Compliance is a defining characteristic of biological systems. Understanding how to exploit soft materials as effectively as living creatures do is consequently a fundamental challenge that is key to recreating the complex array of motor skills displayed in nature. As an important step towards this grand challenge, we propose a model-based trajectory optimization method for dynamic, cable-driven soft robot locomotion. To derive this trajectory optimization formulation, we begin by modeling soft robots using the Finite Element Method. Through a numerically robust implicit time integration scheme, forward dynamics simulations are used to predict the motion of the robot over arbitrarily long time horizons. Leveraging sensitivity analysis, we show how to efficiently compute analytic derivatives that encode the way in which entire motion trajectories change with respect to parameters that control cable contractions. This information is then used in a forward shooting method to automatically generate optimal locomotion trajectories starting from high-level goals such as the target walking speed or direction. We demonstrate the efficacy of our method by generating and analyzing locomotion gaits for multiple soft robots. Our results include both simulation and fabricated prototypes.
This paper presents a method for optimizing visco-elastic material parameters of a finite element simulation to best approximate the dynamic motion of real-world soft objects. We compute the gradient with respect to the material parameters of a least-squares error objective function using either direct sensitivity analysis or an adjoint state method. We then optimize the material parameters such that the simulated motion matches real-world observations as closely as possible. In this way, we can directly build a useful simulation model that captures the visco-elastic behaviour of the specimen of interest. We demonstrate the effectiveness of our method on various examples such as numerical coarsening, custom-designed objective functions, and of course real-world flexible elastic objects made of foam or 3D printed lattice structures, including a demo application in soft robotics.
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