Collision Avoidance

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EE631 Cooperating Autonomous Mobile Robots Lecture 5: Collision Avoidance in Dynamic Environments: 

EE631 Cooperating Autonomous Mobile Robots Lecture 5: Collision Avoidance in Dynamic Environments Prof. Yi Guo ECE Dept.

Plan: 

Plan A Collision Avoidance Algorithm A Global Motion Planning Scheme

Nonholonomic Kinematic Model: 

Nonholonomic Kinematic Model Coordinate transformation and input mapping (, are within (-/2,/2)): Chained form (after transformation):

Assumptions: The Robot: 

Assumptions: The Robot 2-dimensional circle with radius R Knowing its start and goal positions Onboard sensors detecting dynamic obstacles

Assumptions: The Environment: 

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

Problem Formulation: Trajectory Planning: 

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: 

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

Parameterized Feasible Trajectory: 

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: 

Steering Paradigm Polynomial steering: Assume T is the time that takes the robot to get to qf from q0. Choose then

A quick summary: 

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: 

Dynamic Collision Avoidance Criteria Time + space collision

Dynamic Collision Avoidance Criteria: 

Dynamic Collision Avoidance Criteria Time criterion: Assume obstacle moves at constant velocity during sampling period In original coordinate: In transformed coordinate :

Dynamic Collision Avoidance Criteria: 

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 ri+R+l/2, since

Dynamic Collision Avoidance Criteria: 

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: 

Global Path Planning Using D* Search A shortest path returned by D* in 2D environment

Global Motion Planning: 

Global Motion Planning Algorithm flow chart

Simulations: 

Simulations In 2D environment with static obstacles (a6=0)

Collision Trajectory: 

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

Global Collision–Free Trajectory: 

Global Collision–Free Trajectory a61=9.4086*10-6, a62=4.9973*10-6

Global Collision–Free Trajectory: 

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, a62=4.9973*10-6

Readings:: 

Readings: Laumond book Chapter 1 “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