UOBPRM: Uniform OBPRM
Related Projects:  Robot Task and Motion Planning    Sampling-based Planning    Medial Axis Guided Planning    Obstacle-Based Planning    OBPRM: Obstacle-Based PRM    OBRRT: Obstacle-Based RRT  

Sampling near obstacles is important since it improves the configuration coverage in difficult areas of C-space (such as narrow passages). There are several PRM variants proposed to increase sampling in important regions of C-space, particularly near C-obstacle boundaries. None of them could gaurantee the node distribution and those methods are not very efficient. We propose a new obstacle-based sampler, Uniform OBPRM (UOBPRM) which guarantees a uniform distribution near the C-obstacle surfaces. UOBPRM basically generates a set of uniformly distributed segments of fixed length and then finds all the intersections between the segments and the obstacles by checking the validity changes along the segment. The valid configurations adjacent to the invalid configurations are retained as roadmap nodes.

For UOBPRM, if the bounding box is too close to a C-obstacle boundary, then segments that would yield points on C-obstacle surface may be disqualified. Therefore, we temporarily expand the bounding box for node generation which provides enough space to generate line segments around obstacles. Although the bounding box is adjusted, we do not generate nodes outside the original bounding box, because we only retain samples contained in the original bounding box as roadmap nodes.



In order to show how UOBPRM work comparing to other obstacle-based samplers, we study the distribution of configurations and the cost of generating samples .


Configuration Distribution
Here we compare 5 different sampling strategies: PRM, OBPRM, Gaussian, Bridge test and UOBPRM. We study the distribution of configurations obtained by each sampler in different environments. For each environment, we generate samples and then partition the environment into several subregions and count the number of configurations in each subregion. If the nodes are uniformly distributed, the number of nodes should be proportional to the surface area for every region.

(1) A Single Ball Environment: We compute node distribution by putting a grid over space. The grid equally partitions the environment into 16 small cubes. Starting from 1, the cubes are indexed from left to the right, from top to the borrom. Since the ball only occupies the center 4 pieces (number 6, 7, 10, and 11), a similar number of configurations in these four regions is expected if the distribution is uniform around obstacle surfaces. Here we show the snapshots for OBPRM (left) and UOBPRM (middle) and the node distribution comparison. The red bars show the percentage of configurations within the regions that the ball occupies and the blue ones represents the free space. An ideal node distribution around obstacle surfaces will result with each red bar at 25% and blue bar at 0%. As shown, UOBPRM gives a more uniform distribution, and the configurations are closer to the obstacle surface.



(2) Environment With 4 Balls of Equal Size: We partition the space into 4 identical regions, and we separate each ball into 4 same sized regions. Therefore, we have a total of 16 regions which have the same obstacle surface area. If the distribution is uniform, each region will have 6.25% of the nodes. Here we show the sample distribution examples for OBPRM (left) and UOBPRM (middle). OBPRM has fewer nodes on the boundary side than it should for a uniform distribution. From the node distribution comparison plot, it shows UOBPRM and Bridge test sampler produce a distribution that is close to uniform distribution than the other samplers.


(3) Environment With a Mixture of Balls and Cubes: We separate the environment into four regions where one obstacle is either a ball or cube only. The node distribution should be proportional to the surface. So there should be about 1.9 times more nodes in the cube regions than in the ball regions if the nodes are distributed uniformly. We separate each obstacle into 4 same sized regions to get 16 regions for the whole environment. Here we show the sample distribution examples for OBPRM (left) and UOBPRM (middle) in the mixture environment. UOBPRM generates more uniformly distributed configurations within each region than OBPRM especially in the area close to the boundary. The node distribution comparsion plot shows UOBPRM has better distribution than other sampling methods where 4.31% is the ideal percentage of the nodes for the regions containing the balls and 8.19% is the ideal percentage for the regions containing the cubes.

A Heterogeneous Tunnel Environment: This is a real planning problem with a narrow passage. We try to use different sampling methods to find a path between the start and the goal configurations. The more uniform the configurations are, the faster the sampler will be able to find a path in the roadmap by using fewer nodes and edges. The result shows UOBPRM performs teh best and PRM is not good at solving this kind of difficult problem.


We are also interested in the cost of generating samples. PRM is fast when the C-space is freem but it does not work well in difficult problems. Gaussian sampling and Bridge test sampling take longer to generate samples. The cost for OBPRM is largely related to the step size. The smaller the step size, the longer it takes to generate nodes. For UOBPRM, node generation time depends on both the length of the line segment and the step size. We examine cost in the single ball environment (left) and the tunnel environment (right).


View Demo

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Related Publications

UOBPRM: A uniformly distributed obstacle-based PRM, Hsin-Yi Yeh, Shawna Thomas, David Eppstein, Nancy M. Amato, IEEE/RSJ International Conference on Intelligent Robots and Systems, pp. 2655-2662, Oct 2012. DOI: 10.1109/IROS.2012.6385875
Keywords: obstacle-based, Sampling-Based Motion Planning
Links : [Published]

BibTex

@INPROCEEDINGS{6385875,
author={Yeh, Hsin-Yi and Thomas, Shawna and Eppstein, David and Amato, Nancy M.},
booktitle={2012 IEEE/RSJ International Conference on Intelligent Robots and Systems},
title={UOBPRM: A uniformly distributed obstacle-based PRM},
year={2012},
volume={},
number={},
pages={2655-2662},
doi={10.1109/IROS.2012.6385875}}


Abstract

This paper presents a new sampling method for motion planning that can generate configurations more uniformly distributed on C-obstacle surfaces than prior approaches. Here, roadmap nodes are generated from the intersections between C-obstacles and a set of uniformly distributed fixed-length segments in C-space. The results show that this new sampling method yields samples that are more uniformly distributed than previous obstacle-based methods such as OBPRM, Gaussian sampling, and Bridge test sampling. UOBPRM is shown to have nodes more uniformly distributed near C-obstacle surfaces and also requires the fewest nodes and edges to solve challenging motion planning problems with varying narrow passages.


