12_bug2.pdf - COMS W4733 Computational Aspects of Robotics Lecture 12 Bug Algorithms 2 Slide materials from H Choset G D Hager and Z Dodds Instructor

12_bug2.pdf - COMS W4733 Computational Aspects of Robotics...

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COMS W4733: Computational Aspects of Robotics Lecture 12: Bug Algorithms 2 Slide materials from H. Choset, G. D. Hager, and Z. Dodds Instructor: Tony Dear
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Review: Bug Algorithms Path planning algorithms for point particle robots in environments with obstacles Incremental, reactive planning with simple behaviors Sensing limited to tactile and range sensors Bug 1: Exhaustive search, traverse all obstacle boundaries Bug 2: Greedy search, head along m-line whenever possible Bug 2 often outperforms Bug 1 but can be less predictable Both are complete
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Bug 1 Distance ≤ 𝐷 + 1.5 σ ? ? ?
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Bug 2 Distance ≤ 𝐷 + 0.5 σ ? ? ? ? ?
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Range Sensing Detect obstacles some finite distance away Infrared, sonar, radar, lidar… ? = ?, ? 𝑇 is the robot’s current position ? = ? + 𝜆 cos 𝜃 , sin 𝜃 𝑇 is any other point in the plane a distance 𝜆 away at an angle 𝜃 Raw distance function Saturated raw distance function 𝜌(?, 𝜃) = min 𝜆 ?(?, ?) s.t. ? ∈ ∪ ? Boundary( 𝑊? ? ) 𝜌 𝑅 (?, 𝜃) = ቊ 𝜌 ?, 𝜃 , 𝜌 ?, 𝜃 < 𝑅 ∞, ??ℎ???𝑖??
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Range Sensing Distance function 𝜌 𝑅 ?, 𝜃 is discontinuous! Values of 𝜃 at which 𝜌 𝑅 jumps values indicate limits of a sensed obstacle Obstacle boundary interpolated along continuous segment of finite 𝜌 𝑅 𝜌 𝑅 (?, 𝜃) = ቊ 𝜌 ?, 𝜃 , 𝜌 ?, 𝜃 < 𝑅 ∞, ??ℎ???𝑖?? 𝜌(?, 𝜃) = min 𝜆 ?(?, ?) s.t. ? ∈ ∪ ? Boundary( 𝑊? ? )
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Range Sensing for Bug Suppose robot sees obstacle on path to goal No point in heading along this path as we’ll eventually have to turn ? ? : visible obstacle extents ?(?, ?
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