The solution of the inverse kinematics problem of soft manipulators is essential to generate paths in the task space. The inverse kinematics problem of constant curvature or piecewise constant curvature manipulators has already been solved by using different methods, which include closed-form analytical approaches and iterative methods based on the Jacobian method. On the other hand, the inverse kinematics problem of nonconstant curvature manipulators remains unsolved. This study represents one of the first attempts in this direction. It presents both a model-based method and a supervised learning method to solve the inverse statics of nonconstant curvature soft manipulators. In particular, a Jacobian-based method and a feedforward neural network are chosen and tested experimentally. A comparative analysis has been conducted in terms of accuracy and computational time.

The new and promising field of soft robotics has many open areas of research such as the development of an exhaustive theoretical and methodological approach to dynamic modeling. To help contribute to this area of research, this paper develops a dynamic model of a continuum soft robot arm driven by cables and based upon a rigorous geometrically exact approach. The model fully investigates both dynamic interaction with a dense medium and the coupled tendon condition. The model was experimentally validated with satisfactory results, using a soft robot arm working prototype inspired by the octopus arm and capable of multibending. Experimental validation was performed for the octopus most characteristic movements: bending, reaching, and fetching. The present model can be used in the design phase as a dynamic simulation platform and to design the control strategy of a continuum robot arm moving in a dense medium.

In this work we address the inverse kinetics problem of a non-constant curvature manipulator driven by three cables. An exact geometrical model of this manipulator has been employed. The differential equations of the mechanical model are non-linear, therefore the analytical solutions are difficult to calculate. Since the exact solutions of the mechanical model are not available, the elements of the Jacobian matrix can not be calculated. To overcome intrinsic problems of the methods based on the Jacobian matrix, we propose for the first time a neural network learning the inverse kinetics of the soft manipulator moving in three-dimensional space. After the training, a feed-forward neural network (FNN) is able to represent the relation between the manipulator tip position and the forces applied to the cables. The results show that a desired tip position can be achieved with a degree of accuracy of 1.36% relative average error with respect to the total arm length.

Control of soft robots remains nowadays a big challenge, as it does in the larger category of continuum robots. In this paper a direct and inverse kinetics models are described for a non-constant curvature structure. A major effort has been put recently in modelling and controlling constant curvature structures, such as cylindrical shaped manipulators. Manipulators with non-constant curvature, on the other hand, have been treated with a piecewise constant curvature approximation. In this work a non-constant curvature manipulator with a conical shape is built, taking inspiration from the anatomy of the octopus arm. The choice of a conical shape manipulator made of soft material is justified by its enhanced capability in grasping objects of different sizes. A different approach from the piecewise constant curvature approximation is employed for direct and inverse kinematics model. A continuum geometrically exact approach for direct kinetics model and a Jacobian method for inverse case are proposed. They are validated experimentally with a prototype soft robot arm moving in water. Results show a desired tip position in the task-space can be achieved automatically with a satisfactory degree of accuracy.