EE631 Cooperating Autonomous Mobile Robots Lecture: Collision Avoidance in Dynamic Environments - PowerPoint PPT Presentation

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EE631 Cooperating Autonomous Mobile Robots Lecture: Collision Avoidance in Dynamic Environments

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EE631 Cooperating Autonomous Mobile ... Global Path Planning Using D* Search A shortest path returned by D* in 2D environment Robot path Static obstacles ... – PowerPoint PPT presentation

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Title: EE631 Cooperating Autonomous Mobile Robots Lecture: Collision Avoidance in Dynamic Environments


1
EE631 Cooperating Autonomous Mobile
RobotsLecture Collision Avoidance in Dynamic
Environments
  • Prof. Yi Guo
  • ECE Dept.

2
Plan
  • A Collision Avoidance Algorithm
  • A Global Motion Planning Scheme

3
Nonholonomic Kinematic Model
Coordinate transformation and input
mapping (?,? are within (-?/2,?/2))
Chained form (after transformation)
4
Assumptions The Robot
  • 2-dimensional circle with radius R
  • Knowing its start and goal positions
  • Onboard sensors detecting dynamic obstacles

5
Assumptions The Environment
  • 2D environment with static
  • and dynamic obstacles
  • Pre-defined map with static
  • obstacle locations known
  • Dynamic obstacles
  • represented by circles with
  • radius ri

6
Problem Formulation Trajectory Planning
  • Find feasible trajectories for the robot,
    enrouting from its start position to its goal,
    without collisions with static and dynamic
    obstacles.

7
Feasible Trajectory in Free Space
  • A family of feasible trajectories
  • Boundary conditions
  • In original coordinate
  • In transformed coordinate

8
Parameterized Feasible Trajectory
  • Imposing boundary conditions, parameterization of
    the trajectory in terms of a6
  • A, B, Y are constant matrices calculated from
    boundary conditions
  • a6 increases the freedom of maneuver accounting
    for geometric constrains posed by dynamic
    obstacles

9
(No Transcript)
10
Steering Paradigm
  • Polynomial steering
  • Assume T is the time that takes the robot to get
    to qf from q0. Choose
  • then

11
A quick summary
  • System model chained form
  • Feasible trajectories closed form
    parameterization
  • Steering control closed form, piecewise constant
    solution (polynomial steering)
  • Next Collision avoidance -- explicit condition
    based
  • on geometry and time

12
Dynamic Collision Avoidance Criteria
Time space collision
13
Dynamic Collision Avoidance Criteria
  • Time criterion
  • Assume obstacle moves at constant velocity during
    sampling period
  • In original coordinate
  • In transformed coordinate

14
Dynamic Collision Avoidance Criteria
  • Geometry criterion
  • In original coordinate
  • In transformed coordinate

Mapping from x-y plane to z1-z4 plane indicates
collision region within a circle of radius
riRl/2, since
15
Dynamic Collision Avoidance Criteria
  • Time criterion geometrical criterion path
    parameterization
  • g2, g1i, g0i are analytic functions of their
    arguments and can be calculated real time
  • a6k exists if g2gt0
  • g2gt0 holds for every points except boundary points

16
Global Path Planning Using D Search

A shortest path returned by D in 2D environment
17
Global Motion Planning
Algorithm flow chart
18
Simulations
In 2D environment with static obstacles (a60)
19
Collision Trajectory
  • Circles are drawn with 5 second spacing
  • Onboard sensors detect
  • obstacle 1 center 23,15, velocity 0.1,0.2
  • obstacle 2 center 45,20, velocity -0.1,-0.1
  • Collisions occurs

20
Global CollisionFree Trajectory
  • a619.408610-6, a624.997310-6

21
Global CollisionFree Trajectory
  • Moving obstacle changes velocity
  • Original velocity -0.15,-0.1, new velocity
    0.15,-0.29
  • Calculated a629.408610-6, a624.997310-6

22
Readings
  • A new analytical solution to mobile robot
    trajectory generation in the presence of moving
    obstacles, by Zhihua Qu, Jing Wang, Plaisted,
    C.E., IEEE Transactions on Robotics, Volume 20,
    Issue 6, Dec. 2004 Page(s)978 - 993
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