Continuous-time successive convexification for constrained trajectory optimization

We present continuous-time successive convexification (ct- scvx ), a real-time-capable solution method for constrained trajectory optimization, with continuous-time constraint satisfaction and guaranteed convergence. The proposed solution framework only relies on first-order information, and it comb...

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Vydáno v:Automatica (Oxford) Ročník 180; s. 112464
Hlavní autoři: Elango, Purnanand, Luo, Dayou, Kamath, Abhinav G., Uzun, Samet, Kim, Taewan, Açıkmeşe, Behçet
Médium: Journal Article
Jazyk:angličtina
Vydáno: Elsevier Ltd 01.10.2025
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ISSN:0005-1098
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Abstract We present continuous-time successive convexification (ct- scvx ), a real-time-capable solution method for constrained trajectory optimization, with continuous-time constraint satisfaction and guaranteed convergence. The proposed solution framework only relies on first-order information, and it combines several key methods to solve a large class of nonlinear optimal control problems: (i) exterior penalty-based reformulation of the path constraints; (ii) generalized time-dilation; (iii) multiple-shooting discretization; (iv) ℓ1-exact penalization of the nonconvex constraints; and (v) the prox-linear method, a sequential convex programming (SCP) algorithm for convex-composite minimization. The proposed reformulation of the path constraints enables continuous-time constraint satisfaction even on sparse temporal discretization grids and obviates the need for mesh-refinement heuristics. Through the prox-linear method, we guarantee that: (i) ct-scvx converges to stationary points of the penalized problem; (ii) the converged stationary points that are feasible for the discretized and control-parameterized optimal control problem are also Karush–Kuhn–Tucker (KKT) points. Furthermore, we specialize this property to global minimizers of convex optimal control problems and obtain stronger convergence results by exploiting convexity. In addition to theoretical analysis, we demonstrate the effectiveness and real-time performance of ct-scvx by means of numerical examples from real-world optimal control applications: dynamic obstacle avoidance, and 3-degree-of-freedom (3-DoF) and 6-DoF autonomous rocket landing.
AbstractList We present continuous-time successive convexification (ct- scvx ), a real-time-capable solution method for constrained trajectory optimization, with continuous-time constraint satisfaction and guaranteed convergence. The proposed solution framework only relies on first-order information, and it combines several key methods to solve a large class of nonlinear optimal control problems: (i) exterior penalty-based reformulation of the path constraints; (ii) generalized time-dilation; (iii) multiple-shooting discretization; (iv) ℓ1-exact penalization of the nonconvex constraints; and (v) the prox-linear method, a sequential convex programming (SCP) algorithm for convex-composite minimization. The proposed reformulation of the path constraints enables continuous-time constraint satisfaction even on sparse temporal discretization grids and obviates the need for mesh-refinement heuristics. Through the prox-linear method, we guarantee that: (i) ct-scvx converges to stationary points of the penalized problem; (ii) the converged stationary points that are feasible for the discretized and control-parameterized optimal control problem are also Karush–Kuhn–Tucker (KKT) points. Furthermore, we specialize this property to global minimizers of convex optimal control problems and obtain stronger convergence results by exploiting convexity. In addition to theoretical analysis, we demonstrate the effectiveness and real-time performance of ct-scvx by means of numerical examples from real-world optimal control applications: dynamic obstacle avoidance, and 3-degree-of-freedom (3-DoF) and 6-DoF autonomous rocket landing.
ArticleNumber 112464
Author Açıkmeşe, Behçet
Luo, Dayou
Kim, Taewan
Kamath, Abhinav G.
Elango, Purnanand
Uzun, Samet
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  surname: Elango
  fullname: Elango, Purnanand
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  givenname: Dayou
  surname: Luo
  fullname: Luo, Dayou
  email: dayoul@uw.edu
  organization: Department of Applied Mathematics, University of Washington, Seattle, WA, 98195, United States of America
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  givenname: Abhinav G.
  surname: Kamath
  fullname: Kamath, Abhinav G.
  email: agkamath@uw.edu
  organization: William E. Boeing Department of Aeronautics & Astronautics, University of Washington, Seattle, WA, 98195, United States of America
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  givenname: Samet
  surname: Uzun
  fullname: Uzun, Samet
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  organization: William E. Boeing Department of Aeronautics & Astronautics, University of Washington, Seattle, WA, 98195, United States of America
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  givenname: Taewan
  surname: Kim
  fullname: Kim, Taewan
  email: twankim@uw.edu
  organization: William E. Boeing Department of Aeronautics & Astronautics, University of Washington, Seattle, WA, 98195, United States of America
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  givenname: Behçet
  surname: Açıkmeşe
  fullname: Açıkmeşe, Behçet
  email: behcet@uw.edu
  organization: William E. Boeing Department of Aeronautics & Astronautics, University of Washington, Seattle, WA, 98195, United States of America
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Keywords Sequential convex programming
Continuous-time constraint satisfaction
Optimal control
Trajectory optimization
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Snippet We present continuous-time successive convexification (ct- scvx ), a real-time-capable solution method for constrained trajectory optimization, with...
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SubjectTerms Continuous-time constraint satisfaction
Optimal control
Sequential convex programming
Trajectory optimization
Title Continuous-time successive convexification for constrained trajectory optimization
URI https://dx.doi.org/10.1016/j.automatica.2025.112464
Volume 180
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