arXiv subjects

Derya Aksaray

Publications and source records attributed to Derya Aksaray.

At least 19 recordsLinked to original sources

arXiv2026

Specification-Aware Distribution Shaping for Robotics Foundation Models

Robotics foundation models have demonstrated strong capabilities in executing natural language instructions across diverse tasks and environments. However, they remain largely data-driven and lack formal guarantees on safety and satisfaction of time-dependent specifications during deployment. In practice, robots often need to comply with operational constraints involving rich spatio-temporal requirements such as time-bounded goal visits, sequential objectives, and persistent safety conditions. In this work, we propose a specification-aware action distribution optimization framework that enforces a broad class of Signal Temporal Logic (STL) constraints during execution of a pretrained robotics foundation model without modifying its parameters. At each decision step, the method computes a minimally modified action distribution that satisfies a hard STL feasibility constraint by reasoning over the remaining horizon using forward dynamics propagation. We validate the proposed framework in simulation using a state-of-the-art robotics foundation model across multiple environments and complex specifications.

cs.RO↗

arXiv2026

Contingency-Aware Planning via Certified Neural Hamilton-Jacobi Reachability

Hamilton-Jacobi (HJ) reachability provides formal safety guarantees for dynamical systems, but solving high-dimensional HJ partial differential equations limits its use in real-time planning. This paper presents a contingency-aware multi-goal navigation framework that integrates learning-based reachability with sampling-based planning in unknown environments. We use Fourier Neural Operator (FNO) to approximate the solution operator of the Hamilton-Jacobi-Isaacs variational inequality under varying obstacle configurations. We first provide a theoretical under-approximation guarantee on the safe backward reach-avoid set, which enables formal safety certification of the learned reachable sets. Then, we integrate the certified reachable sets with an incremental multi-goal planner, which enforces reachable-set constraints and a recovery policy that guarantees finite-time return to a safe region. Overall, we demonstrate that the proposed framework achieves asymptotically optimal navigation with provable contingency behavior, and validate its performance through real-time deployment on KUKA's youBot in Webots simulation.

cs.RO↗

arXiv2026

Shielded Reinforcement Learning Under Dynamic Temporal Logic Constraints

Reinforcement Learning (RL) has shown promise in various robotics applications, yet its deployment on real systems is still limited due to safety and operational constraints. The safe RL field has gained considerable attention in recent years, which focuses on imposing safety constraints throughout the learning process. However, real systems often require more complex constraints than just safety, such as periodic recharging or time-bounded visits to specific regions. Imposing such spatio-temporal tasks during learning still remains a challenge. Signal Temporal Logic (STL) is a formal language for specifying temporal properties of real-valued signals and provides a way to express such complex tasks. In this paper, we propose a framework that leverages sequential control barrier functions and model-free RL to ensure that the given STL tasks are satisfied throughout the learning process. Our method extends beyond traditional safety constraints by enforcing rich STL specifications, which can involve visits to dynamic targets with unknown trajectories. We also demonstrate the effectiveness of our framework through various simulations.

cs.RO↗

arXiv2026

Temporal-Logic-Aware Frontier-Based Exploration

This paper addresses the problem of temporal logic motion planning for an autonomous robot operating in an unknown environment. The objective is to enable the robot to satisfy a syntactically co-safe Linear Temporal Logic (scLTL) specification when the exact locations of the desired labels are not known a priori. We introduce a new type of automaton state, referred to as commit states. These states capture intermediate task progress resulting from actions whose consequences are irreversible. In other words, certain future paths to satisfaction become not feasible after taking those actions that lead to the commit states. By leveraging commit states, we propose a sound and complete frontier-based exploration algorithm that strategically guides the robot to make progress toward the task while preserving all possible ways of satisfying it. The efficacy of the proposed method is validated through simulations.

cs.RO↗

arXiv2025

Motion Planning Under Temporal Logic Specifications In Semantically Unknown Environments

