Download - EE631 Cooperating Autonomous Mobile Robots Lecture: Collision Avoidance in Dynamic Environments
EE631 Cooperating Autonomous Mobile Robots
Lecture: Collision Avoidance in Dynamic Environments
Prof. Yi GuoECE Dept.
Plan
A Collision Avoidance Algorithm A Global Motion Planning Scheme
Nonholonomic Kinematic Model
Coordinate transformation and input mapping(, are within (-/2,/2)):
Chained form (after transformation):
Assumptions: The Robot 2-dimensional circle with radius R Knowing its start and goal positions Onboard sensors detecting dynamic obstacles
Assumptions: The Environment 2D environment with static
and dynamic obstacles Pre-defined map with static
obstacle locations known Dynamic obstacles
represented by circles withradius ri
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.
Feasible Trajectory in Free Space A family of feasible trajectories:
Boundary conditions In original coordinate:
In transformed coordinate:
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
Steering Paradigm
Polynomial steering:
Assume T is the time that takes the robot to get to qf from q0. Choose
then
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
Dynamic Collision Avoidance Criteria
Time + space collision
Dynamic Collision Avoidance Criteria
Time criterion: Assume obstacle moves at constant velocity during sampling
period In original coordinate:
In transformed coordinate :
))1(,[ 00 ss TktkTtt
Dynamic Collision Avoidance Criteria
Geometry criterion: In original coordinate:
In transformed coordinate:
Mapping from x-y plane to z1-z4 planeindicates collision region within a circle of radius ri+R+l/2, since
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 g2>0
g2>0 holds for every points except boundary points
Global Path Planning Using D* Search
A shortest path returned by D* in 2D environment
Robot path
Static obstacles
Start
Goal
Cost function: ( is distance, is penalty on obstacles)ppf d d=r+ r
Global Motion Planning
Algorithm flow chartAlgorithm flow chart
Simulations
In 2D environment with static obstacles (In 2D environment with static obstacles (a6=0)
Static obstacles
Feasible trajectory
StartStart
GoalGoal
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
RobotMoving obstacles
Static obstacles
Global Collision–Free Trajectory
a61=9.4086*10-6, a6
2=4.9973*10-6
RobotMoving obstacles
Static obstacles
Global Collision–Free Trajectory
Moving obstacle changes velocity: Original velocity [-0.15,-0.1], new velocity [0.15,-0.29]
Calculated a62=9.4086*10-6, a6
2=4.9973*10-6
RobotMoving obstacles
Static obstacles
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