In this paper, we propose a computationally efficient quadratic programming (QP) approach for generating smooth, C1continuous paths for mobile robots using piece-wise quadratic Bezier (PWB) curves. Our method explicitly incorporates safety margins within a structured optimization framework, balancing trajectory smoothness and robustness with manageable numerical complexity suitable for real-time and embedded applications. Comparative simulations demonstrate clear advantages over traditional piece-wise linear (PWL) path planning methods, showing reduced trajectory deviations, enhanced robustness, and improved overall path quality. These benefits are validated through simulations using a Pure-Pursuit controller in representative scenarios, highlighting the practical effectiveness and scalability of our approach for safe navigation.

This paper presents a method for decomposing Linear Temporal Logic (LTL) specifications into independent parts based on structures recognized in their corresponding Büchi automata representations. The goal is to obtain a decomposition that allows the execution of the global mission by identifying and formalizing segments that can be executed concurrently by a team of mobile robots. We introduce formal concurrency characterization for two and three tasks, and provide a structured framework for recognizing these patterns within the automaton. The method algorithmically analyses an accepted run of the trimmed Büchi automaton, partitions it into containers of sequential and concurrent tasks, and incrementally extends this concurrency while reducing the number of synchronization points. Although the current formal framework supports up to three concurrent tasks, it may represent a step towards generalization.

This paper proposes an extension of an algorithm that decomposes a high-level specification into sub-formulas that are called tasks. The extension consists in enabling repetitive (non-terminating) behaviors expressed in Linear Temporal Logic (LTL), rather than only terminating ones, as the previous version of our method allowed. The LTL specification has the meaning of a global mission that must be accomplished by a team of mobile agents, while the decomposition ensures that the tasks can be executed independently by the robots, thus avoiding communications or synchronizations. An example is illustrating the presented work, while future research will be conducted towards inclusion of negations in formulas.

The Unmanned Aerial Vehicles (UAVs), commonly known as drones, are significant in the agriculture sphere to automate the work such as: data acquisition, crop spraying among others. This paper proposes a path planning solution for a team of UAVs that is required to whiten a greenhouse’s roof, this problem having both social-economic impact, as well as scientific-technical impact. First, the space around the roof is partitioned into cells based on a 3D cell decomposition technique, labeling the cells including the surface of the roof as regions of interest (ROIs). Based on this representation, a Petri net (PN) model captures the motion of drones, while their trajectories are returned by a Mixed Integer Linear Programming (MILP) problem which optimizes the energy consumption. An adaptable strategy is used such that the MILP problem considers only the available UAVs with enough energy to reach the ROIs. The algorithm is implemented in MATLAB and the simulation results are captured in a video link, evaluating the impact of the size of the team and the precision used for mapping the environment over the running time.

We consider the problem of obtaining independent trajectories for robots from a team, such that their movement satisfies a global co-safe Linear Temporal Logic (LTL) mission over some regions of interest from the environment. For this, the environment is abstracted into a discrete event system using an underlying partition and an available method is used for decomposing the LTL formula into more parts that can be independently satisfied by a robot. Then, we translate these parts into a conjunction of Boolean formulas and use another approach for planning a team based on Boolean specifications and Petri net models. The proposed combination among the two methods yields independent robot trajectories that are optimal with respect to the number of traversed cells from the partition. The advantages are also illustrated through simulation examples.

In recent years, quadcopters have become popular research platforms in the fields of robotics and control engineering. As a response to the academic community's needs, several open-source hardware and software platforms have emerged with the aim to impose as de-facto development tools. One of these platforms is represented by Crazyflie 2.0, a nano class quadcopter that was used in research projects that span from control architecture designs to high-level swarm synchronization.This paper presents a study of the control architecture employed in the stock firmware. Based on the mathematical model, the dynamic behaviour is thoroughly evaluated to understand the deviation between ideal and real evolution. A comprehensive phase of parameters tuning is conducted and multiple scenarios for real-time testing are employed. These scenarios comply in tracking predefined patterns, the quadcopter's evolution being tracked via a RGB-D sensor.The proposed evaluation procedure can be easily replicated and represents a very important step in obtaining accurate real-time results.

During the last few years, the field of micro aerial vehicles (drones) has encountered a significant focus among the robotics research community. Autonomous maneuvering for indoor environments is highly challenging on one hand due to space topology that can include different storage facilities, and on the other hand due to need for optimal planning that saves drone battery and task accomplishment time. In this paper we study a type of vehicle routing problem applied to an indoor warehouse. In particular, some goods should be transported from storage areas to delivery areas by limited energy drones with finite capacities for transporting goods. The presentation includes a planning solution based on mathematical programming and presents supporting simulations and real-time experiments.

