arXiv subjects

Behçet Açıkmeşe

Publications and source records attributed to Behçet Açıkmeşe.

At least 37 records · Page 2Linked to original sources

arXiv2025

Continuous-Time Line-of-Sight Constrained Trajectory Planning for 6-Degree of Freedom Systems

Perception algorithms are ubiquitous in modern autonomy stacks, providing necessary environmental information to operate in the real world. Many of these algorithms depend on the visibility of keypoints, which must remain within the robot's line-of-sight (LoS), for reliable operation. This paper tackles the challenge of maintaining LoS on such keypoints during robot movement. We propose a novel method that addresses these issues by ensuring applicability to various sensor footprints, adaptability to arbitrary nonlinear system dynamics, and constant enforcement of LoS throughout the robot's path. Our experiments show that the proposed approach achieves significantly reduced LoS violation and runtime compared to existing state-of-the-art methods in several representative and challenging scenarios.

math.OC↗

arXiv2024

Autonomy in the Real-World: Autonomous Trajectory Planning for Asteroid Reconnaissance via Stochastic Optimization

This paper presents the development and evaluation of an optimization-based autonomous trajectory planning algorithm for the asteroid reconnaissance phase of a deep-space exploration mission. The reconnaissance phase is a low-altitude flyby to collect detailed information around a potential landing site. Although such autonomous deep-space exploration missions have garnered considerable interest recently, state-of-the-practice in trajectory design involves a time-intensive ground-based open-loop process that forward propagates multiple trajectories with a range of initial conditions and parameters to account for uncertainties in spacecraft knowledge and actuation. In this work, we introduce a stochastic trajectory optimization-based approach to generate trajectories that satisfy both the mission and spacecraft safety constraints during the reconnaissance phase of the Deep-space Autonomous Robotic Explorer (DARE) mission concept, which seeks to travel to and explore a near-Earth object autonomously, with minimal ground intervention. We first use the Multi-Spacecraft Concept and Autonomy Tool (MuSCAT) simulation framework to rigorously validate the underlying modeling assumptions for our trajectory planner and then propose a method to transform this stochastic optimal control problem into a deterministic one tailored for use with an off-the-shelf nonlinear solver. Finally, we demonstrate the efficacy of our proposed algorithmic approach through extensive numerical experiments and show that it outperforms the state-of-the-practice benchmark used for representative missions.

physics.space-ph↗

arXiv2024

Constraint Preconditioning and Parameter Selection for a First-Order Primal-Dual Method applied to Model Predictive Control

Many techniques for real-time trajectory optimization and control require the solution of optimization problems at high frequencies. However, ill-conditioning in the optimization problem can significantly reduce the speed of first-order primal-dual optimization algorithms. We introduce a preconditioning technique and step-size heuristic for Proportional-Integral Projected Gradient (PIPG), a first-order primal-dual algorithm. The preconditioning technique, based on the QR factorization, aims to reduce the condition number of the KKT matrix associated with the optimization problem. Our step-size selection heuristic chooses step-sizes to minimize the upper bound on the convergence of the primal-dual gap for the optimization problem. These algorithms are tested on two model predictive control problem examples and show a solve-time reduction of at least 3.6x.

math.OC↗

arXiv2024

Expected Time-Optimal Control: a Particle Model Predictive Control-based Approach via Sequential Convex Programming

In this paper, we consider the problem of minimum-time optimal control for a dynamical system with initial state uncertainties and propose a sequential convex programming (SCP) solution framework. We seek to minimize the expected terminal (mission) time, which is an essential capability for planetary exploration missions where ground rovers have to carry out scientific tasks efficiently within the mission timelines in uncertain environments. Our main contribution is to convert the underlying stochastic optimal control problem into a deterministic, numerically tractable, optimal control problem. To this end, the proposed solution framework combines two strategies from previous methods: i) a partial model predictive control with consensus horizon approach and ii) a sum-of-norm cost, a temporally strictly increasing weighted-norm, promoting minimum-time trajectories. Our contribution is to adopt these formulations into an SCP solution framework and obtain a numerically tractable stochastic control algorithm. We then demonstrate the resulting control method in multiple applications: i) a closed-loop linear system as a representative result (a spacecraft double integrator model), ii) an open-loop linear system (the same model), and then iii) a nonlinear system (Dubin's car).