This paper addresses a motion planning problem to achieve spatio-temporal-logical tasks, expressed by syntactically co-safe linear temporal logic specifications (scLTL\next), in uncertain environments. Here, the uncertainty is modeled as some probabilistic knowledge on the semantic labels of the environment. For example, the task is "first go to region 1, then go to region 2"; however, the exact locations of regions 1 and 2 are not known a priori, instead a probabilistic belief is available. We propose a novel automata-theoretic approach, where a special product automaton is constructed to capture the uncertainty related to semantic labels, and a reward function is designed for each edge of this product automaton. The proposed algorithm utilizes value iteration for online replanning. We show some theoretical results and present some simulations/experiments to demonstrate the efficacy of the proposed approach.

cs.RO↗

arXiv2024

Probabilistic Satisfaction of Temporal Logic Constraints in Reinforcement Learning via Adaptive Policy-Switching

Constrained Reinforcement Learning (CRL) is a subset of machine learning that introduces constraints into the traditional reinforcement learning (RL) framework. Unlike conventional RL which aims solely to maximize cumulative rewards, CRL incorporates additional constraints that represent specific mission requirements or limitations that the agent must comply with during the learning process. In this paper, we address a type of CRL problem where an agent aims to learn the optimal policy to maximize reward while ensuring a desired level of temporal logic constraint satisfaction throughout the learning process. We propose a novel framework that relies on switching between pure learning (reward maximization) and constraint satisfaction. This framework estimates the probability of constraint satisfaction based on earlier trials and properly adjusts the probability of switching between learning and constraint satisfaction policies. We theoretically validate the correctness of the proposed algorithm and demonstrate its performance through comprehensive simulations.

cs.AI↗

arXiv2023

Reinforcement Learning Under Probabilistic Spatio-Temporal Constraints with Time Windows

We propose an automata-theoretic approach for reinforcement learning (RL) under complex spatio-temporal constraints with time windows. The problem is formulated using a Markov decision process under a bounded temporal logic constraint. Different from existing RL methods that can eventually learn optimal policies satisfying such constraints, our proposed approach enforces a desired probability of constraint satisfaction throughout learning. This is achieved by translating the bounded temporal logic constraint into a total automaton and avoiding "unsafe" actions based on the available prior information regarding the transition probabilities, i.e., a pair of upper and lower bounds for each transition probability. We provide theoretical guarantees on the resulting probability of constraint satisfaction. We also provide numerical results in a scenario where a robot explores the environment to discover high-reward regions while fulfilling some periodic pick-up and delivery tasks that are encoded as temporal logic constraints.

cs.AI↗

arXiv2022

Temporal Relaxation of Signal Temporal Logic Specifications for Resilient Control Synthesis

We introduce a metric that can quantify the temporal relaxation of Signal Temporal Logic (STL) specifications and facilitate resilient control synthesis in the face of infeasibilities. The proposed metric quantifies a cumulative notion of relaxation among the subtasks, and minimizing it yields to structural changes in the original STL specification by i) modifying time-intervals, ii) removing subtasks entirely if needed. To this end, we formulate an optimal control problem that extracts state and input sequences by minimally violating the temporal requirements while achieving the desired predicates. We encode this problem in the form of a computationally efficient mixed-integer program. We show some theoretical results on the properties of the new metric. Finally, we present a case study of a robot that minimally violates the time constraints of desired tasks in the face of an infeasibility.

eess.SY↗

arXiv2022

Control Barrier Functions with Actuation Constraints under Signal Temporal Logic Specifications

We propose control barrier functions (CBFs) for a family of dynamical systems to satisfy a broad fragment of Signal Temporal Logic (STL) specifications, which may include subtasks with nested temporal operators or conflicting requirements (e.g., achieving multiple subtasks within the same time interval). The proposed CBFs take into account the actuation limits of the dynamical system as well as a feasible sequence of subtasks, and they define time-varying feasible sets of states the system must always stay inside. We show some theoretical results on the correctness of the proposed method. We illustrate the benefits of the proposed CBFs and compare their performance with the existing methods via simulations.

