Proximity Computations between Noisy Point Clouds using Robust Classification

1Jia Pan, 2Sachin Chitta, 1Dinesh Manocha1UNC Chapel Hill 2Willow Garage

http://gamma.cs.unc.edu/POINTC/

Main Result

• Proximity computation and collision detection algorithm between noisy point cloud data

• Computes collision probability instead of simple yes-no result

• Important for safety and feasibility of robotics applications

Proximity and Collision Computations

• Geometric reasoning with noisy point cloud data vs. mesh based representations

• Integral part of motion planning and grasping algorithms

• Contact computations for dynamic simulation

Background

Motion Planning: Assumptions

• Motion planning has a long history (30+ years)• Assumptions

– Exact environment (mesh world)– Exact control– Exact localization– No joint limit and torque limit– No quality control

• Output:– Collision-free path

Environment Uncertainty

• Uncertainty can be large due to sensor error, poor sampling, physical representations, etc.

• Need to model order to improve the safety and robustness of motion planning

• Relative less work – Previous methods only consider 2D cases with

specific assumptions on uncertainty

Sensors

• Robot uses sensors to compute a representation of the physical world

• But sensors are not perfect or may not be very accurate….

Robot Sensors: Data Collection

Cameras: may have low resolution

Robot Sensors: Data Collection

Laser Scanners: may have limited range

Point Clouds Captured by Robot

Recent Trend: Depth Cameras

Primesense

Pr2’s

CamcubeSwissranger 4000

Kinect

Kinect

http://graphics.stanford.edu/~mdfisher/Kinect.html

Kinect Reconstruction

http://groups.csail.mit.edu/rrg/index.php?n=Main.VisualOdometryForGPS-DeniedFlighthttp://www.cs.washington.edu/ai/Mobile_Robotics/projects/rgbd-3d-mapping/

Uncertainty From RGB-D Sensors

• Sensors may have low resolution low resolution of point clouds – Kinect has relatively high resolution, but may still

be not enough for objects far away• Sensors may be influenced by noise, especially

in outdoor environments noise in point clouds

• Sensors may have limited ranges (near range and far range) unknown areas

Handling Noisy Point Cloud

• Planning, navigation and grasping• Scene reasoning• Noisy data• Real-time processing

Related Work

• Collision Detection for meshes– Fast and robust– Not designed for (noisy) point-clouds

• Motion planning with environment uncertainty– 2D polygons– Vehicle planning

Uncertainty Model of Point Cloud

Errors in Point Clouds

Discretization (sampling) error

Errors in Point Clouds

Position error

Point Cloud Collision Detection

In-collision In-collision ?

Point Cloud Collision Detection

In-collision In-collision ?

Point Cloud Collision Detection

collision-free Collision-free ?

Point Cloud Collision DetectionCollision-free

Collision-free?

Handling Point Cloud Collision: Two Methods

Reconstr

uction

Mesh Collision

Point Cloud Collision

Mesh Reconstruction => Collision

Mesh CollisionReconstruction

Reconstruction is more difficult then collision detection

Solve an easier problem by conquering a more difficult one?

Mesh Reconstruction => Collision

• Reconstruction process is not robust, and is sensitive to noise and high order features

• Error in reconstructed result can be amplified by subsequent collision checking

• Reconstruction process is slow (few seconds)• The final result is YES/NO answer, which is

sensitive to noise.

Use Ideas from Classification

• Two methods to classify two sets (Machine Learning)– Generative model

• First estimate the joint distribution (more difficult!)• Then compute the classifier

– Discriminative function• Directly compute the classifier

• If we only need to classify, discriminative function usually is the better choice.

Our Solution• Return to the basic definition of collision-free

– Two objects are collision-free if they are separable by a continuous surface and is in-collision when such surface does not exist.

Classification-based Collision Detection

• Find a separating surface that separates two points clouds as much as possible

Collision Detection based on Robust Classification

• We compute the optimal (i.e. minimize the separating error) separating surface using a SVM-like algorithm

• Use supervised machine learning methods for geometric classification

• Different from standard SVM: each training data point has noise – corresponds to robust classification in machine learning

Robust Classification

Standard SVM Robust Classification: aware of noise

Compute the Separating Surface

Per-point Collision Probability

• Collision probability: the probability that one point is on the wrong side of separating surface.

• Robust classification computes collision probability for each single point sample

Probabilistic Collision between Two Objects

• For each object– Cluster the points and only keep one point in each

cluster: compute collision probability for independent points

– Overall object collision probability

Three Collision Cases

Deep collision In-contact Large distance

Collision probability near 1

Collision probability near 0.5

Collision probability near 0

Difficult: small noise will bring reverse of yes/no answer

EasyEasy

Results: Small Noise

Deep Collision Configurations

Large Distance Configurations

In Contact Configurations (Difficult)

Very few configurations are in the difficult region

Results: Large Noise

Deep Collision Configurations

Large Distance Configurations

In Contact Configurations (Difficult)

More configurations are in the difficult region!

PR2 Robot Sensor Results

Deep Collision Configurations

In Contact Configurations (Difficult)

Large Distance Configurations

same distance to obstacle collision probability with wide spread.

Range of Collision Probability

• Collision probability’s wide range:– It is a more complete description of collision state

than distance or yes/no answer

– Important for grasping or planning in constrained environment

Kinect Data

Office data from Peter Henry,Dieter Fox @RSE-lab UW

Result on Kinect Data

BVH Hierarchy Acceleration

• Bounding volume hierarchy is widely used in mesh collision detection for acceleration

• Basic idea: decomposeobjects into many cells andcull collision test between cells that are far away.

Application to Motion Planning

• Use overall collision probability for the objects as a cost in motion planning algorithms to compute the trajectory with minimum collision probability

Other Applications

• The per-point collision probability is more useful– Provides finer control in terms of handling

environment uncertainty– Can use work space information to guide the

planning procedure in order to avoid collision

Conclusions

• A robust proximity computation and collision detection algorithm for noisy point cloud data

• Problem reduced to robust classification• Initial results on point-cloud data from PR2

sensors

Future Work

• Currently we directly use point clouds, which can only model the space with/without obstacles

• Due to sensor range, part of the space is unknown

• So we will apply our algorithm to the data structure that can encode ‘unknown’ space, such as the octomap in ROS

• Also more useful for sensor with dense resolution, like kinect

Future Work

• Currently implementation is on static models• Extend to dynamic environments

– New objects added or deleted– Handle deformable objects and update sensor

uncertainty • SVM has incremental variations that can

handle dynamic data

Acknowledge

• National Science Foundation• Army Research Office• Willow Garage

Thanks