Motion planning for multirotor aerial robots in indoor environments using convex optimization

Abstract

In this study, we examine the motion planning problem for a multi-rotor aerial vehicle in an indoor environment. We first introduce the traditional motion planning pipeline for a mobile robot that is comprised of mapping, path planning (PP), trajectory planning (TP), trajectory tracking (TT), and local planning. We then explore the methods to overcome the challenges faced by a multirotor micro aerial vehicle (MAV) to navigate in an indoor setting and modify the traditional motion planning pipeline to better serve the objectives of indoor navigation. We process the paths produced by the path planning (PP) stage with our novel path relocation (PR) algorithm and use relocated paths as a guide to plan trajectories. We formulate the trajectory planning (TP) problem as a quadratic program (QP) that maximizes the smoothness of trajectories with obstacle-free corridor (OFC) constraints. The OFC is a collection of convex overlapping polyhedra that model tunnel-like free connecting space from the current configuration to the goal configuration. Faces of the polyhedra in OFC are defined with hyperplanes and these hyperplanes are used as inequality constraints in the QP for real-time optimization performance. Our quadratic program is such that it can be solved with a convex optimization solver for all practical purposes. Our approach allows for the customized imposition of additional constraints like waypoint constraints, continuity constraints, limited field-of-view constraints, and dynamic feasibility constraints. We demonstrate the feasibility of our approach, its performance, and completeness by simulating multiple indoor environments of differing sizes and varying obstacle densities using MATLAB Optimization Toolbox. We found that our approach has higher chances of convergence of optimization solvers as compared to the state-of-the-art approaches for challenging indoor scenarios. We show that our proposed pipeline can plan complete paths and optimize trajectories within the timespans dictated by real-time operational requirements. This thesis also includes a careful analysis of our approach and its comparison with other approaches.