Task-space impedance control of a parallel Delta robot using dual quaternions and a neural network

The Delta robot, widely used in fast pick-and-place applications with pure position control, is a parallel kinematic chain with three rotational inputs resulting in three pure translations at the end-effector. This paper proposes a complete task-space impedance control with inverse dynamics to give this robot compliant behavior, enabling it to be used in tasks involving physical interaction. For that purpose, the well-known usage of dual quaternion algebra for kinematics modeling is novelly integrated with a neural network to compose a compact representation for the forward kinematics function, that is singularity-free and suitable for real-time calculation. This network computes the forward kinematics more than 150 times faster than a numeric equation solving algorithm, with an average estimation error of less than 0.5 mm. The proposed algorithm is implemented in a rigid body simulator, and the performance of the complete system is analyzed.