Affine formation maneuver control of multi-agent systems

A multi-agent formation control task is usually constituted by two control problems:

  • Formation shape control is to steer a group of mobile agents starting from a given initial configuration to form a desired geometric pattern.
  • Formation maneuver control is to steer the mobile agents to maneuver as a whole such that the centroid, orientation, scale, and even shape of the formation can be changed continuously. Formation maneuver control is important for the formation to respond dynamically to the environment to achieve, for example, obstacle avoidance.

We solve the two problems by proposing a leader-follower affine formation control strategy based on stress matrices. With the proposed control laws, not only the desired formation pattern can be achieved, any time-varying affine transformation such as a translation, rotation, scaling, or even shape deformation of the formation can be tracked. The desired formation maneuvers are only accessible to the leaders. The proposed control laws are all globally stable and can be implemented in each agent's local reference frame.

Related publication:

  • S. Zhao, "Affine Formation Maneuver Control of Multi-Agent Systems", IEEE Transactions on Automatic Control, conditionally accepted, Sep 2017

Coordination control of mobile robots with motion constraints

The simplest single-integrator dynamic model has been widely used to derive and analyze coordination control laws for multi-agent systems. It is, however, widely believed that this model is too simple to well approximate real robot dynamics to generate any practically useful control laws. In our work, we defend the practicality of the single-integrator model by proposing a new approach to modify any gradient coordination control laws designed for single integrators to adapt for motion constraints including nonholonomic dynamics and linear/angular velocity saturation, while the convergence property is preserved. The proposed approach may also be applied to obstacle avoidance as demonstrated in the following video.

Related publication:

  • S. Zhao, D. V. Dimarogonas, Z. Sun, and D. Bauso, "A general approach to coordination control of mobile agents with motion constraints," IEEE Transactions on Automatic Control, accepted, Aug 2017
  • S. Zhao and Z. Sun, "Defend the practicality of single-integrator models in multi-robot coordination control," in Proceedings of the 13th IEEE International Conference on Control and Automation, (Ohrid, Macedonia), pp. 666-671, July 2017.

Bearing-based control and estimation over multi-agent systems

  • Bearing rigidity theory: The fundamental problem studied in the bearing rigidity theory is whether or not the shape of a formation of agents (or a framework of nodes) can be uniquely determined by the inter-agent bearings. In our work, we proved that the shape of a formation can be uniquely determined if and only if the formation is infinitesimally bearing rigid. Bearing rigidity theory plays a key role in bearing-based control and estimation over multi-agent systems.
  • Bearing-only formation control: In vision-based formation control of multi-vehicles systems, it is easy for vision to obtain bearing measurements but difficult to get distance measurements. This motivated us studying the problem of bearing-only formation control, where the control is implemented directly based on relative bearing measurements. Bearing-only formation control poses minimal requirements on the end of vision sensing systems and may provide a practical solution to vision-based formation control tasks.
  • Bearing-based formation control: We studied the bearing-based formation control problem where the target formation is specified by inter-agent bearings and each vehicle can obtain the relative positions of their neighbors. Since the bearings are invariant to the translation and scale of the formation, the bearing-based approach provides a simple solution to the problem of translational and scaling formation maneuver control.
  • Bearing-based network localization: We studied the bearing-based network localization problem, which aims to localize all the nodes in a static network given the locations of a subset of nodes termed anchors and inter-node bearings measured in a common reference frame. Our contributions include (a) we prove necessary and sufficient conditions for network localizability with both algebraic and rigidity theoretic interpretations, and (b) we propose and analyze a linear distributed protocol for bearing-based network localization. One novelty of our work is that the localizability analysis and localization protocol are applicable to networks in arbitrary dimensional spaces.

Related publication:

  • S. Zhao and D. Zelazo, "Translational and scaling formation maneuver control via a bearing-based approach," IEEE Transactions on Control of Network Systems, vol. 4, no. 3, pp. 429-438, 2017
  • S. Zhao and D. Zelazo, "Localizability and distributed protocols for bearing-based network localization in arbitrary dimensions," Automatica, vol. 69, pp. 334-341, 2016.
  • S. Zhao and D. Zelazo, "Bearing rigidity and almost global bearing-only formation stabilization," IEEE Transactions on Automatic Control, vol. 61, no. 5, pp. 1255-1268, 2016.
  • S. Zhao and D. Zelazo, "Bearing-based formation stabilization with directed interaction topologies," 54th IEEE Conference on Decision and Control, (Osaka, Japan), pp. 6115-6120, December 2015.

