arXiv subjects

Samet Uzun

Publications and source records attributed to Samet Uzun.

10 recordsLinked to original sources

arXiv2026

OpenSCvx: An Open-Source Modular and Extensible Nonlinear Trajectory Planning Package

Trajectory optimization computes dynamically feasible motions that enable autonomous systems to accomplish complex tasks while satisfying operational and environmental constraints. This tutorial presents OpenSCvx, an open-source Python framework that bridges the gap between high-level problem specification and efficient numerical optimization. Rather than requiring users to derive solver-specific mathematical formulations, OpenSCvx provides a symbolic modeling interface that automatically constructs and solves trajectory optimization problems from modular descriptions of objectives, dynamics, and constraints. Beyond simplifying problem formulation, OpenSCvx supports (i) continuous-time constraint modeling, (ii) temporal and logical specifications, (iii) automatic vectorization for scalable and batched optimization, and (iv) a modular architecture that enables new algorithms, models, and solver backends to be incorporated with minimal effort. These capabilities allow researchers and practitioners to rapidly prototype, solve, and extend state-of-the-art trajectory optimization methods.

cs.RO↗

arXiv2026

Successive Convexification for Trajectory Optimization with Continuous-time Satisfaction of Signal Temporal Logic Specifications

This paper presents a successive convexification framework for trajectory optimization under continuous-time Signal Temporal Logic (CT-STL) specifications. The framework employs generalized mean-based robustness (GMSR), a smooth and exact parameterization of discrete-time STL, as a logical building block for constructing differentiable CT-STL constraints in optimal control. It is integrated with time-dilation for free-final-time problems, finite-dimensional control parameterization, multiple-shooting discretization of the dynamics, and a convergence-guaranteed sequential convex programming method, prox-convex, to solve the nonconvex program. The main CT-STL realization embeds temporal aggregation into augmented continuous-time dynamics. This augmentation-based construction is largely transcription-independent, can be incorporated into existing optimal-control pipelines with minimal structural changes, and enables smooth CT-STL parameterizations with accuracy controlled by a user-selected regularization parameter. We also discuss a complementary dense-time realization that evaluates CT-STL formulas directly on the integration subnodes used for dynamics discretization, yielding a smooth and exact parameterization on the numerical trajectory representation, up to the accuracy of the integration scheme. The proposed GMSR-based formulations mitigate the locality and gradient-masking behavior of standard quantitative semantics and therefore provide a favorable landscape for gradient-based trajectory optimization. The framework is demonstrated through trajectory-optimization examples for a double-integrator system with continuous-time \always{}, \eventually{}, and \until{} specifications, and a 6-DoF quadrotor flight problem with combined \always{}, \implication{}, and \eventually{}-type specifications. The implementation is available at https://github.com/UW-ACL/TrajOpt_CT-STL.

math.OC↗

arXiv2026

Smooth and Exact Parameterization of Continuous-time Signal Temporal Logic Specifications for Trajectory Optimization

This paper presents a smooth parameterization of continuous-time Signal Temporal Logic (CT-STL) specifications for nonconvex trajectory optimization that is sound and complete up to the accuracy of the underlying numerical integration scheme. CT-STL provides a natural framework for encoding rich temporal and logical task requirements, but existing trajectory-optimization formulations typically enforce such specifications only at discrete sampling nodes. In contrast, the proposed method evaluates specifications in dense time, thereby guaranteeing continuous-time satisfaction of always predicates, which is critical for path constraints such as obstacle avoidance, while eliminating the node-induced conservatism of eventually predicates by allowing satisfaction at any time within the prescribed interval. These two dense-time constructions also serve as the main building blocks for handling more general CT-STL formulas, including complex until specifications. Furthermore, the proposed parameterization resolves the locality and gradient-masking issues inherent in standard quantitative semantics, yielding a more favorable landscape for gradient-based solvers. Although dense-time evaluation introduces additional function evaluations during discretization, it also permits substantially coarser temporal grids without sacrificing safety or logical fidelity. This, in turn, reduces the dimension of the resulting nonconvex program, which is often the dominant factor in trajectory-generation cost. The numerical effectiveness and semantic exactness of the proposed framework are demonstrated on an agile quadrotor flight problem subject to a complex continuous-time until specification. The implementation is available at https:// github.com/UW-ACL/TrajOpt_CT-STL

