The concept of entrainment broadly applies the locking of phases between 2 independent systems [17]. This physical phenomenon can be applied to modify neuromuscular movement in humans during bipedal locomotion. Gait entrainment to robotic devices have shown great success as alternatives to labor intensive methods of rehabilitation. By applying additional torque at the ankle joint, previous studies have exhibited consistent gait entrainment to both rigid and soft robotic devices. This entrainment is characterized by consistent phase locking of plantarflexion perturbations to the ‘push off’ event within the gait cycle. However, it is unclear whether such phase locking can be attributed to the plantarflexion assistance from the device or the sensory stimulus of movement at the ankle. To clarify the mechanism of entrainment, an experiment was designed to expose the user to a multitude of varying torques applied at the ankle to assist with plantar flexion. In this experiment, no significant difference in success of subject entrainment occurred when additional torque applied was greater than a detectable level. Force applied at the ankle varied from ~60N to ~130N. This resulted in successful entrainment ~88\% of the time at 98 N, with little to no increase in success as force increased thereafter. Alternatively, success of trials decreased significantly as force was reduced below this level, causing the perturbations to become undetectable by participants. Ultimately this suggests that higher levels of actuator pressure, and thus greater levels of torque applied to the foot, do not increase the likelihood of entrainment during walking. Rather, the results of this study suggest that proper detectable sensory stimulus is the true mechanism for entrainment.

In this paper, we present an approach to designing decentralized robot control policies that mimic certain microscopic and macroscopic behaviors of ants performing collective transport tasks. In prior work, we used a stochastic hybrid system model to characterize the observed team dynamics of ant group retrieval of a rigid load. We have also used macroscopic population dynamic models to design enzyme-inspired stochastic control policies that allocate a robotic swarm around multiple boundaries in a way that is robust to environmental variations. Here, we build on this prior work to synthesize stochastic robot attachment–detachment policies for tasks in which a robotic swarm must achieve non-uniform spatial distributions around multiple loads and transport them at a constant velocity. Three methods are presented for designing robot control policies that replicate the steady-state distributions, transient dynamics, and fluxes between states that we have observed in ant populations during group retrieval. The equilibrium population matching method can be used to achieve a desired transport team composition as quickly as possible; the transient matching method can control the transient population dynamics of the team while driving it to the desired composition; and the rate matching method regulates the rates at which robots join and leave a load during transport. We validate our model predictions in an agent-based simulation, verify that each controller design method produces successful transport of a load at a regulated velocity, and compare the advantages and disadvantages of each method.