This paper presents the higher-order kinematic analyses of a planar parallel robot, addressed by means of the theory of screws. The reduced velocity, acceleration, jerk and hyper-jerk state for the end-effector of robot was developed as a spatial vector by applying the concept of Lie algebra and helicoidal vector field. In order to verify the effectiveness of this theoretical development, the kinematics models obtained was solved and simulated in MATLAB environment, using Freeth’s Nephroid trajectory as reference path for tracking with the end-effector. The simulation results proved that this type of spatial notation is convenient, because it allows us to quickly develop equations of motion and express them succinctly in symbolic form, reducing the volume of algebra, simplifying the modeling tasks, implementation and execution the algorithms used to solve kinematic problems in parallel robots. The major contribution of this work is the possibility of extended the classical kinematic analysis to a high order system; where the application of screw theory becomes a safe and reliable mathematical tool, which may be successfully used on parallel planar robots with singular configurations, represented with helicoidal vector field.
This paper presents the generalized predictive control with constraints, implemented to a planar parallel robot in order to calculate and track the desired trajectory of the end-effector of this robot. The manipulator is driven by three brushless direct current motors, and each one has an encoder to measure the velocity and rotation angles of the motors. Three constraints were considered to interact with the control law: control signal, terminal response and the over impulse constraints. The performance of the control law is evaluated in the simulation environment using Matlab/Simulink with the physic model developed through simscape multibody. The angular position and velocity errors for each of the three motors were calculated. Likewise, the output torques for each one were estimated. The results proved that the control law proposed with the constraints imposed for each motors has a good efficiency with a stable response time of the robot in performing the trajectory tracking, contributing to the scientific community a strategy of predictive optimization of control actions with multiple constraints applied on parallel robots.
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