math.OC↗

arXiv2025

A Proximal Method for Composite Optimization with Smooth and Convex Components

We introduce prox-convex for minimizing $F(x)=g(x)+h(C(x))+s(R(x))$, where $g$ and $h$ are convex, $C$ and $s$ are smooth, and each component of $R$ is convex (possibly nonsmooth). Here $g$ captures general convex objectives and indicator functions for convex constraints, while the composite template simultaneously models convex penalties on smooth features $(h \circ C)$ and smooth couplings of convex (possibly nonsmooth) features $(s \circ R)$. Each prox-convex step forms a convex subproblem by linearizing only the smooth maps while preserving the existing convex structure. The resulting subproblem is made strongly convex with the proximal metric $Q_k=\mu_k I+H_k^+ \succ 0$ where $\mu_k$ is adapted using an implicit trust-region strategy, and $H_k^+ \succeq 0$ is an optional curvature term for local acceleration. Under mild Lipschitz/smoothness and a per-coordinate monotone-or-smooth condition, we prove subdifferential regularity, derive two-sided quadratic model error bounds with explicit constants, and obtain sufficient decrease with $O(\varepsilon^{-2})$ complexity for driving the norm of the metric prox-gradient below $\varepsilon$. Furthermore, a local error-bound condition for $F$ guarantees a metric step-size error bound and hence local $Q$-linear convergence of the function values. Using the Taylor-like model framework of Drusvyatskiy, Ioffe, and Lewis, we show that every cluster point of the iterates is limiting-stationary; under our regularity conditions, this further implies Fr\'echet stationarity. The same framework also establishes robustness to inexact subproblem solves and justifies a model-decrease termination rule.

math.OC↗

arXiv2025

Sequential Convex Programming for 6-DoF Powered Descent Guidance with Continuous-Time Compound State-Triggered Constraints

This paper presents a sequential convex programming (SCP) framework for ensuring the continuous-time satisfaction of compound state-triggered constraints, a subset of logical specifications, in the powered descent guidance (PDG) problem. The proposed framework combines the generalized mean-based smooth robustness measure (D-GMSR), a parameterization technique tailored for expressing discrete-time temporal and logical specifications through smooth functions, with the continuous-time successive convexification (CT-SCvx) method, a real-time solution for constrained trajectory optimization that guarantees continuous-time constraint satisfaction and convergence. The smoothness of the temporal and logical specifications parameterized via D-GMSR enables solving the resulting optimization problem with robust and efficient SCP algorithms while preserving theoretical guarantees. In addition to their smoothness, the parameterized specifications are sound and complete, meaning the specification holds if and only if the constraint defined by the parameterized function is satisfied. The CT-SCvx framework is then applied to solve the parameterized problem, incorporating: (1) reformulation for continuous-time path constraint satisfaction, (2) time-dilation to transform the free-final-time PDG problem into a fixed-final-time problem, (3) multiple shooting for exact discretization, (4) exact penalty functions for penalizing nonconvex constraints, and (5) the prox-linear method, a convergence-guaranteed SCP algorithm, to solve the resulting finite-dimensional nonconvex PDG problem. The effectiveness of the framework is demonstrated through a numerical simulation. The implementation is available at https://github.com/UW-ACL/CT-cSTC

eess.SY↗

arXiv2024

Optimization with Temporal and Logical Specifications via Generalized Mean-based Smooth Robustness Measures

This paper introduces a generalized mean-based C^1-smooth robustness measure over discrete-time signals (D-GMSR) for signal temporal logic (STL) specifications. In conjunction with its C1-smoothness, D-GMSR is proven to be both sound and complete. Furthermore, it demonstrates favorable gradient properties and addresses locality and masking problems, which are critical for numerical optimization. The C^1-smoothness of the proposed formulations enables the implementation of robust and efficient numerical optimization algorithms to solve problems with STL specifications while preserving their theoretical guarantees. The practical utility of the proposed robustness measure is demonstrated on two real-world trajectory optimization problems: i) quadrotor flight, and ii) autonomous rocket landing. A sequential convex programming (SCP) framework, incorporating a convergence-guaranteed optimization algorithm (the prox-linear method) is used to solve inherently non-convex trajectory optimization problems with STL specifications. The implementation is available at https://github.com/UW-ACL/D-GMSR

math.OC↗

arXiv2024

Successive Convexification for Nonlinear Model Predictive Control with Continuous-Time Constraint Satisfaction

