针对无人机在复杂环境中的自主导航问题，设计基于拉普拉斯方程的人工势场，并以人工势场为基础进行无人机的运动控制。对地图中阻碍边界与目标边界分别设置初始条件，采用边界元法求解拉普拉斯方程。由此建立调和势场，它对障碍物形态适应程度高，不存在局部极小点，并可快速计算内部任一点的梯度。以构建的梯度场作为参考速度，采用线性二次型高斯控制器进行速度追踪，从而完成无人机的姿态控制。采用Airsim仿真平台进行不同场景下的模拟实验，结果表明算法可以有效引导无人机完成路径规划与避障控制，且在遭遇意外干扰时具备良好的调整适应能力。
We propose a method for autonomous navigation of unmanned aerial vehicles (UAVs) in cluttered environment utilizing Laplacian potential field. With suitable boundary conditions for obstacles and goal in the map, Laplace’s equations are solved by boundary element method (BEM). Then we establish artificial potential field which is capable of handling obstacles with complex configuration and guarantees nonexistence of local minima. Since such a kind of potential field has easy access to the gradient of arbitrary point in the map, a linear quadratic Gaussian controller (LQG) is designed for velocity tracking to help complete attitude control. The simulation is conducted on Airsim platform with different scenarioes, and the results illustrate that this method is valid for path planning and obstacle avoidance and has adaptability to unexpected disturbance.
[1] Pan J, Manocha D. GPU-based parallel collision detection for fast motion planning[J]. The International Journal of Robotics Research, 2012, 31(2):187-200.
[2] Dunias P. Autonomous robots using artificial potential fields[D]. Eindhoven:Technische Universiteit Eindhoven, 1996.
[3] Liang Y, Juntong Q,Dalei S, et al. Survey of robot 3D path planning algorithms[J]. Journal of Control Science and Engineering, 2016, 2016:1-22.
[4] Yershova A, Jaillet L, Simeon T, et al. Dynamic-domain RRTs:efficient exploration by controlling the sampling domain[C]//Proceedings of the 2005 IEEE International Conference on Robotics and Automation, Barcelona, Spain, 2005:3856-3861.
[5] Karaman S, Frazzoli E. Optimal kinodynamic motion planning using incremental sampling-based methods[C]//49th IEEE Conference on Decision and Control (CDC), Atlanta,GA, 2010:7681-7687.
[6] Khatib O. Real-time obstacle avoidance for manipulators and mobile robots[J]. The International Journal of Robotics Research, 1986, 5(1):90-98.
[7] Yun X, Tan K C. A wall-following method for escaping local minima in potential field based motion planning[C]//19978th International Conference on Advanced Robotics. Proceedings ICAR'97, Monterey, CA, USA, 1997:421-426.
[8] Arambula Cosío F, Padilla Castañeda M A. Autonomous robot navigation using adaptive potential fields[J]. Mathematical & Computer Modelling, 2004, 40(9):1141-1156.
[9] Kim D H, Wang H, Shin S. Decentralized control of autonomous swarm systems using artificial potential functions:analytical design guidelines[C]//IEEE Conference on Decision & Control, Nassau, Bahamas. 2006:159-164.
[10] Connolly C I, Burns J B, Weiss R. Path planning using Laplace's equation[C]//IEEE International Conference on Robotics and Automation, Cincinnati, OH, USA, 1990:2102-2106.
[11] Axler S, Bourdon P, Ramey W. Basic properties of harmonic functions[M]//Harmonic Function Theory. New York:Springer, 2001:1-29.
[12] Bear H S. A new look at the three circles theorem[J]. The American Mathematical Monthly, 1974, 81(5):487-490.
[13] Liu Y. Fast multipole boundary element method:theory and applications in engineering[M]. Cambridge:Cambridge University Press, 2009.
[14] Locatelli A. Optimal control:an introduction[J]. Applied Mechanics Reviews, 2001, 55(3):48-49.
[15] Dorato P, Abdallah C, Cerone V. Linear quadratic control:an introduction[J]. Comment on Circ Res, 2000,87(5):399-405.
[16] Shah S, Dey D, Lovett C, et al. AirSim:high-fidelity visual and physical simulation for autonomous vehicles[C]//Field and Service Robotics. Cham:Springer International Publishing, 2018:621-635.
