Title: EE631 Cooperating Autonomous Mobile Robots Lecture: Collision Avoidance in Dynamic Environments
1EE631 Cooperating Autonomous Mobile
RobotsLecture Collision Avoidance in Dynamic
Environments
2Plan
- A Collision Avoidance Algorithm
- A Global Motion Planning Scheme
3Nonholonomic Kinematic Model
Coordinate transformation and input
mapping (?,? are within (-?/2,?/2))
Chained form (after transformation)
4Assumptions The Robot
- 2-dimensional circle with radius R
- Knowing its start and goal positions
- Onboard sensors detecting dynamic obstacles
5Assumptions 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
6Problem Formulation Trajectory Planning
-
- Find feasible trajectories for the robot,
enrouting from its start position to its goal,
without collisions with static and dynamic
obstacles.
7Feasible Trajectory in Free Space
- A family of feasible trajectories
- Boundary conditions
- In original coordinate
- In transformed coordinate
8Parameterized 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)
10Steering Paradigm
- Polynomial steering
- Assume T is the time that takes the robot to get
to qf from q0. Choose - then
11A 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
12Dynamic Collision Avoidance Criteria
Time space collision
13Dynamic Collision Avoidance Criteria
- Time criterion
- Assume obstacle moves at constant velocity during
sampling period - In original coordinate
- In transformed coordinate
14Dynamic 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
15Dynamic 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
16Global Path Planning Using D Search
A shortest path returned by D in 2D environment
17Global Motion Planning
Algorithm flow chart
18Simulations
In 2D environment with static obstacles (a60)
19Collision 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
20Global CollisionFree Trajectory
- a619.408610-6, a624.997310-6
21Global 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
22Readings
- 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