Consensus-based Distributed 3D Pose Estimation with Noisy Relative Measurements

In this paper we study consensus-based tributed estimation algorithms for estimating the global translation and rotation of each agent in a multi-agent system. We consider the case in which agents measure the noisy relative pose of their neighbors and communicate their estimates to agree upon the global poses in an arbitrary reference frame. The main contribution of this paper is a formal analysis that provides necessary and sufficient conditions to guarantee stability (in a Lyapunov sense) of the estimation system''s equilibria. We prove that consensus-based algorithms will diverge, even with arbitrarily small inconsistencies on the relative pose, unless the measurements satisfy minimum consistency conditions. We determine these consistency conditions for translation-only, rotation-only, and combined 3D pose estimation using the axis-angle rotation representation over undirected graphs. We then propose an initialization method based on these conditions that guarantees consistency and stability of the estimator''s equilibria. Additionally, we show that existing distributed estimation methods in literature exploit these conditions to guarantee convergence of their algorithms. Lastly, we perform simulations that show convergence when consistency conditions hold and divergence when they do not

Optimal role and position assignment in multi-robot freely reachable formations

Many multi-robot problems require the achievement of formations as part of the overall mission. This work considers a scenario in which unlabeled homogeneous robots must adopt a given formation pattern buildable anywhere in the environment. This involves finding the relative pose of the formation in regard to the initial robot positions, understood as a translation and a rotation; and the optimal assignment of the role of each robot within the formation. This paper provides an optimal solution for the combined parameters of translation, rotation and assignment that minimizes total displacement. To achieve this objective we first formally prove that the three decision variables are separable. Since computing the optimal assignment without accounting for the rotation is a computationally expensive problem, we propose an algorithm that efficiently computes the optimal roles together with the rotation. The algorithm is provably correct and finds the optimal solution in finite time. A distributed implementation is also discussed. Simulation results characterize the complexity of our solution and demonstrate its effectiveness

Distributed Dynamic Sensor Assignment of Multiple Mobile Targets

Distributed scalable algorithms are sought in many multi-robot contexts. In this work we address the dynamic optimal linear assignment problem, exemplified as a target tracking mission in which mobile robots visually track mobile targets in a one-to-one capacity. We adapt our previous work on formation achievement by means of a distributed simplex variant, which results in a conceptually simple consensus solution, asynchronous in nature and requiring only local broadcast communications. This approach seamlessly tackles dynamic changes in both costs and network topology. Improvements designed to accelerate the global convergence in the face of dynamically evolving task rewards are described and evaluated with simulations that highlight the efficiency and scalability of the proposal. Experiments with a team of three Turtlebot robots are finally shown to validate the applicability of the algorithm

A Real-Time Game Theoretic Planner for Autonomous Two-Player Drone Racing

In this article, we propose an online 3-D planning algorithm for a drone to race competitively against a single adversary drone. The algorithm computes an approximation of the Nash equilibrium in the joint space of trajectories of the two drones at each time step, and proceeds in a receding horizon fashion. The algorithm uses a novel sensitivity term, within an iterative best response computational scheme, to approximate the amount by which the adversary will yield to the ego drone to avoid a collision. This leads to racing trajectories that are more competitive than without the sensitivity term. We prove that the fixed point of this sensitivity enhanced iterative best response satisfies the first-order optimality conditions of a Nash equilibrium. We present results of a simulation study of races with 2-D and 3-D race courses, showing that our game theoretic planner significantly outperforms amodel predictive control (MPC) racing algorithm. We also present results of multiple drone racing experiments on a 3-D track in which drones sense each others'' relative position with onboard vision. The proposed game theoretic planner again outperforms the MPC opponent in these experiments where drones reach speeds up to 1.25m/s

Accelerated Multi-Stage Discrete Time Dynamic Average Consensus

This paper presents a novel solution for the discrete time dynamic average consensus problem. Given a set of time-varying input signals over the nodes of an undirected graph, the proposed algorithm tracks, at each node, the input signals’ average. The algorithm is based on a sequence of consensus stages combined with a second order diffusive protocol. The former overcomes the need of k-th order differences of the inputs and conservation of the network state average, while the latter overcomes the trade-off between speed and accuracy of the consensus stages by just storing the previous estimate at each node. The result is a protocol that is fast, arbitrarily accurate, and robust against input noises and initializations. The protocol is extended to an asynchronous and randomized version that follows a gossiping scheme that is robust against potential delays and packet losses. We study the convergence properties of the algorithms and validate them via simulations

