator, the students can manually design the state-feedback gains and later test them in the simulator, in order to validate their design and check if they designed these gains correctly. The proposed simulator allows the students to simultaneously validate their designed controllers on the true nonlinear model of the robot and on a linearized version of it, to compare and assess the similarity between the responses of the nonlinear and linearized models under the same controller designed using linear state-feedback techniques. Finally, the students can move the robot to singularities to evaluate how its controllability degrades near them, graphically visualizing how the controllable subspace of the robot changes when approaching singularities. The proposed tool is being used for teaching singularities, controllability, and state-feedback control for MIMO systems in subjects on State-Space Control and Robotics in different bachelors and masters degrees at the Miguel Hernandez University of Elche (Spain). In this paper, some examples of educational exercises or practices that can be done with the proposed simulator are described.

Keywords:

Parallel robot, simulator, state-space control, singularities, controllability.