# Forming, Moving, and Navigating Sparse 2D and 3D Structures

We wish for robots to navigate and manipulate objects flexibly and autonomously in three-dimensional environments, regardless of the presence, absence or direction of gravity. Such robots must have the ability to propel themselves along any direction in three-space in a controlled way. Consider a task in which a robot is to climb up a complicated structure such as the Eiffel Tower, for inspection. The Eiffel tower is made of a web of metal bars. The bars are almost flat, they have varying lengths and directions, and they are oriented arbitrarily in three-space. A robot executing this task requires several skills: the robot should be able to climb vertically, the robot should be able to move inverted, it should be able to travel on arbitrarily oriented surfaces and avoid obstacles, and it should be able to make transitions between adjacent surfaces (bars). We wish to do this task with an autonomous robot. We can view this task as a navigation problem in a three-dimensional space.

## The Inchworm Robot

We have engineered an inchworm robot that is a light linear structure made of four links. The end links are the robot's two feet. Electromagnets placed on the feet allow the robot to attach to arbitrarily oriented surfaces, much like the loopers. Similarly, the robot alternates current to the two electromagnetic feet to simulate the inchworm propelling motion. The basic gait for straight-line motion is a step and consists of four phases: attach the back foot, extend the front foot, attach the front foot, contract the back foot. The length of the steps taken by our robots is proportional to their total length.In our lab, the inchworm walked hundreds of steps over filing cabinets, doors, and closets. The robot also walked up a fire escape outdoors.

The Inchworm robot can also manipulate objects while navigating over three dimensional surfaces. The basic manipulation skills we have developed are pushing an object (moving on a flat surface or climbing on an incline) and pulling an object on a flat surface. In our lab the robot performed these operations with great reliability. The robot was also capable of transitioning between a pure navigation mode to a navigation and manipulation mode.