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Reactive Trajectory Planning Methods for Formation Control and Localization of Multi-Robot System

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Research on multi-robot systems has flourished over the last decades with a number of theoretical and experimental results. A scenario that still motivates considerable research efforts is that of decentralized formation control of multiple mobile robots based on only local (onboard) sensing and communication, with the aim of deploying highly autonomous robot teams in ‘non-trivial’ environments (e.g., inside buildings, underwater, underground, or even in deep space) where centralized measuring/communication facilities (such as GPS) are not available.

The main basic problems when addressing decentralized (and sensor-based) formation control for multiple robots are two: formation control and relative localization. Formation control is the problem of devising control strategies for attaining some desired geometric arrangement in space (e.g., a target shape). Relative localization is the problem of estimating/recovering the robot relative poses from the available onboard sensor measurements (typically, distances or bearing angles). Once one is able to solve these two problems, much more complex tasks/missions become possible (e.g., exploration, patrolling, coverage, but also cooperative manipulation). It is interesting to note that the localization and formation control problems are intimately related: any formation controller needs availability of the robot relative poses which must be estimated/recovered from the sensor measurements by the localization module. However, the localization itself is a nonlinear estimation problem and, therefore, the motion/trajectory followed by the robots (i.e., the action imposed by the formation controller) has a strong impact in the performance/accuracy/convergence rate of the relative pose estimation. This tight loop between formation control and estimation (which is the multi-robot version of the classical “action/perception loop” in robotics) is both scientifically very interesting and practically very relevant (one needs to properly solve it for having the hope of deploying multi-robot teams in real-world conditions).

Over the last years, our team has given several contributions in this broad field: for instance, in [1] the formation control and localization problems have been addressed by resorting to rigidity theory assuming distance measurements, and a decentralized framework for maintaining rigidity over time has been proposed. While [1] has addressed the case of distance measurements, the works [3-6] have instead considered the case of bearing measurements, that is, unit vectors in 3D which are well representative of what onboard cameras can measure. Furthermore, as actual robotic platforms, we have strongly pushed towards the use of quadrotors UAVs (drones) for implementing and validating all the various theoretical and algorithmic contributions [1-6]. To this end, the drones available in our team have been equipped with onboard cameras and small PCs (with WiFi modules) for allowing an onboard processing of the information and communication via WiFi to the other drones in the group.


PhD Topic

All the activities described above are essentially local: they aim at obtaining the best control actions “right now” given the current state of the robot group, but they cannot reason about the future. However, since several years many modern control approaches for non-trivial robotics applications stress the importance of a proper trajectory planning for accomplishing a task in more robust and effective ways. Indeed, (reactive) trajectory planning allows to reason about the future consequences of local actions, to better take into account complex constraints (e.g., obstacle avoidance, limited actuation, sensing constraints), and, finally, to attain optimality w.r.t. a given criterion of interest (e.g., time, energy, control effort). While reactive trajectory planning approaches (or Model Predictive Control – MPC) have gained a lot of ground in the robotics field (one example for all, humanoid robotics), their use in the context of multi-robot formation control and localization is still quite limited. On the other hand, the complexity of controlling a multi-robot group in harsh environments (sensing constraints, limited actuation, limited communication, limited processing power, obstacle and self-collision avoidance, need to localize and estimate the group state during motion) would clearly call for the use of modern reactive trajectory planning approaches in order to better deal with the problems of formation control and localization in unstructured environments.

Our group has recently started several activities on the topic of online/reactive trajectory planning for aggressive flight of (single) quadrotor UAVs [7-10], and for optimal state estimation and execution robustness [11-13] (these latter also in collaboration with the CHORALE robotics group at Inria Sophia Antipolis). These activities show a very promising potential and demonstrate our good grasp on these topics, but, so far, they have not been applied to the specific context of multi-robot formation control/localization. This is not a trivial issue, since one has to address all the typical issues/sensing/communication constraints of multi-robots, as well as comply with the requirements of decentralization and scalability (i.e., ideally, each robot should be able to plan its own future trajectory by only exploiting sensed/communicated information from the closest neighbors).

