Modeling and Optimal Control of an Octopus Tentacle

Abstract

We present a control model for an octopus tentacle, based on the dynamics of an inextensible string with curvature constraints and curvature controls. We derive the equations of motion together with an appropriate set of boundary conditions, and we characterize the corresponding equilibria. The model results in a system of fourth-order evolutive nonlinear controlled PDEs, generalizing the classic Euler's dynamic elastica equation, that we approximate and solve numerically introducing a consistent finite difference scheme. We proceed investigating a reachability optimal control problem associated to our tentacle model. We first focus on the stationary case, by establishing a relation with the celebrated Dubins' car problem. Moreover, we propose an augmented Lagrangian method for its numerical solution. Finally, we address the evolutive case obtaining first order optimality conditions, then we numerically solve the optimality system by means of an adjoint-based gradient descent method.

Optimal Reachability and Grasping for a Soft Manipulator

“…We revise, from a robotic perspective, the main steps of the modeling procedure in [1]. In particular, we provide an analytical description of the constraints as formal limit of a discrete particle system, which in turn models an hyper-redundant manipulator.…”

“…Fixing the total length of the manipulator equal to 1, so that = 1/N , we define the Lagrangian associated to the soft, continuous manipulator by the formal limit (see [1] for details) lim N →+∞ L N (q, q, σ) = L(q, q, σ).…”

“…Here we report only the continuous case, which is the building block for the optimal control problems we address in the next sections. Taking into account also some friction forces, we obtain the following system of nonlinear, evolutive, fourth order PDEs -see [1] for details:…”

“…The control model underlying our study and a first investigation of the related optimal reachability strategies were originally developed in [1], then extended in [2] to the case in which only a portion of the device is controlled. Here, beside a deeper investigation of the model and of its connection with hyper-redundant manipulators, we address the important problem of grasping a prescribed object.…”

Dynamic Modeling and Motion Control of a Cable-Driven Robotic Exoskeleton With Pneumatic Artificial Muscle Actuators

“…However, the dynamic formulation is arduous for a complex system. Several methods such as the Newton-Euler formulation [26,27], virtual work principle [28,29], Kane's method [30], and the Lagrangian formulation in generalized coordinates [31][32][33] have been proposed for modeling and simulation of dynamic systems. Among them, the Lagrangian formulation based on the kinetic and potential energies has more physical insight.…”