Ph.D Thesis

Ph.D StudentShapiro Yoel
SubjectKinematics of Continuous Hyper-Redundant Robots
DepartmentDepartment of Mechanical Engineering
Supervisor PROF. Alon Wolf


Continuum robots are usually soft snake-like manipulators, with multiple degrees of freedom. Soft robotics is of interest for applications in delicate environments such as: minimal-invasive-surgery (MIS), biological laboratories, assistive device for the elderly and more.

In this research we developed a soft bending actuator, the Bi-Bellows, and used it as a test bed to investigate kinematic modeling, sensorization and control. Using soft material increases safety and adaptability but complicates kinematic modeling, as elastic deformation must be taken into consideration. We present a simplified kinematic-elastic model, using a backbone representation, capable of running in near real-time (140 Hz). Our model is can include hysteresis and was used to define a Jacobian that can handle elastic deformation, provided adequate shape feedback.

Several solutions for continuum robots sensorization exist, most are either of limited application or rather expensive. We customized and embedded cheap piezoelectric sensors made of a flexible polymer (Polyvinylidene di-Fluoride, PVDF) which can be applied for many continuum robots. We demonstrate obstacle detection and force sensing using a single PVDF sensor. Furthermore, we developed, analyzed and demonstrated shape feedback using a small sensor array (four sensors) for an actuator and for a passive hyper-flexible beam.

Next we discuss the control of a 2D manipulator comprised of 4 Bi-Bellows actuators. The Jacobian of an articulated robot with N Degrees-of-Freedom (DOF) is defined by N joint parameters. The shape of continuum robots changes under external loads, consequentially the Jacobian can have infinite DOF and additional information is required to calculate it. Previous solutions to this control problem included using N-dimensional approximations or keeping a human operator in the loop. In this research we formulated a partial-derivative Jacobian that applies to any shape, provided proper shape feedback, e.g. from our embedded PVDF sensors or using computer vision. We chose a 2D task, End-Effector (EE) or Tool-Center-Point (TCP) positioning, and treated the redundancy with a classic approach: the pseudo-inverse Jacobian was applied for velocity control while the redundant DOF were used to optimize a cost function. The cost function gradient was projected on the Jacobian null-space in order to limit the optimizing maneuvers to internal motions, which do not affect the EE position. This approach was studied in simulation under different conditions and verified on our manipulator.