Online Evasive Strategy for Aerial Survey using Sierpinski curve Ashay Wakode ∗ Arpita Sinha ∗∗ ∗ Indian Institute Of Technology Bombay, Mumbai, Maharashtra 400076 India (e-mail: ashaywakode@gmail.com). ∗∗ Indian Institute Of Technology Bombay, Mumbai, Maharashtra 400076 India (e-mail: arpita.sinha@iitb.ac.in) Abstract: This paper deals with the aerial survey of a closed region using the Space-Filling curve, particularly Sierpinski curve. The specified region is triangulated, and the Sierpinski curve is used to explore each smaller triangular region. The entire region may have one or more obstacles. An algorithm is presented which suggests evasive manoeuvre (detour) if an obstacle is detected. The algorithm is online; that is, it does not require prior knowledge of the location of obstacles and can be applied while the robotic system is traversing the designated path. The fractal nature of the Sierpinski curve and simple geometric observations were used to formulate and validate the algorithm. The non-uniform coverage and multiple obstacle problems are also dealt with towards the end. Keywords: Autonomous Vehicles, Coverage Path Planning, Online Obstacle evasion, Robotic Exploration, Space-Filling curve, Trajectory and Path Planning 1. INTRODUCTION Space-Filling curves are a special type of curves that pass through every point of closed interval onto which they are mapped. Space-Filling curves are made out of smaller simi- lar curves, which is referred to as the fractal nature of space filling curves (Sagan (1994), Bader (2012)). Due to these interesting properties, space-filling curves are widely used in applications where the agent needs to explore/survey a region and gather data. Other applications of Space-Filling curves can be found in computer graphics (Dafner et al. (2000), Memon et al. (2000)), Computer Aided-Design (Bader (2012)), parallel computing (Zumbusch (2000)) and many more. With advent of Unmanned Aerial Vehicles (UAVs), the robotics exploration/survey task has been simplified. Sur- vey using UAVs is superior due to the following advantages : (1) The search agent no longer need to worry about the region’s topography. (2) The surface of the region being explored remains undisturbed. (3) Cheaper and less bulky UAVs can be deployed in huge numbers, reducing cost and increasing efficiency in terms of both energy and time. A survey of a region using aerial vehicles is theoretically better but requires robust algorithms/strategies for im- plementation in the real world. This paper deals with one such strategy for aerial survey using the Sierpinski curve. The robotics exploration problem is a sub-problem of the Coverage Path Planning problem (CPPP). In CPPP, a robotic agent needs to traverse through a certain region while doing tasks like mowing, painting, or cleaning, to name a few. There are many solutions available for CPPP which can be used for robotic exploration problem and hence for aerial survey: Boustrophedon decomposition, Grid-based methods, Graph-based methods, and many more (Galceran and Carreras (2013)). Space-Filling curves provide a novel solution to robotic exploration problem because of their useful properties. An exhaustive search can be carried out since it passes through every point of the region. The fractal nature allows us to design algorithms/strategies easily since a space-filling curve is a combination of other similar space- filling curves. Space-Filling curves can span both 2D and 3D space, and algorithms built for a 2D region can be easily extended to 3D space. Spires and Goldsmith (1998) suggest the use of a swarm of robots for exploration, each robot following a space- filling curve. This approach is efficient in terms of energy, robust to failures, and assures coverage in finite time, But the presence of obstacles is not considered. Tiwari et al. (2007) and Ban et al. (2013) propose a solution to the exploration problem using a space-filling curve. However, apriori location of obstacles is required making them unsuitable for online implementation. Nair et al. (2017), Joshi et al. (2019) give out online algorithms for robotic exploration using Hilbert’s space-filling curve. However, the obstacles must occupy only single and double neighboring grid locations. But, this approach cannot be used for the Sierpinski curve. So, No online exploration strategy exists for an agent following a Sierpinski curve. We have formulated a strategy for aerial survey when the search agent uses the Sierpinski curve as a guiding path while avoiding obstacles; when the location of obstacles is unknown. The suggested strategy is online; that is, arXiv:2209.01426v1 [cs.RO] 3 Sep 2022