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Hybrid systems, such as bipedal walkers, are challenging to control because of discontinuities in their nonlinear dynamics. Little can be predicted about the systems’ evolution without modeling the guard conditions that govern transitions between hybrid modes, so even systems with reliable state sensing can be difficult to control. We propose an algorithm that allows for determining the hybrid mode of a system in real-time using data-driven analysis. The algorithm is used with data-driven dynamics identification to enable model predictive control based entirely on data. Two examples—a simulated hopper and experimental data from a bipedal walker—are used. In the context of the first example, we are able to closely approximate the dynamics of a hybrid SLIP model and then successfully use them for control in simulation. In the second example, we demonstrate gait partitioning of human walking data, accurately differentiating between stance and swing, as well as selected subphases of swing. We identify contact events, such as heel strike and toe-off, without a contact sensor using only kinematics data from the knee and hip joints, which could be particularly useful in providing online assistance during walking. Our algorithm does not assume a predefined gait structure or gait phase transitions, lending itself to segmentation of both healthy and pathological gaits. With this flexibility, impairment-specific rehabilitation strategies or assistance could be designed. 

Robot locomotion is typically generated by coordinated integration of single-purpose components, like actuators, sensors, body segments, and limbs. We posit that certain future robots could self-propel using systems in which a delineation of components and their interactions is not so clear, becoming robust and flexible entities composed of functional components that are redundant and generic and can interact stochastically. Control of such a collective becomes a challenge because synthesis techniques typically assume known input-output relationships. To discover principles by which such future robots can be built and controlled, we study a model robophysical system: planar ensembles of periodically deforming smart, active particles—smarticles. When enclosed, these individually immotile robots could collectively diffuse via stochastic mechanical interactions. We show experimentally and theoretically that directed drift of such a supersmarticle could be achieved via inactivation of individual smarticles and used this phenomenon to generate endogenous phototaxis. By numerically modeling the relationship between smarticle activity and transport, we elucidated the role of smarticle deactivation on supersmarticle dynamics from little data—a single experimental trial. From this mapping, we demonstrate that the supersmarticle could be exogenously steered anywhere in the plane, expanding supersmarticle capabilities while simultaneously enabling decentralized closed-loop control. We suggest that the smarticle model system may aid discovery of principles by which a class of future “stochastic” robots can rely on collective internal mechanical interactions to perform tasks. 

Self-organization is frequently observed in active collectives as varied as ant rafts and molecular motor assemblies. General principles describing self-organization away from equilibrium have been challenging to identify. We offer a unifying framework that models the behavior of complex systems as largely random while capturing their configuration-dependent response to external forcing. This allows derivation of a Boltzmann-like principle for understanding and manipulating driven self-organization. We validate our predictions experimentally, with the use of shape-changing robotic active matter, and outline a methodology for controlling collective behavior. Our findings highlight how emergent order depends sensitively on the matching between external patterns of forcing and internal dynamical response properties, pointing toward future approaches for the design and control of active particle mixtures and metamaterials.