Automated Real-Time Inspection in Indoor and Outdoor 3D Environments with Cooperative Aerial Robots

This work introduces a cooperative inspection system designed to efficiently control and coordinate a team of distributed heterogeneous UAV agents for the inspection of 3D structures in cluttered, unknown spaces. Our proposed approach employs a two-stage innovative methodology. Initially, it leverages the complementary sensing capabilities of the robots to cooperatively map the unknown environment. It then generates optimized, collision-free inspection paths, thereby ensuring comprehensive coverage of the structure's surface area. The effectiveness of our system is demonstrated through qualitative and quantitative results from extensive Gazebo-based simulations that closely replicate real-world inspection scenarios, highlighting its ability to thoroughly inspect real-world-like 3D structures.

Normal Approximation for Stochastic Gradient Descent via Non-Asymptotic Rates of Martingale CLT

We provide non-asymptotic convergence rates of the Polyak-Ruppert averaged stochastic gradient descent (SGD) to a normal random vector for a class of twice-differentiable test functions. A crucial intermediate step is proving a non-asymptotic martingale central limit theorem (CLT), i.e., establishing the rates of convergence of a multivariate martingale difference sequence to a normal random vector, which might be of independent interest. We obtain the explicit rates for the multivariate martingale CLT using a combination of Stein's method and Lindeberg's argument, which is then used in conjunction with a non-asymptotic analysis of averaged SGD proposed in [PJ92]. Our results have potentially interesting consequences for computing confidence intervals for parameter estimation with SGD and constructing hypothesis tests with SGD that are valid in a non-asymptotic sense.