Human-computer interaction based on hand gestures using RGB-D sensors

In this paper we present a new method for hand gesture recognition based on an RGB-D sensor. The proposed approach takes advantage of depth information to cope with the most common problems of traditional video-based hand segmentation methods: cluttered backgrounds and occlusions. The algorithm also uses colour and semantic information to accurately identify any number of hands present in the image. Ten different static hand gestures are recognised, including all different combinations of spread fingers. Additionally, movements of an open hand are followed and 6 dynamic gestures are identified. The main advantage of our approach is the freedom of the user’s hands to be at any position of the image without the need of wearing any specific clothing or additional devices. Besides, the whole method can be executed without any initial training or calibration. Experiments carried out with different users and in different environments prove the accuracy and robustness of the method which, additionally, can be run in real-time

Cooperative Periodic Coverage With Collision Avoidance

In this paper, we propose a periodic solution to the problem of persistently covering a finite set of interest points with a group of autonomous mobile agents. These agents visit periodically the points and spend some time carrying out the coverage task, which we call coverage time. Since this periodic persistent coverage problem is NP-hard, we split it into three subproblems to counteract its complexity. In the first place, we plan individual closed paths for the agents to cover all the points. Second, we formulate a quadratically constrained linear program to find the optimal coverage times and actions that satisfy the coverage objective. Finally, we join together the individual plans of the agents in a periodic team plan by obtaining a schedule that guarantees collision avoidance. To this end, we solve a mixed-integer linear program that minimizes the time in which two or more agents move at the same time. Eventually, we apply the proposed solution to an induction hob with mobile inductors for a domestic heating application and show its performance with experiments on a real prototype. IEE

Path planning of multirobot systems using Petri net models. Results and open problems

