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Towards Safe Navigation of Quad-copter Amongst Uncertain Dynamic ObstaclesAuthor: Dhaivat Bhatt Date: 2019-04-15 Report no: IIIT/TH/2019/43 Advisor:Madhava Krishna AbstractIn a last few years, there has been a surge of interest in the field of autonomous navigation and exploration using drones. While there have been many advances made in the field, there has been various challenges, yet to be tackled, for a safe navigation of Quad-copters amidst uncertain dynamic obstacles. In this work, we attempt to tackle this problem by incorporating positional uncertainties of drone and moving obstacles into a joint trajectory optimization framework. In this thesis, we formulate a novel trajectory optimization scheme that takes into consideration the state uncertainty of the robot and obstacle into its collision avoidance routine. The collision avoidance under uncertainty is modeled here as an overlap between two distributions that represent the state of the robot and obstacle respectively. Our framework is a generic framework and the idea proposed here can be used to for any sets of distributions with characterizable overlap. In the scope of this thesis, we model these distributions as Gaussian distributions. We adopt the minmax procedure to characterize the area of overlap between two Gaussian distributions, and compare it with the method of Bhattacharyya distance. Bhattacharyya distance is an approximate closed form characterization of overlap between two Gaussian distribution. The Bhattacharyya distance is generalizable to other distributions too, if their overlap can be characterized through some analytical closed form solution. In this work, We provide closed form expressions that can characterize the overlap as a function of control. We establish that our closed form approximations to characterize overlap is less erroneous when compared with entropic distances like Bhattacharyya distance. Our proposed algorithm can avoid overlapping uncertainty distributions in two possible ways. Firstly when a prescribed overlapping area that needs to be avoided is posed as a confidence contour lower bound, control commands are accordingly realized through a MPC framework such that these bounds are respected. Secondly in tight spaces control commands are computed such that the overlapping distribution respects a prescribed range of overlap characterized by lower and upper bounds of the confidence contours. We test our proposal with extensive set of simulations carried out under various constrained environmental configurations. We show usefulness of proposal under tight spaces where finding control maneuvers with minimal risk behavior becomes an inevitable task. Full thesis: pdf Centre for Robotics |
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