Dynamic Compressed Sensing of Unsteady Flows with a Mobile Robot

Large-scale environmental sensing with a finite number of mobile sensors is a challenging task that requires tremendous resources and time. This is especially true when the environmental features of interest are spatiotemporally changing with unknown or partially known dynamics. Fortunately, these dynamic features often evolve in a low-dimensional space, making it possible to capture their dynamics sufficiently well with a finite number of sensor measurements. This paper investigates the problem of dynamic compressed sensing of an unsteady, periodic flow field with a mobile sensor. We take advantage of the inherently low dimensionality of the under-lying flow dynamics to reduce number of critical waypoints for sensor trajectory. The optimal set of sensing waypoints are identified by an iterative compressed sensing algorithm that optimizes the flow reconstruction based on the proper orthogonal decomposition modes. An optimal sampling trajectory is then found to traverse these waypoints while minimizing the energy consumption, time, and flow reconstruction error. Simulation results in a double-gyre flow field is presented to demonstrate the efficacy of the proposed algorithms. Experimental results with an indoor quadcopter are presented to show the tracking feasibility of the resulting trajectory.