math.OC↗

arXiv2024

Fast Monte Carlo Analysis for 6-DoF Powered-Descent Guidance via GPU-Accelerated Sequential Convex Programming

We introduce a GPU-accelerated Monte Carlo framework for nonconvex, free-final-time trajectory optimization problems. This framework makes use of the prox-linear method, which belongs to the larger family of sequential convex programming (SCP) algorithms, in conjunction with a constraint reformulation that guarantees inter-sample constraint satisfaction. Key features of this framework are: (1) continuous-time constraint satisfaction; (2) a matrix-inverse-free solution method; (3) the use of the proportional-integral projected gradient (PIPG) method, a first-order convex optimization solver, customized to the convex subproblem at hand; and, (4) an end-to-end, library-free implementation of the algorithm. We demonstrate this GPU-based framework on the 6-DoF powered-descent guidance problem, and show that it is faster than an equivalent serial CPU implementation for Monte Carlo simulations with over 1000 runs. To the best of our knowledge, this is the first GPU-based implementation of a general-purpose nonconvex trajectory optimization solver.

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↗

arXiv2024

Spacecraft Rendezvous Guidance via Factorization-Free Sequential Convex Programming using a First-Order Method

We implement a fully factorization-free algorithm for nonconvex, free-final-time trajectory optimization. This algorithm is based on sequential convex programming and utilizes an inverse-free, exact discretization procedure to ensure dynamic feasibility of the converged trajectory and PIPG, a fast, first-order conic optimization algorithm as the subproblem solver. Although PIPG requires the tuning of a hyperparameter to achieve fastest convergence, we show that PIPG can be tuned to a nominal trajectory optimization problem and it is robust to variations in initial condition. We demonstrate this with a monte carlo simulation of the free-final-time rendezvous problem, using Clohessy-Wiltshire dynamics, an impulsive thrust model, and various state and control constraints including a spherical keepout zone.

math.OC↗

arXiv2023

Blameless and Optimal Control under Prioritized Safety Constraints

In many resource-limited optimal control problems, multiple constraints may be enforced that are jointly infeasible due to external factors such as subsystem failures, unexpected disturbances, or fuel limitations. In this manuscript, we introduce the concept of blameless optimality to characterize control actions that a) satisfy the highest prioritized and feasible constraints and b) remain optimal with respect to a mission objective. For a general optimal control problem with jointly infeasible constraints, we prove that a single optimization problem cannot find a blamelessly optimal control sequence. Instead, finding blamelessly optimal control actions requires sequentially solving at least two optimal control problems: one to determine the highest priority level of constraints that is feasible and another to determine the optimal control action with respect to these constraints. We apply our results to a rocket landing scenario in which violating at least one safety-induced landing constraint is unavoidable. Leveraging the concept of blameless optimality, we formulate blamelessly optimal controllers that can autonomously prioritize the constraints most critical to a mission.

math.OC↗

arXiv2023

Set-based value operators for non-stationary Markovian environments

This paper analyzes finite state Markov Decision Processes (MDPs) with uncertain parameters in compact sets and re-examines results from robust MDP via set-based fixed point theory. To this end, we generalize the Bellman and policy evaluation operators to contracting operators on the value function space and denote them as \emph{value operators}. We lift these value operators to act on \emph{sets} of value functions and denote them as \emph{set-based value operators}. We prove that the set-based value operators are \emph{contractions} in the space of compact value function sets. Leveraging insights from set theory, we generalize the rectangularity condition in classic robust MDP literature to a containment condition for all value operators, which is weaker and can be applied to a larger set of parameter-uncertain MDPs and contracting operators in dynamic programming. We prove that both the rectangularity condition and the containment condition sufficiently ensure that the set-based value operator's fixed point set contains its own extrema elements. For convex and compact sets of uncertain MDP parameters, we show equivalence between the classic robust value function and the supremum of the fixed point set of the set-based Bellman operator. Under dynamically changing MDP parameters in compact sets, we prove a set convergence result for value iteration, which otherwise may not converge to a single value function. Finally, we derive novel guarantees for probabilistic path-planning problems in planet exploration and stratospheric station-keeping.

