Geometry-Informed Inverse Design for Architecture and Robotics

Through the actuation of their constitutive elements e.g., muscles, motors, three-dimensional systems evolve according to the underlying laws of physics and may exhibit a wide range of behaviors. These phenomena naturally emerge from the structure of the configuration space, typically derived from the energy of the system (elastic, dissipative, kinematic). This structure dictates how the space can be traversed in a physically meaningful way. The control and design of physical systems thus amount to traversing the configuration space by manipulating control parameters, such as the rest shape of the system or an actuation sequence. However, depending on the complexity of the simulation, forward exploration alone may not suffice to obtain an efficient solution.

In this talk, I will describe approaches to formalizing the underlying inverse problem and rendering it amenable to continuous optimization. A subset of well-behaved control problems can be solved readily even from poor initialization strategies, reflecting a lack of prior knowledge. Such instances may be regarded as behavior discovery. However, I will show that some inverse problems require a geometric abstraction of the forward process in order to bootstrap the optimization algorithm. I will further demonstrate how geometric insights can also be leveraged to simplify the inverse problems through regularization or subspace engineering. These concepts will be illustrated in an architectural context, through a study on deployable gridshell design and their rationalization into kit-of-parts, as well as in the control of shape-changing bodies whose trajectories are dictated by geometric locomotion—for example, objects immersed in low Reynolds number environments, crawling systems, and inertia-dominated motion.