Modeling and cascade-based robust dynamic control of a hyper-constrained parallel mechanism for high-precision robotic tasks

This paper presents the mechanical design, constructive aspects, kinematic modeling and control design methodology for a hyper-constrained parallel mechanism (HCPM), composed of six closed kinematic chains and twelve spherical joints, which is developed to carry out high-precision robotic tasks in industrial and agricultural environments. Here, we employ a systematic modeling methodology which considers the kinematic constraints of the mechanism from its structure equations, rather than explicitly using the constraint equations. This allows us to describe the kinematic constraints in the operation velocity space instead of the joint configuration space. From this analytical approach, we can compute the velocity of the non-actuated joints as a function of the velocity of the actuated ones. The control design uses an inverse kinematics algorithm based on the pseudo-inverse Jacobian matrix. In order to deal with many potential singular configurations which may occur during the task execution, we consider a recently proposed approach, called the Filtered Inverse method, which dynamically estimates the inverse of the Jacobian matrix instead of computing its true inverse instantaneously. The dynamic control of the HCPM is achieved using a simplified, Lagrangian-derived model to provide the computed-torque feedforward term for nonlinear compensation and decoupling, enabling motion simulation for high-speed trajectories while dismissing the need for a full explicit model, which is complex and difficult to obtain. Despite the simplifications, a robust cascade control strategy is proposed—featuring a second-order sliding mode (STA) compensator—to handle modeling uncertainties effectively. 3D computer modeling, numerical simulations, and laboratory experiments with two prototypes of the hyper-constrained parallel mechanism were conducted to validate the proposed approach and demonstrate its feasibility for high-precision robotic tasks.