A Fast Semidefinite Convex Relaxation for Optimal Control Problems With Spatio-Temporal Constraints

• URL: http://arxiv.org/abs/2601.03055v1
• Date: Tue, 06 Jan 2026 14:38:19 GMT
• Title: A Fast Semidefinite Convex Relaxation for Optimal Control Problems With Spatio-Temporal Constraints
• Abstract summary: Solving optimal control problems (OCs) of autonomous agents is essential in applications ranging from driving autonomous vehicles to self-driving cars.<n>Most of the OCPs are nonpointing due to the coupling between the event timing and the trajectory.<n>We propose a time-scaling direct multiple shooting scheme that partitions the horizon into segments with time constraints.
• Score: 22.24436694865408
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Solving optimal control problems (OCPs) of autonomous agents operating under spatial and temporal constraints fast and accurately is essential in applications ranging from eco-driving of autonomous vehicles to quadrotor navigation. However, the nonlinear programs approximating the OCPs are inherently nonconvex due to the coupling between the dynamics and the event timing, and therefore, they are challenging to solve. Most approaches address this challenge by predefining waypoint times or just using nonconvex trajectory optimization, which simplifies the problem but often yields suboptimal solutions. To significantly improve the numerical properties, we propose a formulation with a time-scaling direct multiple shooting scheme that partitions the prediction horizon into segments aligned with characteristic time constraints. Moreover, we develop a fast semidefinite-programming-based convex relaxation that exploits the sparsity pattern of the lifted formulation. Comprehensive simulation studies demonstrate the solution optimality and computational efficiency. Furthermore, real-world experiments on a quadrotor waypoint flight task with constrained open time windows validate the practical applicability of the approach in complex environments.

