Quadrotor Path Planning and Polynomial Trajectory Generation Using Quadratic Programming for Indoor Environments

Abstract

This study considers the problem of generating optimal, kino-dynamic-feasible, and obstacle-free trajectories for a quadrotor through indoor environments. We explore methods to overcome the challenges faced by quadrotors for indoor settings due to their higher-order vehicle dynamics, relatively limited free spaces through the environment, and challenging optimization constraints. In this research, we propose a complete pipeline for path planning, trajectory generation, and optimization for quadrotor navigation through indoor environments. We formulate the trajectory generation problem as a Quadratic Program (QP) with Obstacle-Free Corridor (OFC) constraints. The OFC is a collection of convex overlapping polyhedra that model tunnel-like free connecting space from current configuration to goal configuration. Linear inequality constraints provided by the polyhedra of OFCs are used in the QP for real-time optimization performance. We demonstrate the feasibility of our approach, its performance, and its completeness by simulating multiple environments of differing sizes and varying obstacle densities using MATLAB Optimization Toolbox. We found that our approach has higher chances of convergence of optimization solver as compared to current approaches for challenging scenarios. We show that our proposed pipeline can plan complete paths and optimize trajectories in a few hundred milliseconds and within approximately ten iterations of the optimization solver for everyday indoor settings.