This paper considers the path-planning problem in discretized environments, obtained for example by a cell decomposition approach. The specification for the mobile robot can be the classical navigation problem (reach a given region by avoiding the obstacles) or a high-level specification as a Boolean and/or temporal logic formula. We propose a general methodology to compute piecewise linear trajectories consisting in a sequence of intermediate points (waypoints). The waypoints are computed by solving optimization problems whose solutions permit to optimally select the intermediate points on the common facets of traversed cells from the decomposition. The proposed solution is similar to a Model Predictive Control (MPC) strategy, in each step an optimization problem is solved over a finite horizon, the first action is considered and the problem is iterated. The method developed in this paper has been implemented and integrated in Robot Motion Toolbox allowing a comparison with other methods by simulation.

This research proposes a centralized method for planning and monitoring the motion of one or a few mobile robots in an environment where regions of interest appear and disappear based on exponential probability density functions. The motion task is given as a linear temporal logic formula over the set of regions of interest. The solution determines robotic trajectories and updates them whenever necessary, such that the task is most likely to be satisfied with respect to probabilistic information on regions. The robots' movement capabilities are abstracted to finite state descriptions, and operations as product automata and graph searches are used in the provided solution. The approach builds up on temporal logic control strategies for static environments by incorporating probabilistic information and by designing an execution monitoring strategy that reacts to actual region observations yielded by robots. Several simulations are included, and a software implementation of the solution is available. The computational complexity of our approach increases exponentially when more robots are considered, and we mention a possible solution to reduce the computational complexity by fusing regions with identical observations.

This paper proposes a solution for solving a specific problem that requires a team of identical robots to collect in a specific order different types of resources scattered throughout an environment. A Petri net with outputs models the environment, the team possible movements and the regions with resources. An iterative solution plans the team such that each robot collects and assembles resources in the required order. Each iteration step is based on a linear programming problem that is guaranteed to return a feasible firing vector for the Petri net system. A pseudocode description of the procedure is given and a simulation example is included.

This paper provides a strategy for supervising the motion of some mobile robots that evolve in the same environment. Some regions of the environment are assumed to have a limited capacity in terms of the number of robots that can simultaneously occupy them, and a set of possible trajectories is available for each robot. The solution comprises the construction of a specific Petri net model for the available trajectories, and the use of resource-allocation techniques based on restricted-capacity regions and on deadlock-free execution.

The paper presents a procedure for planning and controlling a team of identical mobile robots such that a set of target regions are reached. We consider a partitioned environment cluttered with a set of obstacles that randomly change their positions. Our approach abstracts both the control capabilities of robots and the information on obstacle locations into probabilistic discrete Petri net models, and it uses an online algorithm for planning and adjusting the sequences of regions the robots should traverse. At each iteration of the online algorithm we solve a linear programming problem that optimizes the robot paths by weighting the probabilities of following a sequence of partition regions and the steady-state probabilities of encountering obstacles along the resulted sequences. The approach is implemented as a fully automated Matlab package.

The paper presents a procedure for creating a probabilistic finite-state model for a mobile robot and for finding a sequence of controllers ensuring the highest probability for reaching a desired region. The approach starts by using results for controlling affine systems in simpliceal partitions, and then it creates a finite representation with history-based probabilities on transition. This representation is embedded into a Petri Net model with probabilistic costs on transitions, and a highest probability path to reach a target region is found. This probabilistic framework is suitable for controlling mobile robots based on more complex specifications.

We revisit the problem of automatic deployment of robotic teams from temporal logic specifications over regions of interests in the environment. In our previous work, we developed an algorithm that could accommodate arbitrary communication constraints, but had two main limitations: (1) it only allowed for communicating robots to move, and (2) it was computationally very expensive. In this paper, we present two approaches to address these limitations. First, we show that if identical robots are allowed to communicate for all times, then the computation is cheaper. Second, we develop an algorithm to test if a given global specification can be implemented by the robots without the move-only-when-communicate constraint.

In this paper, we develop an automated framework for formal verification of timed continuous Petri nets (ContPNs). Specifically, we consider two problems: (1) given an initial set of markings, construct a set of unreachable markings and (2) given a Linear Temporal Logic (LTL) formula over a set of linear predicates in the marking space, construct a set of initial states such that all trajectories originating there satisfy the LTL specification. The starting point for our approach is the observation that a ContPN system can be expressed as a Piecewise Affine (PWA) system with a polyhedral partition. We propose an iterative method for analysis of PWA systems from specifications given as LTL formulas over linear predicates. The computation mainly consists of polyhedral operations and searches on graphs, and the developed framework was implemented as a freely downloadable software tool. We present several illustrative numerical examples.