cs.LG↗

arXiv2023

Optimization-based Constrained Funnel Synthesis for Systems with Lipschitz Nonlinearities via Numerical Optimal Control

This paper presents a funnel synthesis algorithm for computing controlled invariant sets and feedback control gains around a given nominal trajectory for dynamical systems with locally Lipschitz nonlinearities and bounded disturbances. The resulting funnel synthesis problem involves a differential linear matrix inequality (DLMI) whose solution satisfies a Lyapunov condition that implies invariance and attractivity properties. Due to these properties, the proposed method can balance maximization of initial invariant funnel size, i.e., size of the funnel entry, and minimization of the size of the attractive funnel for attenuating the effect of disturbance. To solve the resulting funnel synthesis problem with the DLMI as constraints, we employ a numerical optimal control approach that uses a multiple shooting method to convert the problem into a finite dimensional semidefinite programming problem. This framework does not require piecewise linear system matrices and funnel parameters, which is typically assumed in recent related work. We illustrate the proposed funnel synthesis method with a numerical example.

math.OC↗

arXiv2023

Real-Time Sequential Conic Optimization for Multi-Phase Rocket Landing Guidance

We introduce a multi-phase rocket landing guidance framework that can handle nonlinear dynamics and does not mandate any additional mixed-integer or nonconvex constraints to handle discrete temporal events/switching. To achieve this, we first introduce sequential conic optimization (SeCO), a new paradigm for solving nonconvex optimal control problems that is entirely devoid of matrix factorizations and inversions. This framework combines sequential convex programming (SCP) and first-order conic optimization and can solve unified multi-phase trajectory optimization problems in real-time. The novel features of this framework are: (1) time-interval dilation, which enables multi-phase trajectory optimization with free-transition-time; (2) single-crossing compound state-triggered constraints, which are entirely convex if the trigger and constraint conditions are convex; (3) virtual state, which is a new approach to handling artificial infeasibility in SCP methods that preserves the shapes of the constraint sets; and, (4) the use of the proportional-integral projected gradient method (PIPG), a high-performance first-order conic optimization solver, in tandem with the penalized trust region (PTR) SCP algorithm. We demonstrate the efficacy and real-time capability of SeCO by solving a relevant multi-phase rocket landing guidance problem with nonlinear dynamics and convex constraints only, and observe that our solver is 2.7 times faster than a state-of-the-art convex optimization solver.

math.OC↗

arXiv2022

Real-Time Quadrotor Trajectory Optimization with Time-Triggered Corridor Constraints

One of the keys to flying quadrotors is to optimize their trajectories within the set of collision-free corridors. These corridors impose nonconvex constraints on the trajectories, making real-time trajectory optimization challenging. We introduce a novel numerical method that approximates the nonconvex corridor constraints with time-triggered convex corridor constraints. This method combines bisection search and repeated infeasibility detection. We further develop a customized C++ implementation of the proposed method, based on a first-order conic optimization method that detects infeasibility and exploits problem structure. We demonstrate the efficiency and effectiveness of the proposed method using numerical simulation on randomly generated problem instances as well as indoor flight experiments with hoop obstacles. Compared with mixed integer programming, the proposed method is about 50--200 times faster.

math.OC↗

arXiv2022

Extrapolated Proportional-Integral Projected Gradient Method for Conic Optimization