[EN] This paper presents a trajectory planning approach in multirobot systems based on Petri net models. This type of models is very useful for high-level specifications since, in this case, the classical planning methods (potential functions, RRT algorithms, RRT*) cannot be used being dicult to determine a priori the sequence of configurations for each robot. This work presents the formal definition of the Robot Motion Petri net t hat i s obtained from a partition of the environment in cells. Using the s tructure of the Petri net, in case of specifications defined as Boolean or Linear Temporal Logic (LTL) formulas, dierent optimization problems are presented that can be used to obtain trajectories for robots. The main advantage of models based on Petri nets is their scalability with respect to the number of robots. This makes it possible to reciently solve planning problems with a large number of robots. In the second part of the paper, some extensions and new results for distributed planning in unknown environments and with partial communications between robots are presented.[ES] Este trabajo presenta una estrategia de planificacón de trayectorias en equipos de robots moviles basada en el uso de modelos definidos con redes de Petri. Estos tipos de modelos son muy útiles para especificaciones de alto nivel ya que, en este caso, los métodos clásicos de planificación (funciones potenciales, algoritmos RRT, RRT*) no se pueden utilizar, siendo difícil determinar a priori la secuencia de configuraciones para cada robot. Este trabajo presenta la definición formal de la Red de Petri de Movimiento de Robots que se obtiene a partir de una partición del entorno en celdas. Utilizando la estructura de la red de Petri, en caso de especificaciones definidas como fórmulas Booleanas o fórmulas en lógica temporal lineal (LTL), se presentan diferentes problemas de optimización que se pueden utilizar para obtener trayectorias para los robots. La principal ventaja de los modelos basados en redes de Petri es su escalabilidad con respecto al número de robots. Ello permite resolver con eficiencia problemas de planificación de equipos con un número grande de robots. En la segunda parte del trabajo, se presentan algunas extensiones y resultados nuevos para la planificación distribuida en entornos desconocidos y con comunicaciones parciales entre los robots.Los resultados de esta línea de investigación son fruto de la participación de varios compañeros, investigadores de la Universidad de Zaragoza y de otras Universidades extranjeras. Queremos agradecer la participación de todos ellos, mencionando muy especialmente a Marius Kloetzer (profesor de la Universidad Técnica de Iasi, Rumanía). Este trabajo ha sido financiado parcialmente por los proyectos PGC2018-098719-B-I00 and PGC2018-098817-A-I00 (MCIU/AEI/FEDER, UE) y la ONR Global NICOP grant N62909-19-1-2027.Mahulea, C.; González, R.; Montijano, E.; Silva, M. (2020). Planificación de trayectorias en sistemas multirobot utilizando redes de Petri. Resultados y problemas abiertos. Revista Iberoamericana de Automática e Informática industrial. 18(1):19-31. https://doi.org/10.4995/riai.2020.13785OJS1931181Baier, C., Katoen, J.P., 2008. Principles of model checking. MIT Press.Belta, C., Bicchi, A., Egerstedt, M., Frazzoli, E., Klavins, E., Pappas, G.-J., 2007. Symbolic planning and control of robot motion. IEEE Robotics and Automation Magazine 14 (1), 61-71. https://doi.org/10.1109/MRA.2007.339624Belta, C., Habets, L., 2006. Controlling a class of nonlinear systems on rectangles. IEEE Transactions on Automatic Control 51 (11), 1749-1759. https://doi.org/10.1109/TAC.2006.884957Brown, F., 2012. Boolean Reasoning: The Logic of Boolean Equations, 2nd Edition. Dover Publications.Castellanos, J. G., Cervantes, M. V., Santana, J. S., Martínez, S. R., 2014. Seguimiento de trayectorias de un robot movil (3,0) mediante control acotado. Rev. Iberoamericana de Automatica e Informática industrial 11 (4), 426-434. https://doi.org/10.1016/j.riai.2014.09.005Choset, H., Lynch, K. M., Hutchinson, S., Kantor, G., Burgard, W., Kavraki, L. E., Thrun, S., 2005. Principles of Robot Motion: Theory, Algorithms, and Implementations. MIT Press, Boston.Clarke, E.-M.-M., Peled, D., Grumberg, O., 1999. Model checking. MIT Press.DeCastro, J., Ehlers, R., Runggers, M., Balkan, A., Kress-Gazit, H., 2016. Automated generation of dynamics-based runtime certificates for high-level control. Discrete Event Dynamic Systems 27 (2), 371-405. https://doi.org/10.1007/s10626-016-0232-7Ding, X., Smith, S.