A Reduced-Order Analytical Solution to Mobile Robot Trajectory Generation in the Presence of Moving Obstacles

Transcription

1 A Reduced-Order Analytical Solution to Mobile Robot Trajectory Generation in the Presence of Moving Obstacles Jing Wang, Zhihua Qu,, Yi Guo and Jian Yang Electrical and Computer Engineering University of Central Florida ICRA 04 April 30, New Orleans, LA

2 Outline Introduction Problem Formulation Proposed Steering Paradigm Simulations

3 Introduction Review of Motion planning Steering of Nonholonomic Systems Dynamic Trajectory Generation

4 Motion Planning: Standard algorithms for Terrain Maneuver Probabilistic Path Planner (PPP): roadmap construction phase - a data structure is incrementally constructed in a probabilistic way; query phase --- this data structure is used for solving individual path planning problems. Random Path Planner (RPP) generates two types of paths: gradient paths to get closer to the goal; random walks to escape the local minima. Potential field based reactive planner: define attractive potential function to the final point; repulsive potential function away from the obstacles; a path is generated to attract the robot to the final point and repulse away from the obstacles. Dynamic Programming

5 Steering of Nonholonomic Systems Sinusoidal Steering Polynomial Steering Piecewise Constant Steering Discontinuous Feedback Control Etc.

6 Dynamic Trajectory Generation 3-leg Stool Approach: Models of robotic vehicles and canonical forms Steering control of robotic vehicles Criterion (in both distance and time) for avoiding dynamically moving obstacles Characteristics: Geometrically and physically motivated Model-based, general, analytical solution

7 Problem Formulation General Setting Trajectory planning: car-like robot (centered guide-point)

8 General Setting

9 Trajectory planning: car-like robot (centered guide-point) Guidepoint --- center of the robot Generalized coordinates: q=[x y θφ] T Kinematic model

10 Characteristic of (2,4) Canonical Form Under-actuated Inherent possibility of singularity in any control design (no backstepping) every point is an equilibrium point Movement for one point to another must be done by a steering process No smooth feedback for steering

11 Proposed Steering Paradigm System model: chained form Feasible path: closed form parameterization Steering control: closed form solution Collision avoidance: explicit condition based on geometry ( any time) Dynamically moving objects Piecewise constant sceneries Piecewise constant parameterization of feasible paths (differentiable) Piecewise constant solution to steering control Timed condition for object avoidance

12 Simplified Setting t [t 0 +kt s, t 0 +(k+1)t s ]

13 Feasible Trajectories in Free Work Space

14 Collision Avoidance Robot and i-th moving object in the work space t [t 0 +kt s, t 0 +(k+1)t s ] Constant velocity projected for t [t 0 +kt s, t 0 +T]

15 Collision Avoidance Criterion Robot relative velocity and static object Static criterion

16 Alternative Criterion Place the circle around the robot (rather than the object) yields In the transformed space

17 Dynamic Collision Avoidance Criterion Time Criterion Geometrical Criterion

18 Collision Free Paths Time criterion + Geometrical criterion + path parameterizaion provide

19 Collision Free Paths Solving a k according to: Steering inputs :

20 Simulation Setting

21 Collsion Free Path with Limited Sensing Range

22 Entire trajectory of φ(t)