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Continuum Jacobian-Based Computational Morphogenesis for Soft Robotic Workspace Optimization
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DOI：10.1109/tro.2026.3716051.png)
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Abstract
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The robot workspace, which defines the complete set of reachable end-effector positions and orientations, is critical for functional capability. However, quantitative workspace design remains an open challenge in soft robotics. This is due to the complicated implicit kinematics governed by nonlinear continuum mechanics and the prohibitive computational cost of evaluating deformations across the full actuation spectrum. This article presents a computational morphogenesis framework for the automatic optimization of position and orientation workspaces in multichamber soft pneumatic actuators. Our approach is built on three key innovations: 1) a continuum Jacobian, defined as the derivative of the end-effector’s degrees of freedom with respect to the actuation inputs, which transforms the workspace integral from the configuration space to the actuation space, making the volume computation analytically tractable; 2) a second-order adjoint method to derive the analytical shape derivatives of both the displacement field and this Jacobian, providing the explicit gradient of the workspace volume with respect to the robot's morphology; and 3) a differentiable singularity-free geometric model, complemented by an adaptive surface reconstruction algorithm, to represent and evolve the robot's free-form shape. The framework is validated by designing multichamber pneumatic soft actuators, achieving an eightfold increase in the 3-D positional workspace volume and a 1.6-fold increase in the 2-D orientational workspace volume compared to the baseline Pneu-Nets actuators.
Keywords:
Computational morphogenesis
Jacobian shape derivative
soft robotics
workspace optimization
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