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Unformatted text preview: MEM380: Fundamental Robotics I Assignment 2 Due: Wednesday, 10/7/09, 11:59pm EST 1 Objective: In this exercise, you are tasked to program and implement a closed-loop motion controller for a differential-drive robot. The controller will be first be simulated in Matlab, without USARSim, and then be tested on a Pioneer 3DX robot in USARSim. 2 Implementation of an odometry-based position estimator For a differential-drive robot, the kinematic model is described by the following equations: v = r ( ˙ ϕ R + ˙ ϕ L ) 2 (1a) ω = r ( ˙ ϕ R- ˙ ϕ L ) 2 l (1b) where: v,ω : Linear and rotational speed of the robot (m) ˙ ϕ R , ˙ ϕ L : Spinning speed of each wheel (rad/s) r,l : Robot dimensions: wheel radius and half of the wheel distance (m) . Recall v and ω is related to the robot’s pose as follows: ˙ x ˙ y ˙ θ = cos θ sin θ 1 v ω (2) where x , y , and θ denotes the robot’s pose (position and orientation) in the intertial frame (see Figure 1. This pose can be estimated by integrating the movement (summing the incremental travel distances). For a discrete system with a fixed sampling interval δt the incremental travel distances ( δx,δy,δθ ) are: δx = δs R + δs L 2 cos θ (3a) δy = δs R + δs L 2 sin θ (3b) δθ = δs R- δs L 2 l (3c) θ = s R- s L 2 l (3d) where δx,δy,δθ : Path travelled and orientation change in the last sampling interval (m,m,rad) δs R ,δs L : Travelled distances during sampling interval for right and left wheels (m) s R ,s L : Total travelled distances for right and left wheels (m) 1 Figure 1: Schematic for closed-loop motion control.Figure 1: Schematic for closed-loop motion control....
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This note was uploaded on 03/29/2010 for the course MEM MEM380 taught by Professor Zhou during the Spring '09 term at Drexel.
- Spring '09