A Geometrical Approach To Multicopter Motion Planning

With simple structures and three-dimensional maneuverability,multicopters have been in-troduced in many applications such as search and rescue,aerial videography,and industrial inspection.However,multicopters have always been used as tools that expand the boundaries of human sensation rather than as unmanned systems for autonomous missions.The safe nav-igation and aerial operations of multicopters are still accomplished by human pilots.Since the onboard resources for sensing,computing,and actuating are quite limited,fully autonomous navigation and mission are still challenging for existing multicopters.The full autonomy of multicopters cannot be achieved without reliable perception and plan-ning algorithms.With the miniaturization of sensors and the development of localization and mapping,the bottleneck now becomes the lack of high-performance motion planners.A variety of general-purpose planning algorithms for robots,including sampling-based and optimization-based ones,demand unrealistic resources so as to meet the needs of multicopters.Some tai-lored methods,albeit lightweight,sacrifice either the model fidelity,planning quality,or multi-mission adaptability.There are reasons for their unsatisfactory performance: 1.Nonsmooth and discretized environment data are directly incorporated into planning,making the iteration cumbersome.2.Existing trajectory representation still introduces redundant parameters even if most multicopters are underactuated.3.Low-dimensional geometrical structures of constraints are not well exploited in multicopter planning,resulting in the waste of computing power.To overcome the practical challenges in multicopter motion planning,studying the compu-tationally efficient full-state trajectory planning for high-fidelity multicopter dynamics is nec-essary.After examining the inadequacies in existing approaches,this research redesigns the in-terface between environment and planners,and also the sparse parameterization of trajectories.By exploiting problem structures,the spatial-temporal deformation of flat-output trajectories is proposed to solve planning problems.The research contents are listed as follows:1.Since environment data are necessary to ensure the safety of mobile robots,our research proposes the formulation of feasible region extraction,which applies to commonly used kinds of mapping data.The fast iterative region inflation algorithm efficiently generates high-quality polyhedral approximations of feasible regions,which serves as a reliable interface between environment information and planning modules of mobile robots.2.The under-actuation and differential flatness of multicopter make it possible to sparsely parameterize the flat-output trajectory instead of the entire state-input one.Therefore,our re-search studies the multi-stage minimum control effort problem for integrator chains in flat-output spaces and provides the necessary and sufficient conditions along with proof.A spatial-temporal parameterization scheme is proposed to reduce trajectory dimension while retaining flexibility in both space and time domains.Two linear-time operations are further designed such that the trajectory can be directly incorporated into optimization.3.Since differential and geometrical constraints of multicopter possess well-studied struc-tures,we formulate the multicopter dynamics subject to nonlinear drag effects and validates its differential flatness.Flatness transformations and coordinate transformations are utilized to eliminate both the differential and geometrical constraints such that trajectories and variables to be optimized are all in flat spaces.To meet various mission requirements,smoothing penalty functionals are adopted to deform the trajectory in the space-time domain,thus producing high-quality solutions to motion planning.4.Extensive benchmarks and simulations are conducted to show that the proposed frame-work can generate high-quality solutions while retaining the computation speedup over exist-ing schemes by orders of magnitude.Furthermore,this framework also enables aggressive high-speed maneuvers of multicopters in complex environments in extreme flight experiments,demonstrating its practical performance.The motion planning module has shown great potential in the navigation of multicopters as the development of sensation,communication,and actuation hardware and perception software.This research proposes a geometrical approach to multicopter motion planning by combing practical techniques from different aspects.It aims to provide a reference for the development of planning modules in the future of autonomous multicopters.