Quasi-static Optimal Design of a Pneumatic Soft Robot to Maximize Pressure-to-Force Transference

The design of a pneumatic soft robot represents a challenging problem of multidisciplinary nature due to the blurred domain of its components, which gives rise to complex coupled nonlinear dynamic models (of the body and its input matrix), wherein the actuator is itself the deformable robot. In this paper, we consider a continuum Lagrangian dynamic model of a 3 DoF pneumatic soft robot to address optimization of the input matrix B(q) to maximize the transfer of pneumatic pressure field p control into generalized torque τ since τ = B(q)p, given the desired behaviour, shape and topology of actuators (embedded pressure chambers). The byproduct aim is to achieve a given behaviour (coded as the desired configuration) with less of such a pressure. To satisfy this objective, we firstly consider quasi-static optimal design to yield geometric parameters from the maximization of the spectral norm of B(q), for state q; then, we parameterize the initial length of the soft robot to the desired pressure. The result stands for a novel methodology that guarantees the regulation task with less pneumatic pressure control, given both a desired configuration and a desired pressure. Comparative simulation illustrates the advantages of design optimization, showing that it is instrumental to handle energy efficiency through actuator geometric variables, i.e. the internal dimensions and internal topology of pressure chambers. Remarkably, optimal design leads to improvement of several orders of magnitude of the pressure-force transference ratio ∥τ∥/∥p∥, for a given regulation error, as it can be observed in the case study, where a maximum increase of 86-fold is obtained. This highlights the importance of optimal design for soft robot, an issue surprisingly neglected so far in the literature of this highly cited new topic in robotics.