Therefore, the goal of this PhD thesis is to close this gap and develop novel reactive trajectory planning algorithms tailored to the multi-robot case. The PhD activities will naturally leverage the strong internal competences on multi-robot control/optimal estimation and on trajectory planning, and will be performed in cooperation with Inria Sophia Antipolis (in particular P. Salaris as co-encadrant). The devised algorithms will be first tested in a simulation environment and then implemented and validated on the quadrotor UAVs available in the team. If successful, this Thesis will then obtain two main goals: (1) advance the state-of-the-art in the multi-robot research by demonstrating how modern trajectory planning approaches can greatly improve the performance and execution robustness, and (2) further increase the visibility of the IRISA/Inria Rennes “drone platform” in the community by implementing the proposed approaches our quadrotor UAVs.


1.  D. Zelazo, A. Franchi, H. H. Bülthoff, and P. Robuffo Giordano. Decentralized Rigidity Maintenance Control with Range Measurements for Multi-Robot Systems. The Interna- tional Journal of Robotics Research, 34(1):105–128, 2015

2.  T. Nestmeyer, P. Robuffo Giordano, H. H. Bülthoff, and A. Franchi. Decentralized Simultaneous Multi-target Exploration using a Connected Network of Multiple Robots. Autonomous Robots, 41(4):989-1011, 2017

3.  F. Schiano and P. Robuffo Giordano. Bearing Rigidity Maintenance for Formations of Quadrotor UAVs. In 2017 IEEE Int. Conf. on Robotics and Automation (ICRA 2017), 2017

4.  F. Schiano, A. Franchi, D. Zelazo, and P. Robuffo Giordano. A Rigidity-Based Decentralized Bearing Formation Controller for Groups of Quadrotor UAVs. In 2016 IEEE/RSJ Int. Conf. on Intelligent Robots and Systems (IROS 2016), 2016

5.  F. Schiano, R. Tron. The Dynamic Bearing Observability Matrix Nonlinear Observability and Estimation for Multi-Agent Systems. In 2018 IEEE Int. Conf. on Robotics and Automation (ICRA 2018), 2018

6.  R. Spica and P. Robuffo Giordano. Active Decentralized Scale Estimation for Bearing Based Localization. In 2016 IEEE/RSJ Int. Conf. on Intelligent Robots and Systems (IROS 2016), 2016

7.  B. Penin, R. Spica, P. Robuffo Giordano, and F. Chaumette. Vision-Based Minimum- Time Trajectory Generation and Control of a Quadrotor UAV. In 2017 IEEE/RSJ Int. Conf. on Intelligent Robots and Systems (IROS 2017), 2017

8.  B. Penin, P. Robuffo Giordano, and F. Chaumette. Minimum-Time Trajectory Planning Under Intermittent Measurements. IEEE Robotics and Automation Letters, 2018

9.  B. Penin, P. Robuffo Giordano, and F. Chaumette. Vision-Based Reactive Planning for Aggressive Target Tracking while Avoiding Collisions and Occlusions. IEEE Robotics and Automation Letters, 2018

10.  Q. Delamare, P. Robuffo Giordano, and A. Franchi. Towards Aerial Physical Locomotion: the Contact-Fly-Contact Problem. IEEE Robotics and Automation Letters, Special Issue on Aerial Manipulation, 2018

11.  P. Salaris, R. Spica, P. Robuffo Giordano, and P. Rives. Online Optimal Active Sensing Control. In 2017 IEEE Int. Conf. on Robotics and Automation (ICRA 2017), 2017

12.  M. Cognetti, P. Salaris, and P. Robuffo Giordano. Optimal Active Sensing with Process and Measurement Noise. In 2018 IEEE Int. Conf. on Robotics and Automation (ICRA 2018), 2018

13.  P. Robuffo Giordano, Q. Delamare, and A. Franchi. Trajectory Generation for Minimum Closed-Loop State Sensitivity. In 2018 IEEE Int. Conf. on Robotics and Automation (ICRA 2018), 2018

Work start date: 
multi-robots, trajectory planning, localization, formation control, quadrotor UAVs
IRISA - Campus universitaire de Beaulieu, Rennes