# 2008 Research Summary

## Actuator Networks: Inducing Potential Fields to Guide a Moving Element to a Desired Position Using Push-Cage-Squeeze Cycles

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Ken Goldberg, Jeremy Ryan Schiff, Danny Bazo and Vincent Duindam

Building on recent work in sensor networks and distributed manipulation, we propose actuator networks--networks of devices capable of exerting influence on their environment in addition to monitoring it. We show how an actuator network can be used to guide a moving element to a desired location through the creation of potential gradients, and introduce an algorithm capable of calculating the required actuation. In this algorithm, motion is achieved with three steps: "push, cage, and squeeze," whose sequential application we term a PCS cycle. Guiding a moving element via PCS cycles is robust to modeled trajectory error and provides a framework into which path planning and obstacle avoidance can be integrated. We explore the PCS cycle as an example of one of the types of distributed actuation possible with an actuator network.

We introduce models, notation, terms, and properties related to the nature of actuator networks, describe the distributed guidance algorithm, and have performed simulations showing how an actuator network with eight nodes can guide a moving element to a desired location while avoiding obstacles.

We are beginning to explore the behavior of biological systems within actuation networks, focusing on classes of insects which exhibit phototaxy--direct correlation between perceived light levels and direction of movement.

Figure 1: A triangulated actuator network with actuators shown as squares, the moving element's locations over time depicted with circles, and an obstacle represented by the black rectangle. The hashed regions depict increasing uncertainty in the moving element's trajectory over time due to a single actuator performing a push step. The solid triangular regions show the reduction in trajectory uncertainty due to cage and squeeze steps. This figure illustrates how the PCS algorithm is robust to trajectory uncertainty and capable of being integrated with path planning for obstacle avoidance.

Figure 2: An example of repeated PCS cycles, followed by a final squeeze. The squares correspond to actuators, and the circle represents the moving element. The letters P, C, and S indicate which step was performed.

Figure 3: Results from a simulation of the PCS algorithm with an obstacle (black) within the actuator network's workspace. Plot 1 shows the calculated capture regions (shaded) for each triangle's incenter along the path from x_0 (top left circle) to x_f (bottom right circle). Plots 2-5 show alternating push, cage and squeeze steps. The entire trajectory of the moving element is shown in Plot 6.