An Obstacle-Based Rapidly-Exploring Random Tree, Samuel Rodriguez, Xinyu Tang, Jyh-Ming Lien, Nancy M. Amato, In Proc. IEEE International Conference on Robotics and Automation (ICRA), Orlando, Florida, USA, May 2006. DOI: 10.1109/ROBOT.2006.1641823
Keywords: obstacle-based, Rapidly-exploring Random Tree (RRT), Sampling-Based Motion Planning
Links : [Published]

BibTex

@INPROCEEDINGS{1641823, author={ {Rodriguez} and {Xinyu Tang} and {Jyh-Ming Lien} and N. M. {Amato}}, booktitle={Proceedings 2006 IEEE International Conference on Robotics and Automation, 2006. ICRA 2006.}, title={An obstacle-based rapidly-exploring random tree}, year={2006}, volume={}, number={}, pages={895-900}, doi={10.1109/ROBOT.2006.1641823}}


Abstract

Tree-based path planners have been shown to be well suited to solve various high dimensional motion planning problems. Here we present a variant of the Rapidly-Exploring Random Tree (RRT) path planning algorithm that is able to explore narrow passages or difficult areas more effectively. We show that both workspace obstacle information and C-space information can be used when deciding which direction to grow. The method includes many ways to grow the tree, some taking into account the obstacles in the environment. This planner works best in difficult areas when planning for free flying rigid or articulated robots. Indeed, whereas the standard RRT can face difficulties planning in a narrow passage, the tree based planner presented here works best in these areas


Ligand Binding with OBPRM and Haptic User Input: Enhancing Automatic Motion Planning with Virtual Touch, O. Burchan Bayazit , Guang Song , Nancy M. Amato , ACM Digital Library, College Station, Texas, USA, Oct 2000.
Keywords: Ligand Binding, Sampling-Based Motion Planning
Links : [Published]

BibTex

@MISC{Bayazit00ligandbinding,
author = {O. Burchan Bayazit and Guang Song and Nancy M. Amato},
title = {Ligand Binding with OBPRM and Haptic User Input: Enhancing Automatic Motion Planning with Virtual Touch},
year = {2000}
}


Abstract

In this paper, we present a framework for studying ligand binding which is based on techniques recently developed in the robotics motion planning community. We are especially interested in locating binding sites on the protein for a ligand molecule. Our work investigates the performance of a fully automated motion planner, as well improvements obtained when supplementary user input is collected using a haptic device. Our results applying an obstacle-based probabilistic roadmap motion planning algorithm (obprm) to some known protein-ligand pairs are very encouraging. In particular, we were able to automatically generate congurations close to, and correctly identify, the true binding site in the three protein-ligand complexes we tested. We nd that user input helps the planner, and a haptic device helps the user to understand the protein structure by enabling them to feel the forces which are hard to visualize.


OBPRM: An Obstacle-Based PRM for 3DWorkspaces, Nancy M. Amato, O. Burchan Bayazit, Lucia K. Dale, Christopher Jones, Daniel Vallejo, Robotics: The Algorithmic Perspective (Third Workshop on Algorithmic Foundations of Robotics, WAFR 1998), pp. 155-168, Houston, TX, Mar 1998.
Keywords: obstacle-based, Sampling-Based Motion Planning
Links : [Published]

BibTex

@inproceedings{ABDJV-wafr98-c
, author = "N. M. Amato and O. B. Bayazit and L. K. Dale and C. V. Jones and D. Vallejo"
, title = "{OBPRM:} An Obstacle-Based {PRM} for {3D} Workspaces"
, booktitle = "Proc. of Workshop on Algorithmic Foundations of Robotics {(WAFR'98)}"
, month = "March"
, pages = "155-168"
, year = "1998"
}


Abstract

Recently, a new class of randomized path planning methods, known as Probabilistic Roadmap Methods (prms) have shown great potential for solving compli­ cated high-dimensional problems, pr m s use randomiza­ tion (usually during preprocessing) to construct a graph of representative paths in C-space (a roadmap) whose vertices correspond to collision-free configurations of the robot and in which two vertices are connected by an edge if a path between the two corresponding config­ urations can be found by a local planning method.


A Randomized Roadmap Method for Path and Manipulation Planning, Nancy M. Amato, Yan Wu, Proceedings of IEEE International Conference on Robotics and Automation, Vol: 1, pp. 113-120, Minneapolis, MN, Apr 1996. DOI: 10.1109/ROBOT.1996.503582
Keywords: Sampling-Based Motion Planning
Links : [Published]

BibTex

@INPROCEEDINGS{503582,
author={Amato, N.M. and Wu, Y.},
booktitle={Proceedings of IEEE International Conference on Robotics and Automation},
title={A randomized roadmap method for path and manipulation planning},
year={1996},
volume={1},
number={},
pages={113-120 vol.1},
doi={10.1109/ROBOT.1996.503582}}


Abstract

This paper presents a new randomized roadmap method for motion planning for many DOF robots that can be used to obtain high quality roadmaps even when C-space is crowded. The main novelty in the authors' approach is that roadmap candidate points are chosen on C-obstacle surfaces. As a consequence, the roadmap is likely to contain difficult paths, such as those traversing long, narrow passages in C-space. The approach can be used for both collision-free path planning and for manipulation planning of contact tasks. Experimental results with a planar articulated 6 DOF robot show that, after preprocessing, difficult path planning operations can often be carried out in less than a second.