[en] This paper presents an integrated approach that combines trajectory optimization and Artificial Potential Field (APF) method for real-time optimal Unmanned Aerial Vehicle (UAV) trajectory planning and dynamic collision avoidance. A minimum-time trajectory optimization problem is formulated with initial and final positions as boundary conditions and collision avoidance as constraints. It is transcribed into a nonlinear programming problem using Chebyshev pseudospectral method. The state and control histories are approximated by using Lagrange polynomials and the collocation points are used to satisfy constraints. A novel sigmoid-type collision avoidance constraint is proposed to overcome the drawbacks of Lagrange polynomial approximation in pseudospectral methods that only guarantees inequality constraint satisfaction only at nodal points. Automatic differentiation of cost function and constraints is used to quickly determine their gradient and Jacobian, respectively. An APF method is used to update the optimal control inputs for guaranteeing collision avoidance. The trajectory optimization and APF method are implemented in a closed-loop fashion continuously, but in parallel at moderate and high frequencies, respectively. The initial guess for the optimization is provided based on the previous solution. The proposed approach is tested and validated through indoor experiments.Experiment video link: https://youtu.be/swSspfvYjJs
H2020 - 101017258 - SESAME - Secure and Safe Multi-Robot Systems
FnR Project :
FNR13713801 - Interconnecting The Sky In 5g And Beyond - A Joint Communication And Control Approach, 2019 (01/06/2020-31/05/2023) - Bjorn Ottersten
Funders :
Union Européenne
Funding text :
D. M. K. K. Venkateswara Rao, H. Habibi, J. L. Sanchez-Lopez, and H. Voos are with Automation and Robotics Research Group, Interdisciplinary Centre for Security, Reliability and Trust, University of Luxembourg, Luxembourg. H. Voos is also with Faculty of Science, Technology and Medicine (FSTM), Department of Engineering, University of Luxembourg, {mohan.dasari,hamed.habibi,holger.voos, joseluis.sanchezlopez}@uni.lu *This research was partially supported by the European Union’s Horizon 2020 project Secure and Safe Multi-Robot Systems (SESAME) under the grant agreement no. 101017258 and by the Department of Media, Telecommunications and Digital Policy (SMC) of the Government of the Gran Duchy of Luxembourg under the project reference SMC/CFP-2019/010/IRANATA, ”Interference and RAdiation in Network PlAnning of 5G AcTive Antenna Systems,” and Fonds National de la Recherche of Luxembourg (FNR), under the projects C19/IS/13713801/5G-Sky.This research was partially supported by the European Union s Horizon 2020 project Secure and Safe Multi-Robot Systems (SESAME) under the grant agreement no. 101017258 and by the Department of Media, Telecommunications and Digital Policy (SMC) of the Government of the Gran Duchy of Luxembourg under the project reference SMC/CFP-2019/010/IRANATA, Interference and RAdiation in Network PlAnning of 5G AcTive Antenna Systems, and Fonds National de la Recherche of Luxembourg (FNR), under the projects C19/IS/13713801/5G-Sky.
M. Castillo-Lopez, P. Ludivig, S. A. Sajadi-Alamdari, J. L. Sanchez-Lopez, M. A. Olivares-Mendez, and H. Voos, "A real-time approach for chance-constrained motion planning with dynamic obstacles, " IEEE Robot. Autom. Lett., vol. 5, no. 2, pp. 3620-3625, 2020.
J. L. Sanchez-Lopez, M. Castillo-Lopez, M. A. Olivares-Mendez, and H. Voos, "Trajectory tracking for aerial robots: An optimization-based planning and control approach, " J. Intell. Robot. Syst., vol. 100, no. 2, pp. 531-574, 2020.
F. Gao, W. Wu, W. Gao, and S. Shen, "Flying on point clouds: Online trajectory generation and autonomous navigation for quadrotors in cluttered environments, " Journal of Field Robotics, vol. 36, no. 4, pp. 710-733, 2019.
B. Zhou, F. Gao, J. Pan, and S. Shen, "Robust real-time uav replanning using guided gradient-based optimization and topological paths, " in 2020 IEEE International Conference on Robotics and Automation (ICRA), pp. 1208-1214, IEEE, 2020.
X. Zhou, J. Zhu, H. Zhou, C. Xu, and F. Gao, "Ego-swarm: A fully autonomous and decentralized quadrotor swarm system in cluttered environments, " in 2021 IEEE International Conference on Robotics and Automation (ICRA), pp. 4101-4107, IEEE, 2021.
M. Hoy, A. S. Matveev, and A. V. Savkin, "Algorithms for collisionfree navigation of mobile robots in complex cluttered environments: A survey, " Robotica, vol. 33, no. 3, pp. 463-497, 2015.
C. Richter, A. Bry, and N. Roy, "Polynomial trajectory planning for aggressive quadrotor flight in dense indoor environments, " in Robotics research, pp. 649-666, Springer, 2016.
J. Chen, K. Su, and S. Shen, "Real-time safe trajectory generation for quadrotor flight in cluttered environments, " in 2015 IEEE International Conference on Robotics and Biomimetics (ROBIO), pp. 1678-1685, IEEE, 2015.
S. Liu, M. Watterson, K. Mohta, K. Sun, S. Bhattacharya, C. J. Taylor, and V. Kumar, "Planning dynamically feasible trajectories for quadrotors using safe flight corridors in 3-d complex environments, " IEEE Robotics and Automation Letters, vol. 2, no. 3, pp. 1688-1695, 2017.