We present a computational framework for automatic synthesis of decentralized communication and control strategies for a robotic team from global specifications, which are given as temporal and logic statements about visiting regions of interest in a partitioned environment. We consider a purely discrete scenario, where the robots move among the vertices of a graph. However, by employing recent results on invariance and facet reachability for dynamical systems in environments with polyhedral partitions, the framework from this paper can be directly implemented for robots with continuous dynamics. While allowing for a rich specification language and guaranteeing the correctness of the solution, our approach is conservative in the sense that we might not find a solution, even if one exists. The overall amount of required computation is large. However, most of it is performed offline before the deployment. Illustrative simulations and experimental results are included.

We present a computational framework and experimental setup for deployment of autonomous cars in a miniature Robotic Urban-Like Environment (RULE). The specifications are given in rich, human-like language as temporal logic statements about roads, intersections, and parking spaces. We use transition systems to model the motion and sensing capabilities of the robots and the topology of the environment and use tools resembling model checking to generate robot control strategies and to verify the correctness of the solution. The experimental setup is based on Khepera III robots, which move autonomously on streets while observing traffic rules.

We present a computational framework for automatic synthesis of decentralized communication and control strategies for a robotic team from global specifications given as temporal and logic statements about visiting regions of interest in a partitioned environment. We consider a purely discrete scenario where the robots move among the vertices of a graph. However, by employing recent results on invariance and facet reachability for dynamical system in environments with polyhedral partitions, the framework from this paper can be directly implemented for robots with nontrivial dynamics. While providing a rich specification language and guaranteeing the correctness of the solution, our approach is conservative, in the sense that we might not find a solution even if one exists. The overall amount of required computation is large. However, most of it is performed off-line before the deployment.

We study the problem of designing control strategies for non-deterministic transitions systems enforcing the satisfaction of linear temporal logic (LTL) formulas over their set of states. We focus on finite transition systems with inputs, which are often encountered when solving motion planning problems by using discrete quotients induced by a given partition of the state space. Our approach solves the problem conservatively using LTL games, and consists of the following three steps: (1) the original transition system is transformed into a transition system on which an LTL game can be played, (2) a solution of the LTL game on the new transition system is obtained, and (3) an interface between this solution and the initial transition system is constructed. The correctness of the method is ensured by design. The advantages and conservativeness of our approach are discussed and illustrated by simple examples.

We develop a hierarchical framework for planning and control of arbitrarily large groups (swarms) of fully actuated robots with polyhedral velocity bounds moving in polygonal environments with polygonal obstacles. At the first level of hierarchy, we aggregate the high-dimensional control system of the swarm into a small-dimensional control system capturing its essential features. These features describe the position of the swarm in the world and its size. At the second level, we reduce the problem of controlling the essential features of the swarm to a model-checking problem. In the obtained hierarchical framework, high-level specifications given in natural language, such as linear temporal logic formulas over linear predicates in the essential features, are automatically mapped to provably correct robot control laws. For the particular case of an abstraction based on centroid and variance, we show that swarm cohesion, interrobot collision avoidance, and environment containment can also be specified and automatically guaranteed in our framework. The obtained communication architecture is centralized.

We develop a hierarchical framework for planning and control of arbitrarily large groups of fully actuated robots with polyhedral velocity bounds (swarm) moving in polygonal environments with polygonal obstacles. At the first level of hierarchy, we aggregate the high dimensional control system of the swarm into a small dimensional control system capturing its essential features. These features describe the position of the swarm in the world and its size. At the second level, we reduce the problem of controlling the essential features of the swarm to a model checking problem. In the obtained hierarchical framework, high level specifications given in natural language such as linear temporal logic formulas over linear predicates in the essential features are automatically mapped to probably correct robot control laws

We present a computational framework for automatic deployment of robots in 2D and 3D rectangular environments with polytopal obstacles. The results are derived for polytopal robots that can only translate with velocities restricted to polyhedral sets. Our approach consists of three steps: (1) constructing a discrete representation of the problem by using hierarchical partitions in the form of quad-trees and oct-trees, (2) planning the motion in the finite dimensional quotient produced by the partition, and (3) generating provably correct robot feedback control laws by constructing a hybrid system. Given the environment and robot geometry and constraints, generation of control laws is completely automated. The computation consists of polyhedral operations and searches on graphs