-L., Belta, C., Rus, D., 2014. Optimal control of Markov decision processes with linear temporal logic constraints. IEEE Transactions on Automatic Control 59 (5), 1244-1257. https://doi.org/10.1109/TAC.2014.2298143Duret-Lutz, A., Lewkowicz, A., Fauchille, A., Michaud, T., Renault, E., Xu, L., 2016. Spot 2.0 - a framework for ltl and ω-automata manipulation. In: Proc. of ATVA'16. pp. 122-129. https://doi.org/10.1007/978-3-319-46520-3_8Fainekos, G. E., Girard, A., Kress-Gazit, H., Pappas, G. J., 2009. Temporal logic motion planning for dynamic robots. Automatica 45 (2), 343-352. https://doi.org/10.1016/j.automatica.2008.08.008Garrido, S., Moreno, L., Gomez, J.-V., Lima, P.-U., 2013. International Journal ' of Advanced Robotic Systems 10 (1), 64. https://doi.org/10.5772/53999Gastin, P., Oddoux, D., 2001. Fast ltl to buchi automata translation. In: Proc. of the 13th Conference on Computer Aided Verification (CAV). pp. 53-65. https://doi.org/10.1007/3-540-44585-4_6Gonzalez, R., Mahulea, C., Kloetzer, M., 2015. A Matlab-Based Interactive Simulator for Mobile Robotics. In: IEEE CASE'2015: Int. Conf. on Autom. Science and Engineering. Gothenburg, Sweden, pp. 310-315. https://doi.org/10.1109/CoASE.2015.7294097Gonzalez, R., Rodriguez, F., Guzman, J. L., 2014. Autonomous Tracked Robots in Planar Off-Road Conditions. Modelling, Localization and Motion Control. Series: Studies in Systems, Decision and Control. Springer. https://doi.org/10.1007/978-3-319-06038-5Guo, M., Dimarogonas, D.-V., 2015. Multi-agent plan reconfiguration under local LTL specifications. Int. Journal of Robotics Research 34 (2), 218-235. https://doi.org/10.1177/0278364914546174Habets, L. C. G. J. M., Collins, P. J., van Schuppen, J. H., 2006. Reachability and control synthesis for piecewise-affine hybrid systems on simplices. IEEE Transactions on Automatic Control 51, 938-948. https://doi.org/10.1109/TAC.2006.876952Julian, B.-J., Angermann, M., Schwager, M., Rus, D., 2012. Distributed robotic sensor networks: An information-theoretic approach. The International Journal of Robotics Research 31 (10), 1134-1154. https://doi.org/10.1177/0278364912452675Kloetzer, M., Mahulea, C., 2014. A Petri net based approach for multi-robot path planning. Discrete Event Dynamic Systems: Theory and Applications 24 (4), 417-445. https://doi.org/10.1007/s10626-013-0162-6Kloetzer, M., Mahulea, C., 2014. An assembly problem with mobile robots. In: ETFA'2014: IEEE Emerging Technology and Factory Automation. pp. 1-7. https://doi.org/10.1109/ETFA.2014.7005116Kloetzer, M., Mahulea, C., 2015. LTL-based planning in environments with probabilistic observations. IEEE Transactions on Automation Science and Engineering 12 (4), 1407-1420. https://doi.org/10.1109/TASE.2015.2454299Kloetzer, M., Mahulea, C., 2020. Path planning for robotic teams based on LTL specifications and Petri net models. Discrete Event Dynamic Systems: Theory and Applications 30 (1), 55-79. https://doi.org/10.1007/s10626-019-00300-1Lacerda, B., Lima, P. U., 2019. Petri net based multi-robot task coordination from temporal logic specifications. Robotics and Autonomous Systems 122, 343-352. https://doi.org/10.1016/j.robot.2019.103289LaValle, S. M., 2006. Planning Algorithms. Cambridge, available at http://planning.cs.uiuc.edu. https://doi.org/10.1017/CBO9780511546877Leahy, K., Cristofalo, E., Vasile, C.-I., Jones, A., Montijano, E., Schwager, M., Belta, C., 2019. Control in belief space with temporal logic specifications using vision-based localization. The International Journal of Robotics Research 38 (6), 702-722. https://doi.org/10.1177/0278364919846340Mahulea, C., Kloetzer, M., 2018. Robot Planning based on Boolean Specifications using Petri Net Models. IEEE Trans. on Automatic Control 63 (7), 2218-2225. https://doi.org/10.1109/TAC.2017.2760249Mahulea, C., Kloetzer, M., Gonzalez, R., 2020a. Path Planning of Cooperative ' Mobile Robots Using Discrete Event Models. IEEE Wiley. https://doi.org/10.1002/9781119486305Mahulea, C., Kloetzer, M., Lesage, J.-J., 2020b. Multi-robot path planning with boolean specifications and collision avoidance. In: WODES'2020: 15th Workshop on Discrete Event Systems.Mahulea, C., Montijano, E., Kloetzer, M., 2020c. Distributed Multirobot Path Planning in Unknown Maps Using Petri Net Models. IFACPapersOnLine21th IFAC World Congress.Mesbahi, M., Egerstedt, M., 2010. Graph theoretic methods in multiagent networks. Princeton University Press. https://doi.org/10.1515/9781400835355Montijano, E., Montijano, J.-I., Sagues, C., Feb 2013. Chebyshev polynomials in distributed consensus applications. 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Intelligent control of temperature with dynamic voltage-frequency scaling (DVFS) in embedded processors

