Morphological Design for Pneumatic Soft Actuators and Robots With Desired Deformation Behavior

homogeneous pneumatic soft robot may generate complex output motions using a simple input pressure, resulting from its morphological shape that locally deforms the soft material to different degrees by simultaneously tailoring the structural characteristics and orienting the input pressure. To date, design of the morphological shape (inverse problem) has not been fully addressed. This article outlines a geometry-mechanics-optimization integrated approach to automatically shaping a pneumatic soft actuator or robot that achieves the desired deformation behavior. Instead of constraining the robot's geometry within any predefined regular shape, we employ B-splines to allow generation of freeform boundary surfaces, and use nonlinear mechanical modelling and shape derivative based optimization to navigate the high-dimensional design space. Our design framework can readily regulate the surface quality during the morphological evolution, by imposing the geometric constraints in terms of the principal curvatures and the minimal distance between surfaces as penalty functions. The effect of external forces including the gravity and the interaction force at the end-effector is also taken into account to generalize the method for design problems in which the load capability is also pursued. To improve the computational efficiency, suboptimization problems are constructed within a trust region in which the displacement-dependent objective function is approximated by its first-order Taylor polynomial based on the gradient information to avoid frequently performing time-consuming nonlinear finite element analysis. The suboptimization problems are then solved by the quasi-Newton method combined with the backtracking line search strategy. We showcase various applications to validate our design approach, including actuators for basic extension, bending, and twisting motions, and continuous robot arms that can perform desired in-plane and out-of-plane configurations. We also show that our method can address design of multiple chambers for achieving multiple target deformation behaviors, by co-optimizing the morphological shape and air pressures, which is validated by two examples.