Numerous tasks in robotics and character animation involve solving combinations of inverse kinematics and motion planning problems that require the precise design of pose sequences to achieve desired motion objectives. Accounting for the complex interplay between body deformations and resulting motion, especially through interactions with the environment, poses significant challenges for the design of such pose sequences. We propose a computational framework to address these challenges in scenarios where the motion of a deformable body is entirely determined by dynamic changes of its shape. Complementing recent methods on the forward problem—mapping shape sequences to global motion trajectories based on a geometric formulation of locomotion—we address the inverse problem of optimizing shape sequences to achieve user-defined motion objectives. We demonstrate the effectiveness of our method through a diverse set of examples, producing realistic shape sequences that result in desired motion trajectories.

We introduce C-tubes , 3D tubular structures composed of developable surface strips. C-tubes can be understood as a generalization of Monge surfaces—a special class of sweep surfaces—towards the recently introduced conenets. This observation allows formulating a constructive algorithm to create tubular structures that ensures developability of the constituent surfaces, while significantly broadening the design space. Our novel form-finding tool enables design exploration by solving for the input variables of the constructive algorithm so that the C-tube best conforms to user-specified objectives. We discuss several case studies that illustrate the versatility of our approach for the design and fabrication of complex structures, with applications in architecture, furniture, and lighting design.

Bending-active structures are composed of elastic elements that deform to achieve a desired target shape. To support effective design, inverse algorithms have been proposed that optimize the geometry of each element specifically for each design. This makes it difficult to reuse elements across designs or gain efficiency in fabrication through mass production. We address this issue and propose a computational framework to rationalize bending-active structures into a sparse kit of parts. Our method solves for the optimal part geometry such that multiple input designs can be faithfully realized with the same kit of parts. Assigning parts to different assemblies leads to a combinatorial explosion that makes exhaustive search intractable. Instead, we propose a relaxed continuous optimization incorporating a physics-based simulation in its inner loop to model the elastic deformation of the bending-active structure accurately. Our algorithm allows analyzing different design trade-offs of a kit of parts to tune the balance between fabrication complexity and fidelity to the original designs. We demonstrate our method on three different classes of bending-active structures, showcasing the effectiveness of our approach for part reuse and sustainable practices in fabrication-driven design.

We introduce a computational pipeline for simulating and designing C-shells , a new class of planar-to-spatial deployable linkage structures. A C-shell is composed of curved flexible beams connected at rotational joints that can be assembled in a stress-free planar configuration. When actuated, the elastic beams deform and the assembly deploys towards the target 3D shape. We propose two alternative computational design approaches for C-shells: (i) Forward exploration simulates the deployed shape from a planar beam layout provided by the user. Once a satisfactory overall shape is found, a subsequent design optimization adapts the beam geometry to reduce the elastic energy of the linkage while preserving the target shape. (ii) Inverse design is facilitated by a new geometric flattening method that takes a design surface as input and computes an initial layout of piecewise straight linkage beams. Our design optimization algorithm then calculates the smooth curved beams to best reproduce the target shape at minimal elastic energy. We find that C-shells offer a rich space for design and show several studies that highlight new shape topologies that cannot be achieved with existing deployable linkage structures.