[EN] The increment in computing power of embedded processors has fueled a revolution in many application domains such as mobile computing or robotics. Dissipating the energy consumed by those processors on a very small area has made power management a first-order constraint. On one hand, it is impossible to directly apply active dissipation techniques. On the other hand, design requirements prevent the correct behaviour of known passive detection techniques. To alleviate this problem, we present a new control approach to keep the temperature of the system controlled through the Dynamic Voltage and Frequency Scaling (DVFS) system. The solution includes a feedback control scheme together with a supervisor that adjusts the control parameters based on the system load. To ease experimentation without compromising real use, the code can run in user space and as a Linux kernel driver. The experiments in a real platform prove that, compared to the current control methodology, our approach handles the processor’s temperature with more precision, keeping similar performance levels in the execution of well known benchmarks.[ES] El aumento de la capacidad de cálculo de los procesadores embebidos ha generado una revolución en numerosos dominios de aplicación como la computación móvil o la robótica. La disipación del consumo producido por estos cálculos en una superficie tan pequeña hace que la disipación de energía suponga un problema de primer orden. Por un lado, no es posible aplicar técnicas de disipación activas y, por otro, las exigencias de diseño impiden una correcta disipación pasiva. Para resolver este problema, este trabajo presenta una metodología de control para el mantenimiento de una temperatura bajo control mediante el uso de escalado dinámico de la frecuencia del procesador (DVFS, Dynamic Voltage Frequency Scaling). La solución incluye un esquema de control de temperatura basado en realimentación junto con un supervisor que ajusta los parámetros del controlador en base al tipo de carga del trabajo. La estrategia de control propuesta se ha implementado tanto en espacio de usuario como driver dentro del kernel de Linux. Los experimentos realizados en una plataforma real demuestran que, comparado con el control existente en la actualidad, nuestra propuesta es capaz de gestionar la temperatura del procesador con más precisión, manteniendo niveles similares de eficiencia en la ejecución de benchmarks conocidos.Este artículo ha sido financiado parcialmente por los proyectos PGC2018-098817-A-I00 (MCIU/AEI/FEDER, UE), MIG20201006, PID2019-105660RB-C21 ( MINECO/AEI/FEDER), Grupos T58 20R y T45 20R ( Gobierno de Aragón) y FEDER 2014-2020 “Construyendo Europa desde Aragón”. Los autores agradecen el apoyo recibido.Hernández-Almudi, P.; Suárez, D.; Montijano, E.; Merino, J. (2021). Control inteligente mediante escalado dinámico voltaje-frecuencia (DVFS) de la temperatura en procesadores embebidos. Revista Iberoamericana de Automática e Informática industrial. 18(4):396-406. https://doi.org/10.4995/riai.2021.14200OJS396406184Alastruey,J.,Briz,J.L.,Ibanez,P.,Vinals,V.,2006. Software demand,hardware supply. IEEE Micro 26, 72-82. https://doi.org/10.1109/MM.2006.80arm, . Workload automation. URL: https://github.com/ARM-software/workload-automation.Brooks, D., Martonosi, M., 2001. Dynamic thermal management for highperformance microprocessors, in: Proceedings HPCA Seventh International Symposium on High-Performance Computer Architecture, IEEE. pp. 171- 182.Canonical, . Stress-ng. URL: https://wiki.ubuntu.com/Kernel/Reference/stress-ng.Chen, H., Han, Y., Tang, G., Zhang, X., 2020. A dynamic control system for server processor direct liquid cooling. 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An Experimental Study of Robust Distributed Multi-Robot Data Association from Arbitrary Poses

2014 International Symposium on Experimental Robotics (ISER 2014), June 15–18, 2014, Morocco.In this work, we experimentally investigate the problem of computing the relative transformation between multiple vehicles from corresponding interrobot observations during autonomous operation in a common unknown environment. Building on our prior work, we consider an EM-based methodology which evaluates sensory observations gathered over vehicle trajectories to establish robust relative pose transformations between robots. We focus on experimentally evaluating the performance of the approach as well as its computational complexity and shared data requirements using multiple autonomous vehicles (aerial robots). We describe an observation subsampling technique which utilizes laser scan autocovariance to reduce the total number of observations shared between robots. Employing this technique reduces run time of the algorithm significantly, while only slightly diminishing the accuracies of computed inter-robot transformations. Finally, we provide discussion on data transfer and the feasibility of implementing the approach on a mesh network