Guidance using bearing-only measurements with three beacons in the plane Minh Hoang Trinh a , Gwi-Han Ko a , Viet Hoang Pham a , Kwang-Kyo Oh b , Hyo-Sung Ahn a,n a School of Mechatronics, Gwangju Institute of Science and Technology (GIST), 1 Oryong-dong, Buk-gu, Gwangju 500-712, South Korea b Automotive Components and Materials R& D Group, Korea Institute of Industrial Technology, Gwangju, South Korea article info Article history: Received 13 August 2015 Received in revised form 29 February 2016 Accepted 18 March 2016 Available online 4 April 2016 Keywords: Navigation Guidance Bearing-only measurements (BOM) UAV abstract This paper proposes a bearing-only measurement based guidance algorithm for a mobile agent to na- vigate in a two-dimensional plane. Based on the bearing vectors and the subtended angles related to three stationary beacons, the proposed algorithm allows the agent to reach its desired location. We show that the agent reaches its desired location globally asymptotically based on Lyapunov stability theory. Under some assumptions, the agent is also proved to reach the desired location exponentially based on Lyapunov's indirect method. Simulations and actual experimental tests on quadrotor system are also provided to verify the effectiveness of the proposed algorithm in outdoor environment. & 2016 Published by Elsevier Ltd. 1. Introduction Recently, small-sized unmanned aerial vehicles (UAVs) have attracted a significant amount of interest (Sullivan, 2006) from researchers in the control system society. Due to their mobility, UAVs are useful in a variety of applications including surveillance, search and rescue, assessing disaster areas, etc. (Bouabdallah, Becker, & Siegwart, 2007). A fundamental task of the UAVs is au- tonomous navigation, which allows them to reach a desired lo- cation without human interaction. In order to achieve the navi- gation task, global positioning system (GPS) is usually used for outdoor operation. However, in many scenarios, such as indoor operation, urban cityscapes or rugged mountainous terrain, GPS information is either unavailable or unreliable. Hence, it is im- portant to design an effective navigation strategy for UAVs. In the literature, we can find several navigation strategies based on simultaneous localization and mapping (SLAM) (Dissanayake, Newman, Clark, Durrant-Whyte, & Csorba, 2011). Using measure- ments corresponding to some stationary beacons, an autonomous agent can localize its relative position with respect to the beacons and decide its navigation strategy accordingly (Madhavan & Dur- rant-Whyte, 2004). For example, SLAM strategies based on min- iature laser sensor (Aghamohammadi, Tamjidi, & Taghirad, 2008; Grzonka, Grisetti, & Burgard, 2012), optical flow sensor (Kendoula, Fantoni, & Nonami, 2009), or embedded camera (Courbon, Mezouar, Guenard, & Martinet, 2010; Huili Yu & Randy Beard, 2010) have been extensively studied. Generally, distances and bearing angles are both estimated from agent's sensors. The agent, then, maintains a local coordinate frame, where relative positions of the beacons are all represented. The goal of this work is to design a bearing-only measurement (BOM) based guidance algorithm for an agent in the plane. There are several motivations for this work. Firstly, BOM based algo- rithms permit us to reduce the number of equipped sensors of UAVs for navigation task. Secondly, one could reduce the overall system cost by using BOM based algorithms when designing a multi-agent system consisting of a large number of UAVs, e.g., the formation control problems (Oh, Park, & Ahn, 2015). Finally, BOM based algorithms are useful in radio silent applications (Deghat, Shames, Anderson, & Yu, 2014). The bearings can be obtained from image sensors (Choi & Kim, 2014), thus no signal has to be transmitted when the UAVs are on maneuvers. For related works, BOM based tracking and guidance problems have been extensively studied in the literature. Considering a slowly moving target in a 2D plane, the authors in Deghat, Xia, Anderson, and Hong (2016) proposed a BOM based algorithm that simultaneously estimates the location of a moving target and cir- cumnavigates around it. Navigation based on some stationary beacons were exploited, for examples, in Argyros, Bekris, and Kavraki (2004) and Loizou and Kumar (2007). Assuming that there are three noncolinear stationary beacons, the authors in Argyros et al. (2004) introduced a moving-along-the-bisector strategy for a mobile robot to reach almost all location in the entire plane. In a Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/conengprac Control Engineering Practice http://dx.doi.org/10.1016/j.conengprac.2016.03.013 0967-0661/& 2016 Published by Elsevier Ltd. n Corresponding author. E-mail address: hyosung@gist.ac.kr (H.-S. Ahn). Control Engineering Practice 51 (2016) 81–91