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Architected materials are innervated with air-filled channels, integrating programmed mechanical behavior, sensing, and actuation. 

Soft robots can be incredibly robust and safe but typically fail to match the strength and precision of rigid robots. This dichotomy between soft and rigid is recently starting to break down, with emerging research interest in hybrid soft-rigid robots. In this work, we draw inspiration from Nature, which achieves the best of both worlds by coupling soft and rigid tissues—like muscle and bone—to produce biological systems capable of both robustness and strength. We present foundational, general-purpose pipelines to simulate and fabricate cable-driven soft-rigid robots with embedded skeletons. We show that robots built using these methods can fluidly mimic biological systems while achieving greater force output and external load resistance than purely soft robots. Finally, we show how our simulation and fabrication pipelines can be leveraged to create more complex robots and do model- based control. 

Trajectory optimization o↵ers mature tools for motion planning in high-dimensional spaces under dynamic constraints. However, when facing complex configuration spaces, cluttered with obstacles, roboticists typically fall back to sampling-based planners that struggle in very high dimensions and with continuous di↵erential constraints. Indeed, obstacles are the source of many textbook examples of problematic nonconvexities in the trajectory-optimization prob- lem. Here we show that convex optimization can, in fact, be used to reliably plan trajectories around obstacles. Specifically, we consider planning problems with collision-avoidance constraints, as well as cost penalties and hard constraints on the shape, the duration, and the velocity of the trajectory. Combining the properties of B ́ezier curves with a recently-proposed framework for finding shortest paths in Graphs of Convex Sets (GCS), we formulate the planning problem as a compact mixed-integer optimization. In stark contrast with existing mixed-integer planners, the convex relaxation of our programs is very tight, and a cheap round- ing of its solution is typically sufficient to design globally-optimal trajectories. This reduces the mixed-integer program back to a simple convex optimization, and automatically provides optimality bounds for the planned trajectories. We name the proposed planner GCS, after its underlying optimization framework. We demonstrate GCS in simulation on a variety of robotic platforms, including a quadrotor flying through buildings and a dual-arm manipulator (with fourteen degrees of freedom) moving in a confined space. Using numerical experiments on a seven-degree-of-freedom manipulator, we show that GCS can outperform widely-used sampling-based planners by finding higher-quality trajectories in less time. 

Combing hair involves brushing away the topological tangles in a collective curl, defined as a bundle of interacting elastic filaments. Using a combination of experiment and computation, we study this problem that naturally links topology, geometry and mechanics. Observations show that the dominant interactions in hair are those of a two-body nature, corresponding to a braided homochiral double helix. This minimal model allows us to study the detangling of an elastic double helix driven by a single stiff tine that moves along it and leaves two untangled filaments in its wake. Our results quantify how the mechanics of detangling correlates with the dynamics of a topological quantity, the link density, that propagates ahead of the tine and flows out the free end as a link current. This in turn provides a measure of the maximum characteristic length of a single combing stroke in the many-body problem on a head of hair, producing an optimal combing strategy that balances trade-offs between comfort, efficiency and speed of combing in hair curls of varying geometrical and topological complexity. 

Geometric graph models of systems as diverse as proteins, robots, and mechanical structures from DNA assemblies to architected materials point towards a unified way to represent and control them in space and time. While much work has been done in the context of characterizing the behavior of these networks close to critical points associated with bond and rigidity percolation, isostaticity, etc., much less is known about floppy, under-constrained networks that are far more common in nature and technology. Here we combine geometric rigidity and algebraic sparsity to provide a framework for identifying the zero-energy floppy modes via a representation that illuminates the underlying hierarchy and modularity of the network, and thence the control of its nestedness and locality. Our framework allows us to demonstrate a range of applications of this approach that include robotic reaching tasks with motion primitives, and predicting the linear and nonlinear response of elastic networks based solely on infinitesimal rigidity and sparsity, which we test using physical experiments. Our approach is thus likely to be of use broadly in dissecting the geometrical properties of floppy networks using algebraic sparsity to optimize their function and performance. 

Given a graph, the shortest-path problem requires finding a sequence of edges with minimum cumulative length that connects a source vertex to a target vertex. We consider a generalization of this classical problem in which the position of each vertex in the graph is a continuous decision variable, constrained to lie in a corresponding convex set. The length of an edge is then defined as a convex function of the positions of the vertices it connects. Problems of this form arise naturally in motion planning of autonomous vehicles, robot navigation, and even optimal control of hybrid dynamical systems. The price for such a wide applicability is the complexity of this problem, which is easily seen to be NP-hard. Our main contribution is a strong mixed-integer convex formulation based on perspective functions. This formulation has a very tight convex relaxation and makes it possible to efficiently find globally-optimal paths in large graphs and in high-dimensional spaces. 

Today’s use of large-scale industrial robots is enabling extraordinary achievement on the assembly line, but these robots remain isolated from the humans on the factory floor because they are very powerful, and thus dangerous to be around. In contrast, the soft robotics research community has proposed soft robots that are safe for human environments. The current state of the art enables the creation of small-scale soft robotic devices. In this article we address the gap between small-scale soft robots and the need for human-sized safe robots by introducing a new soft robotic module and multiple human-scale robot configurations based on this module. We tackle large-scale soft robots by presenting a modular and reconfigurable soft robotic platform that can be used to build fully functional and untethered meter-scale soft robots. These findings indicate that a new wave of human-scale soft robots can be an alternative to classic rigid-bodied robots in tasks and environments where humans and machines can work side by side with capabilities that include, but are not limited to, autonomous legged locomotion and grasping. 

The brushing of hair requires a complex un- derstanding of the interaction between soft hair fibers and the soft brushing device. It is also reliant on having both visual and tactile information. Guided by a recently developed model of soft tangled fiber bundles, we develop a method for optimizing hair brushing by robots which seeks to minimize pain and avoid the build up of jammed entanglements. Using an experimental setup with a custom force measuring sensor and a soft brush end effector, we perform closed-loop experiments on hair brushing of different curliness. This utilizes computer vision to assess the curliness of the hair, after which the hair is brushed using a closed loop controller. To demonstrate this approach hair brushing experiments have been performed on a wide variety of wigs with amount of curl. In addition to hair brushing the insight provided by this model driven approach could be applied to brushing of fibers for textiles, or animal fibers.