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This paper presents a novel method for reformulating non-differentiable collision avoidance constraints into smooth nonlinear constraints using strong duality of convex optimization.
A Formal Basis for the Heuristic Determination of Minimum Cost Paths
P. E. Hart, N. J. Nilsson, and B. Raphael · 1968
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Convex Analysis
T.R. Rockafellar · 1970
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Correction to “A Formal Basis for the Heuristic Determination of Minimum Cost Paths"
Peter E. Hart, Nils J. Nilsson, and Bertram Raphael · 1972
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Real-time obstacle avoidance for manipulators and mobile robots
Oussama Khatib · 1986
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Determining the minimum translational distance between two convex polyhedra
S. Cameron and R. Culley · 1986
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The complexity of robot motion planning
J. Canny · 1988
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Computing the intersection-depth of polyhedra
D. Dobkin, J. Hershberger, D. Kirkpatrick, and S. Suri · 1993
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Conflict resolution for air traffic management: a study in multiagent hybrid systems
C. Tomlin, G. J. Pappas, and S. Sastry · 1998
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Direct trajectory optimization by a Chebyshev pseudospectral method
F. Fahroo and I. Ross · 2000
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Randomized Kinodynamic Planning
S. M. LaValle and J. J. Kuffner · 2001
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Aircraft trajectory planning with collision avoidance using mixed integer linear programming
A. Richards and J. P. How · 2002
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Review of Nonlinear Mixed-Integer and Disjunctive Programming Techniques
I. E. Grossmann · 2002
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Collision-free UAV formation flight using decentralized optimization and invariant sets
F. Borrelli, T. Keviczky, and G. J. Balas · 2004
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Convex Optimization
S. Boyd and L. Vandenberghe · 2004
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Fast Direct Multiple Shooting Algorithms for Optimal Robot Control
M. Diehl, H.G. Bock, H. Diedam, and P.-B. Wieber · 2006
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Optimal manipulator path planning with obstacles using disjunctive programming
L. Blackmore and B. Williams · 2006
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Planning Algorithms
S. M. LaValle · 2006
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On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming
A. Wächter and L. Biegler · 2006
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Navigating car-like robots in unstructured environments using an obstacle sensitive cost function
J. Ziegler and M. Werling · 2008
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Planning long dynamically feasible maneuvers for autonomous vehicles
M. Likhachev and D. Ferguson · 2009
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Predictive control of autonomous ground vehicles with obstacle avoidance on slippery roads
Y. Gao, T. Lin, F. Borrelli, E. Tseng, and D. Hrovat · 2010
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Path Planning for Autonomous Vehicles in Unknown Semi-structured Environments
D. Dolgov, S. Thrun, M. Montemerlo, and J. Diebel · 2010
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Autonomous driving in urban environments: approaches, lessons and challenges
M. Campbell, M. Egerstedt, How J, and R. Murray · 2010
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Trajectory generation for aircraft avoidance maneuvers using online optimization
Automatic parallel parking with geometric continuous-curvature path planning
H. Vorobieva, S. Glaser, N. Minoiu-Enache, and S. Mammar · 2014
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Optimization-based autonomous racing of 1:43 scale RC cars
A. Liniger, A. Domahidi, and M. Morari · 2015
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Real-time motion planning methods for autonomous on-road driving: State-of-the-art and future research directions
C. Katrakazas, M. Quddus, W. Chen, and L0 Deka · 2015
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A unified motion planning method for parking an autonomous vehicle in the presence of irregularly placed obstacles
B. Li and Z. Shao · 2015
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A dynamic programming approach for nonholonomic vehicle maneuvering in tight environments
G. Schildbach and F. Borrelli · 2016
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Multi-Heuristic A*
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R. Patel and P. J. Goulart · 2011
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Chance-constrained optimal path planning with obstacles
L. Blackmore, M. Ono, and B. C. Williams · 2011
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Hamilton-Jacobi Formulation for Reach-Avoid Differential Games
K. Margellos and J. Lygeros · 2011
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Sampling-based algorithms for optimal motion planning
S. Karaman and E. Frazzoli · 2011
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STOMP: Stochastic trajectory optimization for motion planning
M. Kalakrishnan, S. Chitta, E. Theodorou, P. Pastor, and S. Schaal · 2011
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ITOMP: Incremental trajectory optimization for real-time replanning in dynamic environments
Chonhyon Park, Jia Pan, and Dinesh Manocha · 2012
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Trajectory generation and control for precise aggressive maneuvers with quadrotors
D. Mellinger, N. Michael, and V. Kumar · 2012
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S. Aine, S. Swaminathan, V. Narayanan, V. Hwang, and M. Likhachev · 2016
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A Survey of Motion Planning and Control Techniques for Self-Driving Urban Vehicles
B. Paden, M. Cáp, S. Yong, D. S. Yershov, and E0 Frazzoli · 2016
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A review of motion planning techniques for automated vehicles
D. González, J. Pérez, V. Milanés, and F. Nashashibi · 2016
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BiRRTOpt: A combined sampling and optimizing motion planner for humanoid robots
L. Li, X. Long, and M. A. Gennert · 2016
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Autonomous racing using learning model predictive control
U. Rosolia, A. Carvalho, and F. Borrelli · 2017
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Collision avoidance and stabilization for autonomous vehicles in emergency scenarios
J. Funke, M. Brown, S. M. Erlien, and J. C. Gerdes · 2017
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Hybrid curvature steer: A novel extend function for sampling-based nonholonomic motion planning in tight environments
H. Banzhaf, L. Palmieri, D. Nienhuser, T. Schamm, S. Knopp, and J.M. Zollner · 2017
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Autonomous vehicle control: A nonconvex approach for obstacle avoidance
U. Rosolia, S. DeBruyne, and A. Alleyne · 2017
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Real-Time Motion Planning for Aerial Videography With Dynamic Obstacle Avoidance and Viewpoint Optimization
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Predictive control for linear and hybrid systems
F. Borrelli, A. Bemporad, and M. Morari · 2017
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Jump: A modeling language for mathematical optimization
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Autonomous Parking using Optimization-based Collision Avoidance
Xiaojing Zhang, Alexander Liniger, and Francesco Borrelli · 2018
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