Modeling, Simulation and Control of the Double Delta Surgical Robot

Robotic surgery has been steadily growing, with many new platforms entering the field. Research platforms, however, are limited in number, require a sizable capital expenditure or are difficult to access. This paper presents the analysis and development of a novel surgical manipulator based on parallel kinematics, utilizing the Delta robot as a foundational element. We investigate various aspects including kinematics, statics, workspace and constraints of the manipulator. Additionally, a physics-based model is constructed to validate the analysis and facilitate the creation of a control algorithm aimed at input tracking, particularly for teleoperation purposes. Two experiments are conducted to evaluate the manipulator's performance: one focusing on circle tracking and a second one employing real kinematic data from a suturing task. The results indicate a maximum tracking error under 1 mm and an RMS error below 0.6 mm for the first trial and 0.3 mm by 2 mm for the suturing tracking task, respectively. Furthermore, through non-linear Bode analysis we demonstrate that the closed-loop system effectively decouples input-output cross-gain terms while maintaining minimal amplification in the diagonal terms. This suggests that the system is well-suited for the intricate and precise motions required in surgical procedures.