Loop-shaped distributed learning of an object with data-independent performance certificates

This paper addresses distributed learning of object shapes using multiple robots, and proposes a systematic design procedure for distributed optimization algorithms with data-independent performance certificates. We start with formulating the object shape learning as a distributed classification problem based on so-called kernel method. A distributed algorithm, continuous-time alternating direction method of multipliers, is then applied to the problem, wherein poor transient performances are observed. To improve the performance, we reformulate the classification problem so that singular values of sub-blocks in the algorithm are appropriately scaled. We then propose a systematic design procedure of the algorithm based on the concept of loop-shaping. The procedure is further extended so that the performance is independent of the data, and its effectiveness is verified through a numerical example. The proposed method is finally demonstrated through simulation on a high fidelity simulator.