F. Gao, W. Wu, Y. Lin, and S. Shen, "Online safe trajectory generation for quadrotors using fast marching method and bernstein basis polynomial, " in 2018 IEEE International Conference on Robotics and Automation (ICRA), pp. 344-351, IEEE, 2018.
W. Ding, W. Gao, K. Wang, and S. Shen, "An efficient b-spline-based kinodynamic replanning framework for quadrotors, " IEEE Transactions on Robotics, vol. 35, no. 6, pp. 1287-1306, 2019.
J. Tordesillas, B. T. Lopez, M. Everett, and J. P. How, "Faster: Fast and safe trajectory planner for navigation in unknown environments, " IEEE Transactions on Robotics, vol. 38, no. 2, pp. 922-938, 2021.
M. Zucker, N. Ratliff, A. D. Dragan, M. Pivtoraiko, M. Klingensmith, C. M. Dellin, J. A. Bagnell, and S. S. Srinivasa, "Chomp: Covariant hamiltonian optimization for motion planning, " The International Journal of Robotics Research, vol. 32, no. 9-10, pp. 1164-1193, 2013.
F. Gao, Y. Lin, and S. Shen, "Gradient-based online safe trajectory generation for quadrotor flight in complex environments, " in 2017 IEEE/RSJ international conference on intelligent robots and systems (IROS), pp. 3681-3688, IEEE, 2017.
V. Usenko, L. Von Stumberg, A. Pangercic, and D. Cremers, "Realtime trajectory replanning for mavs using uniform b-splines and a 3d circular buffer, " in 2017 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pp. 215-222, IEEE, 2017.
X. Zhou, Z. Wang, H. Ye, C. Xu, and F. Gao, "Ego-planner: An esdffree gradient-based local planner for quadrotors, " IEEE Robotics and Automation Letters, vol. 6, no. 2, pp. 478-485, 2020.
H. Oleynikova, M. Burri, Z. Taylor, J. Nieto, R. Siegwart, and E. Galceran, "Continuous-time trajectory optimization for online uav replanning, " in 2016 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pp. 5332-5339, IEEE, 2016.
F. Gao, L. Wang, B. Zhou, X. Zhou, J. Pan, and S. Shen, "Teachrepeat-replan: A complete and robust system for aggressive flight in complex environments, " IEEE Transactions on Robotics, vol. 36, no. 5, pp. 1526-1545, 2020.
B. Zhou, F. Gao, L. Wang, C. Liu, and S. Shen, "Robust and efficient quadrotor trajectory generation for fast autonomous flight, " IEEE Robotics and Automation Letters, vol. 4, no. 4, pp. 3529-3536, 2019.
C. Rösmann, F. Hoffmann, and T. Bertram, "Integrated online trajectory planning and optimization in distinctive topologies, " Robotics and Autonomous Systems, vol. 88, pp. 142-153, 2017.
C. Rösmann, W. Feiten, T. Wösch, F. Hoffmann, and T. Bertram, "Trajectory modification considering dynamic constraints of autonomous robots, " in ROBOTIK 2012; 7th German Conference on Robotics, pp. 1-6, VDE, 2012.
L. Jaillet and T. Siméon, "Path deformation roadmaps: Compact graphs with useful cycles for motion planning, " The International Journal of Robotics Research, vol. 27, no. 11-12, pp. 1175-1188, 2008.
J. Alonso-Mora, T. Naegeli, R. Siegwart, and P. Beardsley, "Collision avoidance for aerial vehicles in multi-agent scenarios, " Autonomous Robots, vol. 39, no. 1, pp. 101-121, 2015.
D. H. Shim, H. J. Kim, and S. Sastry, "Decentralized nonlinear model predictive control of multiple flying robots, " in 42nd IEEE International Conference on Decision and Control (IEEE Cat. No. 03CH37475), vol. 4, pp. 3621-3626, IEEE, 2003.
T. Nägeli, L. Meier, A. Domahidi, J. Alonso-Mora, and O. Hilliges, "Real-time planning for automated multi-view drone cinematography, " ACM Transactions on Graphics (TOG), vol. 36, no. 4, pp. 1-10, 2017.
B. Gopalakrishnan, A. K. Singh, M. Kaushik, K. M. Krishna, and D. Manocha, "Chance constraint based multi agent navigation under uncertainty, " in Proceedings of the Advances in Robotics, pp. 1-6, 2017.
L. Blackmore, M. Ono, A. Bektassov, and B. C. Williams, "A probabilistic particle-control approximation of chance-constrained stochastic predictive control, " IEEE transactions on Robotics, vol. 26, no. 3, pp. 502-517, 2010.
F. Fahroo and I. M. Ross, "Direct trajectory optimization by a chebyshev pseudospectral method, " Journal of Guidance, Control, and Dynamics, vol. 25, no. 1, pp. 160-166, 2002.
R. H. Byrd, M. E. Hribar, and J. Nocedal, "An interior point algorithm for large-scale nonlinear programming, " SIAM Journal on Optimization, vol. 9, no. 4, pp. 877-900, 1999.
A. Wächter and L. T. Biegler, "On the implementation of an interiorpoint filter line-search algorithm for large-scale nonlinear programming, " Mathematical programming, vol. 106, no. 1, pp. 25-57, 2006.
J. A. Andersson, J. Gillis, G. Horn, J. B. Rawlings, and M. Diehl, "Casadi: A software framework for nonlinear optimization and optimal control, " Mathematical Programming Computation, vol. 11, pp. 1-36, 2019.
J. Ren, K. A. McIsaac, R. V. Patel, and T. M. Peters, "A potential field model using generalized sigmoid functions, " IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), vol. 37, no. 2, pp. 477-484, 2007.
