VO seminar

Robotics & Intelligent System Laboratory Department of Electrical Engineering Seoul National University

RISL | Robotics & Intelligent Systems Lab.Seoul National University

Motion Planning in Dynamic Envi-ronments using Velocity Obstacles

August , 2016

JunHyuk Shin



Contents

1. Introduction

2. Velocity Obstacle

3. Avoidance Maneuver

4. Computing the Avoidance Trajectories

5. Conclusion & Limitation



1. Introduction

Motion planning in dynamic environment : simultaneous solving ‘path planning’ and ‘velocity planning’ problem- Path planning : kinematic problem, involving the computation of a collision-free path- Velocity planning : dynamic problem, requiring the consideration of robot dynamic and actuator constraints Dynamic environment i.e.,

1) Robot manipulators avoiding moving obstacle2) Intelligent vehicles negotiating free-way traffic

Avoidance Maneuver Avoiding static and moving obstacles in velocity space : based on the current positions and velocities (first-order method) Trajectory computing from start to goal : Searching a tree of feasible avoidance maneuver - Global search : off-line planning - Heuristic search : on-line planning

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Assumption- Circular objects- Planar problem with no rotations- Arbitrary obstacle trajectory- Instantaneous state of obstacle is known or measurable (position and velocity)

A. Collision Cone Environment formulation

- Two circular objects (A : robot, B : obstacle) with velocity - Configuration space circle : , point

Collision Cone Definition: set of colliding relative velocities

where and is line of - Any relative velocity that lies between two tangent to , and , will cause a collision- Specified as particular robot/obstacle pair

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B. Velocity Obstacle - VO Velocity Obstacle Definition

: set of colliding absolute velocities of ( : Minkowski vector sum operator)- Collision avoidance with selection

Union of individual VO ( is # of obstacle): considering multiple obstacle avoidance

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C. Imminent Collision VO conditions

- VO is based on a linear approximation of the obstacle’s trajectory- Remote collision prediction may be inaccurate if the obstacle does not move along straight line

Imminent collision: collision occurs at some time , where is suit-able time horizon

Collision Velocity Set beyond Time Horizon where is the shortest relative distance between the robot and the obstacle

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A. Reachable Avoidance Velocity - RAV Set of feasible accelerations FA

- is the position vector- represents the robot dynamics- is the vector of the actuator efforts- is the set of admissible controls

Set of reachable velocities RV : scaling FA(t) by and adding to the

Set of reachable avoidance velocities RAV - Avoiding maneuver can be computed by selecting any velocity in RAV

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B. Dynamic versus Kinematic Constraints Dynamic constraints

: RV accounts only for this constraints, which on the robot accelerations- generally more restrictive with high speed

Kinematic constraints: nonholonomic constraints which prevent the vehicle from moving sideways- relevant only at low speed

Disregard the nonholonomic kinematic con-straints

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C. Structure of the Reachable Avoidance Velocity Single type of avoidance maneuver

: Most three non-overlapping subdivided subset- front - rear - diverging : takes the robot away from obstacle

Multiple type of avoidance maneuver

Given a robot and moving obstacles , the reachable avoidance set RAV consists of at most 3 subsets, each including velocities corresponding to a unique type of avoidance maneuver.

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A. Global Search : Off-line application Search tree definition

Node Operator Branch at time , expanding to with

Cost assign : cost to each branch and can be searched for the trajectory that maximizes some objec-tive functions, such as distance traveled, motion time, or energy

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B. Heuristic Search : On-line application On-line problem

: trajectory can be only generated by expanding current node Basic heuristic

The TG(to goal) strategy: choose the highest avoidance velocity along the line to the goal- It takes the robot toward its target

The MV(maximum velocity) strategy: within some specified angle from the line to the goal, select the maximum avoidance velocity- It makes robot move at high speed, even if it does not aim directly at the goal

The ST(structure) strategy: Select the velocity that avoids the obstacles according to their perceived risk

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C. Avoidance of Static and Moving Obstacles Static obstacles

- Trajectory shown in figure 15 were computed ev-ery 1 sec using the MV heuristics and time horizon - When the time horizon was set higher, to , result in no solution

Fixed and Moving Obstacles- First avoiding the small static obstacles, and then avoiding the large moving obstacles, using the MV heuristics- The trajectory is shown in three snapshots in Fig-ures 16b, 16c, and 16d, corresponding to times , , and the final time , respectively

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5. Conclusion

Motion Planning in Dynamic Environment using VO- First order method, only relies on velocity information : general trajectories are approximated by a sequence of piecewise constant segments- Avoidance maneuver using Velocity Obstacle- Divided subset of reachable potential avoidance velocities by the set of admissible ac-celerations over a given time interval

Key Feature of this Approach(1) it provides a simple geometric representation of potential avoidance maneuvers(2) any number of moving obstacles can be avoided by considering the union of their VOs(3) it unifies the avoidance of moving as well as stationary obstacles(4) it allows for the simple consideration of robot dynamics and actuator constrains

Limitation for such environments- First order linear approximation of trajectory | highly nonlinear trajectory- 2-D dynamic environment | 3-D dynamic environment- Planar problem with no rotations | rotating obstacles- Using heuristic search with on-line problem | no optimization to each situation- Point to point arbitrary path | bounded trajectory condition

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