Conic optimization is the minimization of a convex quadratic function subject to conic constraints. We introduce a novel first-order method for conic optimization, named \emph{extrapolated proportional-integral projected gradient method (xPIPG)}, that automatically detects infeasibility. The iterates of xPIPG either asymptotically satisfy a set of primal-dual optimality conditions, or generate a proof of primal or dual infeasibility. We demonstrate the application of xPIPG using benchmark problems in model predictive control. xPIPG outperforms many state-of-the-art conic optimization solvers, especially when solving large-scale problems.

math.OC↗

arXiv2021

Proportional-Integral Projected Gradient Method for Conic Optimization

Conic optimization is the minimization of a differentiable convex objective function subject to conic constraints. We propose a novel primal-dual first-order method for conic optimization, named proportional-integral projected gradient method (PIPG). PIPG ensures that both the primal-dual gap and the constraint violation converge to zero at the rate of $O(1/k)$, where $k$ is the number of iterations. If the objective function is strongly convex, PIPG improves the convergence rate of the primal-dual gap to $O(1/k^2)$. Further, unlike any existing first-order methods, PIPG also improves the convergence rate of the constraint violation to $O(1/k^3)$. We demonstrate the application of PIPG in constrained optimal control problems.

math.OC↗

arXiv2021

Variable Demand and Multi-commodity Flow in Markovian Network Equilibrium

Markovian network equilibrium generalizes the classical Wardrop equilibrium in network games. At a Markovian network equilibrium, each player of the game solves a Markov decision process instead of a shortest path problem. We propose two novel extensions of Markovian network equilibrium by considering 1) variable demand, which offers the players a quitting option, and 2) multi-commodity flow, which allows players to have heterogeneous ending time. We further develop dynamic-programming-based iterative algorithms for the proposed equilibrium problems, together with their arithmetic complexity analysis. Finally, we illustrate our network equilibrium model via a multi-commodity ride-sharing example, and compare the computational efficiency of our algorithms against state-of-the-art optimization software Mosek over extensive numerical experiments.

math.OC↗

arXiv2021

Discrete-Time Linear-Quadratic Regulation via Optimal Transport

In this paper, we consider a discrete-time stochastic control problem with uncertain initial and target states. We first discuss the connection between optimal transport and stochastic control problems of this form. Next, we formulate a linear-quadratic regulator problem where the initial and terminal states are distributed according to specified probability densities. A closed-form solution for the optimal transport map in the case of linear-time varying systems is derived, along with an algorithm for computing the optimal map. Two numerical examples pertaining to swarm deployment demonstrate the practical applicability of the model, and performance of the numerical method.

math.OC↗

arXiv2021

On Controllability and Persistency of Excitation in Data-Driven Control: Extensions of Willems' Fundamental Lemma

Willems' fundamental lemma asserts that all trajectories of a linear time-invariant system can be obtained from a finite number of measured ones, assuming that controllability and a persistency of excitation condition hold. We show that these two conditions can be relaxed. First, we prove that the controllability condition can be replaced by a condition on the controllable subspace, unobservable subspace, and a certain subspace associated with the measured trajectories. Second, we prove that the persistency of excitation requirement can be relaxed if the degree of a certain minimal polynomial is tightly bounded. Our results show that data-driven predictive control using online data is equivalent to model predictive control, even for uncontrollable systems. Moreover, our results significantly reduce the amount of data needed in identifying homogeneous multi-agent systems.

eess.SY↗

arXiv2021

Stability of Gradient Learning Dynamics in Continuous Games: Vector Action Spaces

Towards characterizing the optimization landscape of games, this paper analyzes the stability of gradient-based dynamics near fixed points of two-player continuous games. We introduce the quadratic numerical range as a method to characterize the spectrum of game dynamics and prove the robustness of equilibria to variations in learning rates. By decomposing the game Jacobian into symmetric and skew-symmetric components, we assess the contribution of a vector field's potential and rotational components to the stability of differential Nash equilibria. Our results show that in zero-sum games, all Nash are stable and robust; in potential games, all stable points are Nash. For general-sum games, we provide a sufficient condition for instability. We conclude with a numerical example in which learning with timescale separation results in faster convergence.

cs.GT↗