We propose a nonlinear model predictive control (NMPC) framework based on a direct optimal control method that ensures continuous-time constraint satisfaction and accurate evaluation of the running cost, without compromising computational efficiency. We leverage the recently proposed successive convexification framework for trajectory optimization, where: (1) the path constraints and running cost are equivalently reformulated by augmenting the system dynamics, (2) multiple shooting is used for exact discretization, and (3) a convergence-guaranteed sequential convex programming (SCP) algorithm, the prox-linear method, is used to solve the discretized receding-horizon optimal control problems. The resulting NMPC framework is computationally efficient, owing to its support for warm-starting and premature termination of SCP, and its reliance on first-order information only. We demonstrate the effectiveness of the proposed NMPC framework by means of a numerical example with reference-tracking and obstacle avoidance. The implementation is available at https://github.com/UW-ACL/nmpc-ctcs

math.OC↗

arXiv2024

Successive Convexification for Trajectory Optimization with Continuous-Time Constraint Satisfaction

We present successive convexification, a real-time-capable solution method for nonconvex trajectory optimization, with continuous-time constraint satisfaction and guaranteed convergence, that only requires first-order information. The proposed framework 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) $\ell_1$ exact penalization of the nonconvex constraints; and (v) the prox-linear method, a sequential convex programming (SCP) algorithm for convex-composite minimization. The reformulation of the path constraints enables continuous-time constraint satisfaction even on sparse discretization grids and obviates the need for mesh refinement heuristics. Through the prox-linear method, we guarantee convergence of the solution method to stationary points of the penalized problem and guarantee that the converged solutions that are feasible with respect to the discretized and control-parameterized optimal control problem are also Karush-Kuhn-Tucker (KKT) points. Furthermore, we highlight the specialization of this property to global minimizers of convex optimal control problems, wherein the reformulated path constraints cannot be represented by canonical cones, i.e., in the form required by existing convex optimization solvers. In addition to theoretical analysis, we demonstrate the effectiveness and real-time capability of the proposed framework with numerical examples based on popular optimal control applications: dynamic obstacle avoidance and rocket landing.

math.OC↗

arXiv2020

Decentralized State-Dependent Markov Chain Synthesis with an Application to Swarm Guidance

This paper introduces a decentralized state-dependent Markov chain synthesis (DSMC) algorithm for finite-state Markov chains. We present a state-dependent consensus protocol that achieves exponential convergence under mild technical conditions, without relying on any connectivity assumptions regarding the dynamic network topology. Utilizing the proposed consensus protocol, we develop the DSMC algorithm, updating the Markov matrix based on the current state while ensuring the convergence conditions of the consensus protocol. This result establishes the desired steady-state distribution for the resulting Markov chain, ensuring exponential convergence from all initial distributions while adhering to transition constraints and minimizing state transitions. The DSMC's performance is demonstrated through a probabilistic swarm guidance example, which interprets the spatial distribution of a swarm comprising a large number of mobile agents as a probability distribution and utilizes the Markov chain to compute transition probabilities between states. Simulation results demonstrate faster convergence for the DSMC based algorithm when compared to the previous Markov chain based swarm guidance algorithms.

math.OC↗

arXiv2020

A Probabilistic Guidance Approach to Swarm-to-Swarm Engagement Problem

This paper introduces a probabilistic guidance approach for the swarm-to-swarm engagement problem. The idea is based on driving the controlled swarm towards an adversary swarm, where the adversary swarm aims to converge to a stationary distribution that corresponds to a defended base location. The probabilistic approach is based on designing a Markov chain for the distribution of the swarm to converge a stationary distribution. This approach is decentralized, so each agent can propagate its position independently of other agents. Our main contribution is the formulation of the swarm-to-swarm engagement as an optimization problem where the population of each swarm decays with each engagement and determining a desired distribution for the controlled swarm to converge time-varying distribution and eliminate agents of the adversary swarm until adversary swarm enters the defended base location. We demonstrate the validity of proposed approach on several swarm engagement scenarios.

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