Survey of Numerical Methods for Trajectory Optimization

By John T. Betts. 1998

Subfields: Numerical Methods & Scientific Computing, Robotics & Control

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Citations in the corpus

Visual Foresight: Model-Based Deep Reinforcement Learning for Vision-Based Robotic Control (2018, methodology): “Test time control : At test time , we use a sampling-based, gradient free optimization procedure, similar to a shooting method [41], to ﬁnd the sequence of actions that minimizes a cost function.”
A Survey of Motion Planning and Control Techniques for Self-Driving Urban Vehicles (2016, background): “See [84], [85] for dedicated surveys on this topic.”
On the convergence of nonlinear optimal control using pseudospectral methods for feedback linearizable systems (2007, background): “As a result of significant progress in large-scale computational algorithms and nonlinear programming, the so-called direct computational methods have become the industry standard for solving nonlinear optimal control problems [1, 2], particularly in aerospace applications [3, 4].”
Low-Thrust Transfers in the Earth-Moon System, Including Applications to Libration Point Orbits (2010, methodology): “Both direct single shooting and direct multiple shooting [9] are employed to minimize a performance index of final spacecraft mass using a VSI engine model.”
Asymptotically optimal sampling-based kinodynamic planning (2014, background): “- Numerical optimization (Betts, 1998; Fernandes et al., 1993; Ostrowski et al., 2000) can be used but it can be expensive for global trajectories and suffers from local minima.”
An Introduction to Trajectory Optimization: How to Do Your Own Direct Collocation (2017, methodology): “Finally, in order to obtain an accurate solution for an indirect method, it is typically necessary to construct the necessary and sufficient conditions analytically, which can be challenging [5].”
Temporal Difference Variational Auto-Encoder (2018, background): “Having a model of the environment allows us to consider consequences of different actions without acting in the real environment and to formulate a plan (Browne et al., 2012; Silver et al., 2016; Betts, 1998; Bertsekas et al., 1995) or simply learn from simulated experience (Sutton, 1991).”
A direct method for trajectory optimization of rigid bodies through contact (2014, background): “For a more detailed comparison, see the survey article [6].”
Optimal trajectory planning for trains – A pseudospectral method and a mixed integer linear programming approach (2013, unknown): “(29) In general, phase boundary constraints (Betts, 1998; Becerra, 2010a) that link all the states and controls across the boundaries can be included in ΨL ≤ Ψ(x(1)(s(1)0 ),u(1)(s (1) 0 ),x (1)(s (1) f ),u (1)(s (1) f ),s (1) 0 ,s (1) f , x(2)(s (2) 0 ),u (2)(s (2) 0 ),x (2)(s (2) f ),u (2)(s (2) f…”
On optimal two-impulse Earth–Moon transfers in a four-body model (2013, background): “Direct transcription maps a differential optimal control problem into an algebraic nonlinear programming (NLP) problem; see Enright and Conway (1992); Betts (1998) for details.”