eess.SY↗

arXiv2021

Probabilistically Guaranteed Satisfaction of Temporal Logic Constraints During Reinforcement Learning

We propose a novel constrained reinforcement learning method for finding optimal policies in Markov Decision Processes while satisfying temporal logic constraints with a desired probability throughout the learning process. An automata-theoretic approach is proposed to ensure the probabilistic satisfaction of the constraint in each episode, which is different from penalizing violations to achieve constraint satisfaction after a sufficiently large number of episodes. The proposed approach is based on computing a lower bound on the probability of constraint satisfaction and adjusting the exploration behavior as needed. We present theoretical results on the probabilistic constraint satisfaction achieved by the proposed approach. We also numerically demonstrate the proposed idea in a drone scenario, where the constraint is to perform periodically arriving pick-up and delivery tasks and the objective is to fly over high-reward zones to simultaneously perform aerial monitoring.

cs.RO↗

arXiv2021

Distributed Planning for Serving Cooperative Tasks with Time Windows: A Game Theoretic Approach

We study distributed planning for multi-robot systems to provide optimal service to cooperative tasks that are distributed over space and time. Each task requires service by sufficiently many robots at the specified location within the specified time window. Tasks arrive over episodes and the robots try to maximize the total value of service in each episode by planning their own trajectories based on the specifications of incoming tasks. Robots are required to start and end each episode at their assigned stations in the environment. We present a game theoretic solution to this problem by mapping it to a game, where the action of each robot is its trajectory in an episode, and using a suitable learning algorithm to obtain optimal joint plans in a distributed manner. We present a systematic way to design minimal action sets (subsets of feasible trajectories) for robots based on the specifications of incoming tasks to facilitate fast learning. We then provide the performance guarantees for the cases where all the robots follow a best response or noisy best response algorithm to iteratively plan their trajectories. While the best response algorithm leads to a Nash equilibrium, the noisy best response algorithm leads to globally optimal joint plans with high probability. We show that the proposed game can in general have arbitrarily poor Nash equilibria, which makes the noisy best response algorithm preferable unless the task specifications are known to have some special structure. We also describe a family of special cases where all the equilibria are guaranteed to have bounded suboptimality. Simulations and experimental results are provided to demonstrate the proposed approach.

cs.RO↗

arXiv2021

Control Synthesis using Signal Temporal Logic Specifications with Integral and Derivative Predicates

In many applications, the integrals and derivatives of signals carry valuable information (e.g., cumulative success over a time window, the rate of change) regarding the behavior of the underlying system. In this paper, we extend the expressiveness of Signal Temporal Logic (STL) by introducing predicates that can define rich properties related to the integral and derivative of a signal. For control synthesis, the new predicates are encoded into mixed-integer linear inequalities and are used in the formulation of a mixed-integer linear program to find a trajectory that satisfies an STL specification. We discuss the benefits of using the new predicates and illustrate them in a case study showing the influence of the new predicates on the trajectories of an autonomous robot.

eess.SY↗

arXiv2020

Decentralized Safe Reactive Planning under TWTL Specifications

We investigate a multi-agent planning problem, where each agent aims to achieve an individual task while avoiding collisions with others. We assume that each agent's task is expressed as a Time-Window Temporal Logic (TWTL) specification defined over a 3D environment. We propose a decentralized receding horizon algorithm for online planning of trajectories. We show that when the environment is sufficiently connected, the resulting agent trajectories are always safe (collision-free) and lead to the satisfaction of the TWTL specifications or their finite temporal relaxations. Accordingly, deadlocks are always avoided and each agent is guaranteed to safely achieve its task with a finite time-delay in the worst case. Performance of the proposed algorithm is demonstrated via numerical simulations and experiments with quadrotors.

