ENERGY-EFFICIENT ROUTE PLANNING FOR AUTONOMOUS AERIAL VEHICLES BASED ON GRAPH SIGNAL RECOVERY Tianxi Ji 1 , Siheng Chen 1 , Rohan Varma 1 , Jelena Kovaˇ cevi´ c 1,2 1 Dept. of ECE, 2 Dept. of BME , Carnegie Mellon University, Pittsburgh, PA, USA ABSTRACT We use graph signal sampling and recovery techniques to plan routes for autonomous aerial vehicles. We propose a novel method that plans an energy-efficient flight trajectory by con- sidering the influence of wind. We model the weather stations as nodes on a graph and model wind velocity at each station as a graph signal. We observe that the wind velocities at two close stations are similar, that is, the graph signal of wind ve- locities is smooth. By taking advantages of the smoothness, we only query a small fraction of it and recover the rest by using a novel graph signal recovery algorithm, which solves an optimization problem. To validate the effectiveness of the proposed method, we first demonstrate the necessity to take wind into account when planning route for autonomous aerial vehicles, and then show that the proposed method produces a reliable and energy-efficient route. Index Terms— Graph signal processing, sampling and re- covery, route planning, autonomous vehicle 1. INTRODUCTION As a generalization of classical discrete signal processing, sig- nal processing on graphs is an effective tool to analyze arbi- trary signals residing on irregular, complex structures. The framework of signal processing on graphs models the under- lying structures as graphs and the supported signals as graph signals, and the basic concepts such as filters, convolution, z- transform, Fourier transform, frequency components are also generalized to have their corresponding counterparts in this framework [1, 2]. One of the most fundamental problems in signal process- ing is sampling and recovery. Some recent works study graph signal recovery based on either smoothness [3] or a bandlim- ited assumptions [4, 5]. For example, in [3], the authors for- The authors gratefully acknowledge support from the NSF through awards 1130616,1421919, the University Transportation Center grant (DTRT12-GUTC11) from the US Department of Transportation, and the CMU Carnegie Institute of Technology Infrastructure Award. This paper is a project extension from course 18-790 at Carnegie Mellon University, the authors gratefully acknowledge the contribution from teammates George Le- derman and Khoi Nguyen. mulate the recovery task as an optimization problem; in [6], the authors show that perfect recovery is possible for bandlim- ited graph signals; in [7], the authors relax the constraint of bandlimited graph signal, propose approximately bandlimited graph signal, and evaluate the performance of recovery strate- gies based on random and experimentally designed sampling on two types of graph. In this paper, we study an application of sampling and recovery of graph signals. With the rise of autonomous vehicles, a lot of approaches have been proposed for the task of route planning. Previ- ous applications for route planning involve planning optimal route for electric vehicles with limited battery storage capac- ity [8], real-time route planning for autonomous aerial vehi- cles to handle unforeseeable changes of environments [9], and planning path to avoid obstacles for underwater vehicles [10]. A widely used route planning algorithm is Dijkstra’s algo- rithm, which uses the distance between each pair of accessible nodes to plan a shortest path that minimize the travel cost. Di- jkstra’s algorithm requires the accessibility of data recorded at all nodes, which makes it vulnerable to the inaccessibility or loss of data. This is common in many problems when dealing with data of huge volume and complex structure. In this paper, we propose a framework to plan energy- efficient route for autonomous aerial vehicles, such as the Amazon octocopter drone. As far as we know, this is the first work to plan routes for aerial vehicles based on the wind in- formation. Instead of using the data recorded at all positions, we only query a small fraction of data at certain positions. The data is then interpolated using graph signal recovery techniques. In the the proposed framework, we also propose a series of procedure to compute the energy consumption between each pair of accessible nodes as the input of Dijk- stra’s algorithm. We show the necessity of taking wind into consideration for route planning, validate the framework on real wind dataset and show that it produces a reliable and energy-efficient route with high effectiveness. 2. BACKGROUND In this section we briefly review the basic concept of signal processing on graphs. For more details, see [2, 1].