Related papers

• Biconvex Optimization for Smooth Minimum-Time Trajectories around Convex Obstacles [49.315843050082925]
  We present a bi approach for minimum-time motion planning convex obstacles that is guaranteed to converge.<n>We find that the proposed method produces high-quality trajectories with times to produce state-of-the-art decomposition of variables.
  arXiv  Detail & Related papers  (2026-08-03T19:48:24Z)
• Motion Planning for Autonomous Vehicles using Optimization over Graphs of Convex Sets [0.6445605125467574]
  Motion planning for autonomous vehicles requires generating collision-free and dynamically feasible trajectories under real-time constraints.<n>In this paper, we introduce a new geometric control method to approximate nonlinear motion planning problems.<n>The method provides a structured approximation of nonlinear motion planning problems, capturing dominant geometric dynamic effects while preserving convexity in the continuous relaxation.
  arXiv  Detail & Related papers  (2026-05-13T23:29:54Z)
• Accelerated Spline-Based Time-Optimal Motion Planning with Continuous Safety Guarantees for Non-Differentially Flat Systems [6.862015448582809]
  State-of-the-art approaches formulate spline-based motion planning as a single Control Problem (OCP)<n>By treating separation as an independent classification problem solvable via a linear system or quadratic program, the proposed method eliminates hyperplane parameters from the OCP variables.<n> Experimental validation demonstrates that this decoupled approach reduces trajectory times up to almost 60% compared to fully-rich environments.
  arXiv  Detail & Related papers  (2026-03-25T09:53:04Z)
• Fast Near Time-Optimal Motion Planning for Holonomic Vehicles in Structured Environments [8.195916347194315]
  The approach aims to solve the problem of motion planning for planar motion systems using magnetic levitation.<n>The presented approach encodes the environment representation using free-space corridors and represents the motion of the vehicle through such a corridor using a motion primitive.<n>The method achieves significantly lower times compared to the state-of-the-art and is validated on a real-world Beckhoff XPlanar system.
  arXiv  Detail & Related papers  (2026-02-02T21:26:30Z)
• A Convex Obstacle Avoidance Formulation [1.7904458681854372]
  This work presents the first general convex obstacle avoidance, enabled by integrating logic.<n>A key property of the formulation is that obstacle avoidance remains effective even when shorter outside the horizon.
  arXiv  Detail & Related papers  (2025-12-15T19:16:47Z)
• Single-loop Algorithms for Stochastic Non-convex Optimization with Weakly-Convex Constraints [49.76332265680669]
  This paper examines a crucial subset of problems where both the objective and constraint functions are weakly convex.<n>Existing methods often face limitations, including slow convergence rates or reliance on double-loop designs.<n>We introduce a novel single-loop penalty-based algorithm to overcome these challenges.
  arXiv  Detail & Related papers  (2025-04-21T17:15:48Z)
• A Hybrid Tabu Scatter Search Algorithm for Simulation-Based Optimization of Multi-Objective Runway Operations Scheduling [0.0]
  dissertation addresses the challenge of air traffic flow management by proposing a simulation-based optimization (SbO) approach for runway operations scheduling.<n>The goal is to optimize airport capacity utilization while minimizing delays, fuel consumption, and environmental impacts.<n>The proposed SbO framework integrates a discrete-event simulation model to handle runway conditions and a hybrid Tabu-Scatter Search algorithm to identify optimal solutions.
  arXiv  Detail & Related papers  (2025-02-08T14:42:05Z)
• OTClean: Data Cleaning for Conditional Independence Violations using Optimal Transport [51.6416022358349]
  sys is a framework that harnesses optimal transport theory for data repair under Conditional Independence (CI) constraints. We develop an iterative algorithm inspired by Sinkhorn's matrix scaling algorithm, which efficiently addresses high-dimensional and large-scale data.
  arXiv  Detail & Related papers  (2024-03-04T18:23:55Z)
• DiffuSolve: Diffusion-based Solver for Non-convex Trajectory Optimization [9.28162057044835]
  Optimal trajectory local is computationally expensive for nonlinear and high-dimensional dynamical systems. In this paper we introduce Diffu-based general model for non-dimensional optima problems. We also present Diff+, a novel constrained diffusion model with an additional loss in that further reduces the problem violations.
  arXiv  Detail & Related papers  (2024-02-22T03:52:17Z)
• Primal-Dual Contextual Bayesian Optimization for Control System Online Optimization with Time-Average Constraints [21.38692458445459]
  This paper studies the problem of online performance optimization of constrained closed-loop control systems. A primal-dual contextual Bayesian optimization algorithm is proposed that achieves sublinear cumulative regret with respect to the dynamic optimal solution.
  arXiv  Detail & Related papers  (2023-04-12T18:37:52Z)
• Accelerated First-Order Optimization under Nonlinear Constraints [61.98523595657983]
  We exploit between first-order algorithms for constrained optimization and non-smooth systems to design a new class of accelerated first-order algorithms.<n>An important property of these algorithms is that constraints are expressed in terms of velocities instead of sparse variables.
  arXiv  Detail & Related papers  (2023-02-01T08:50:48Z)
• Optimization on manifolds: A symplectic approach [127.54402681305629]
  We propose a dissipative extension of Dirac's theory of constrained Hamiltonian systems as a general framework for solving optimization problems. Our class of (accelerated) algorithms are not only simple and efficient but also applicable to a broad range of contexts.
  arXiv  Detail & Related papers  (2021-07-23T13:43:34Z)
• Combining Deep Learning and Optimization for Security-Constrained Optimal Power Flow [94.24763814458686]
  Security-constrained optimal power flow (SCOPF) is fundamental in power systems. Modeling of APR within the SCOPF problem results in complex large-scale mixed-integer programs. This paper proposes a novel approach that combines deep learning and robust optimization techniques.
  arXiv  Detail & Related papers  (2020-07-14T12:38:21Z)
• Goal Kernel Planning: Linearly-Solvable Non-Markovian Policies for Logical Tasks with Goal-Conditioned Options [54.40780660868349]
  We introduce a compositional framework called Linearly-Solvable Goal Kernel Dynamic Programming (LS-GKDP)<n>LS-GKDP combines the Linearly-Solvable Markov Decision Process (LMDP) formalism with the Options Framework of Reinforcement Learning.<n>We show how an LMDP with a goal kernel enables the efficient optimization of meta-policies in a lower-dimensional subspace defined by the task grounding.
  arXiv  Detail & Related papers  (2020-07-06T05:13:20Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.