cs.RO↗

arXiv2020

Tractable Reinforcement Learning of Signal Temporal Logic Objectives

Signal temporal logic (STL) is an expressive language to specify time-bound real-world robotic tasks and safety specifications. Recently, there has been an interest in learning optimal policies to satisfy STL specifications via reinforcement learning (RL). Learning to satisfy STL specifications often needs a sufficient length of state history to compute reward and the next action. The need for history results in exponential state-space growth for the learning problem. Thus the learning problem becomes computationally intractable for most real-world applications. In this paper, we propose a compact means to capture state history in a new augmented state-space representation. An approximation to the objective (maximizing probability of satisfaction) is proposed and solved for in the new augmented state-space. We show the performance bound of the approximate solution and compare it with the solution of an existing technique via simulations.

cs.LG↗

arXiv2019

Distributed Path Planning for Executing Cooperative Tasks with Time Windows

We investigate the distributed planning of robot trajectories for optimal execution of cooperative tasks with time windows. In this setting, each task has a value and is completed if sufficiently many robots are simultaneously present at the necessary location within the specified time window. Tasks keep arriving periodically over cycles. The task specifications (required number of robots, location, time window, and value) are unknown a priori and the robots try to maximize the value of completed tasks by planning their own trajectories for the upcoming cycle based on their past observations in a distributed manner. Considering the recharging and maintenance needs, robots are required to start and end each cycle at their assigned stations located in the environment. We map this problem to a game theoretic formulation and maximize the collective performance through distributed learning. Some simulation results are also provided to demonstrate the performance of the proposed approach.

cs.RO↗

arXiv2019

Persistent Surveillance With Energy-Constrained UAVs and Mobile Charging Stations

We address the problem of achieving persistent surveillance over an environment by using energy-constrained unmanned aerial vehicles (UAVs), which are supported by unmanned ground vehicles (UGVs) serving as mobile charging stations. Specifically, we plan the trajectories of all vehicles and the charging schedule of UAVs to minimize the long-term maximum age, where age is defined as the time between two consecutive visits to regions of interest in a partitioned environment. We introduce a scalable planning strategy based on 1) creating UAV- UGV teams, 2) decomposing the environment into optimal partitions that can be covered by any of the teams in a single fuel cycle, 3) uniformly distributing the teams over a cyclic path traversing those partitions, and 4) having the UAVs in each team cover their current partition and be transported to the next partition while being recharged by the UGV. We show some results related to the safety and performance of the proposed strategy.

eess.SY↗

arXiv2016

Q-Learning for Robust Satisfaction of Signal Temporal Logic Specifications

This paper addresses the problem of learning optimal policies for satisfying signal temporal logic (STL) specifications by agents with unknown stochastic dynamics. The system is modeled as a Markov decision process, in which the states represent partitions of a continuous space and the transition probabilities are unknown. We formulate two synthesis problems where the desired STL specification is enforced by maximizing the probability of satisfaction, and the expected robustness degree, that is, a measure quantifying the quality of satisfaction. We discuss that Q-learning is not directly applicable to these problems because, based on the quantitative semantics of STL, the probability of satisfaction and expected robustness degree are not in the standard objective form of Q-learning. To resolve this issue, we propose an approximation of STL synthesis problems that can be solved via Q-learning, and we derive some performance bounds for the policies obtained by the approximate approach. The performance of the proposed method is demonstrated via simulations.

eess.SY↗

arXiv2016

Time Window Temporal Logic

This paper introduces time window temporal logic (TWTL), a rich expressivity language for describing various time bounded specifications. In particular, the syntax and semantics of TWTL enable the compact representation of serial tasks, which are typically seen in robotics and control applications. This paper also discusses the relaxation of TWTL formulae with respect to deadlines of tasks. Efficient automata-based frameworks to solve synthesis, verification and learning problems are also presented. The key ingredient to the presented solution is an algorithm to translate a TWTL formula to an annotated finite state automaton that encodes all possible temporal relaxations of the specification. Case studies illustrating the expressivity of the logic and the proposed algorithms are included.

cs.FL↗