Controllability degree of dynamical networks

Controllability of complex dynamical networks has attracted extensive attention in recent years. Instead of focusing on the binary problem whether or not a network is controllable, we study the controllability degree problem. That is if a network is controllable, then how hard the network can be controlled in terms of the required minimum control energy. While it has been shown in the literature that for a large class of networks the required control energy increases exponentially with the scale of the networks, we study whether or not there exist networks that merely require little control energy even if the network scale is extremely large. We also aim at designing networks that have desired control energy properties.

Previous Research Topics

Vision-based navigation for cargo transportation

Motivated by the 2013 International UAV Innovation Grand Prix, we designed and implemented a real-time vision system for an unmanned helicopter autonomously transferring cargoes between two platforms. In the competition, four cargoes were initially placed inside four circles on one platform and required to be transferred one by one into the four circles on the other platform. This paper presents the core algorithms of the proposed vision system on ellipse detection, ellipse tracking, and single-circle-based position estimation. Experiments and the great success of our team in the competition have verified the efficiency, accuracy, and robustness of the algorithms.

Flight video!

Related publication:

  • S. Zhao, Z. Hu, M. Yin, K. Z. Y. Ang, P. Liu, F. Wang, X. Dong, F. Lin, B. M. Chen, and T. H. Lee, "A robust real-time vision system for autonomous cargo transfer by an unmanned helicopter," IEEE Transactions on Industrial Electronics, vol. 62, no. 2, pp. 1210-1219, 2015.
  • F. Wang, P. Liu, S. Zhao, B. M. Chen, S. K. Phang, S. Lai, T. Pang, B. Wang, C. Cai, and T. H. Lee, "Development of an unmanned helicopter for vertical replenishment," Unmanned Systems, vol. 3, no. 1, pp. 63-87, 2015.

Vision-aided inertial navigation for quad-rotors

We studied vision-aided inertial navigation of small-scale unmanned aerial vehicles (UAVs) in GPS-denied environments. The objectives of the navigation system are to firstly online estimate and compensate the unknown inertial measurement biases, secondly provide drift-free velocity and attitude estimates which are crucial for UAV stabilization control, and thirdly give relatively accurate position estimation such that the UAV is able to perform at least a short-term navigation when the GPS signal is not available. To achieve these objectives, we propose a novel homography-based vision-aided navigation system that adopts four common sensors: a low-cost inertial measurement unit, a downward-looking monocular camera, a barometer, and a compass. The measurements of the sensors are fused by an extended Kalman filter. Based on both analytical and numerical observability analyses of the navigation system, we theoretically verify that the proposed navigation system is able to achieve the navigation objectives. We also show comprehensive simulation and real fight experimental results to verify the effectiveness and robustness of the proposed navigation system.

Related publication:

  • S. Zhao, F. Lin, K. Peng, X. Dong, B. M. Chen, and T. H. Lee, "Vision-aided estimation of attitude, velocity, and inertial measurement bias for UAV stabilization," Journal of Intelligent & Robotic Systems, vol. 81, no. 3, pp. 531-549, 2016.
  • S. Zhao, F. Lin, K. Peng, B. M. Chen, and T. H. Lee, "Homography-based vision-aided inertial navigation of UAVs in unknown environments," in Proceedings of the 2012 AIAA Guidance, Navigation and Control Conference, (Minneapolis, USA), August 2012.

Optimal placement of sensor networks for target localization and tracking

Vision sensing is fundamentally a bearing‐only sensing approach. When localizing a target using multiple cameras, the placement of the cameras can greatly influence the target localization accuracy. In our work, we studied optimal placement of bearing‐only sensor networks for target localization. Although this topic has already been studied by many researchers, most of the existing results are only applicable to two‐dimensional space. We proved the necessary and sufficient conditions for optimal sensor placement in both two‐ and three‐dimensional spaces, which is a nontrivial generalization of the existing results. We further extended our results from bearing‐only sensors to other types of sensors including range‐only and received‐signal‐strength based sensors. We proposed a unified framework to analyze different types of sensor networks in three-dimensional spaces.

Related publication:

  • S. Zhao, B. M. Chen, and T. H. Lee, "Optimal sensor placement for target localization and tracking in 2D and 3D," International Journal of Control, vol. 86, no. 10, pp. 1687-1704, 2013.
  • S. Zhao, B. M. Chen, and T. H. Lee, "Optimal placement of bearing-only sensors for target localization," in Proceedings of the 2012 American Control Conference, (Montreal, Canada), pp. 5108-5113, June 2012.
  • S. Zhao, B. M. Chen, and T. H. Lee, "Optimal deployment of mobile sensors for target tracking in 2D and 3D spaces," IEEE/CAA Journal of Automatica Sinica, vol. 1, no. 1, pp. 24-30, 2014.