Internal Localization of Modular Robot Ensembles

The determination of the relative position and pose of every robot in a modular robotic ensemble is a necessary preliminary step for most modular robotic tasks. Localization is particularly important when the modules make local noisy observations and are not significantly constrained by inter- robot latches. In this paper, we propose a robust hierarchical approach to the internal localization problem that uses normal- ized cut to identify subproblems with small localization error. A key component of our algorithm is a simple method to reduce the cost of normalized cut computations. The result is a robust algorithm that scales to large, non-homogeneous ensembles. We evaluate our algorithm in simulation on ensembles of up to 10,000 modules. I. INTRODUCTION A key challenge in scaling to very large modular robotic ensembles is internal localization, the establishment of rela- tive pose amongst the robot's many individual components. In systems such as Claytronics (1), internal localization must be performed on ensembles consisting of many thousands to millions of tiny modules, using only local sensing in- formation between neighboring modules. The scale of the system, the unconstrained manner in which spheres can pack together, and uncertain intermodule sensing make developing a robust and scalable algorithm for internal localization a significant challenge. Existing work on internal localization falls into two gen- eral categories. Constraint-based approaches (2), (3), (4) rely on strong assumptions about the ensemble structure or exact observations to scale up to large ensembles. Typically, these approaches resolve uncertainty locally, by using exact observations and geometric constraints and then propagate the solution to the rest of the ensemble. While scalable, they are neither robust to noise nor irregular, non-lattice structure. Local probabilistic approaches (5), employed in systems such as PolyBot (6), address the robustness aspects of the internal localization problem. By combining a forward kinematic model with local sensing, these approaches can eliminate as much as 90% of the positioning error. The positioning error can be further reduced using the system's mechanical latching. While local probabilistic approaches work very well at a small scale, they tend to quickly accumulate error as the size of the ensemble increases, especially in the absence of mechanical latching. In order to obtain accurate position This work was supported in part by Intel Corporation and NSF grant