teaching robot motion planning mark moll , janice bordeaux ...mmoll/publications/moll... ·...

Teaching Robot Motion Planning

Mark Moll1, Janice Bordeaux2 and Lydia E. Kavraki11 Department of Computer Science, Rice University, Houston, TX 77005, USA

2 George R. Brown School of Engineering, Rice University, Houston, TX 77005, USA{mmoll,jbordeau,kavraki}@rice.edu

Abstract

Robot motion planning is a fairly intuitive andengaging topic, yet it is difficult to teach. Thematerial is taught in undergraduate and gradu-ate robotics classes in computer science, elec-trical engineering, mechanical engineering andaeronautical engineering, but at an abstract level.Deep learning could be achieved by having stu-dents implement and test different motion plan-ning strategies. However, a full implementationof motion planning algorithms by undergraduatesis practically impossible in the context of a sin-gle class, even by students proficient in program-ming. By helping undergraduates grasp motionplanning concepts in series of courses designedfor increasing advanced levels, we can open thefield to young and enthusiastic talent. This cannotbe done by asking students to implement motionplanning algorithms from scratch or access thou-sands of lines of code and just figure out howthings work. We present an ongoing project todevelop microworld software and a modeling cur-riculum that supports undergraduate acquisitionof motion planning knowledge and tool use bycomputer science and engineering students.

1 Introduction

Robots have fascinated people for generations.Today, robots are built for applications as diverseas exploring Mars and the Earth’s deep seas, de-mining war zones, cleaning toxic waste, assem-bling cars, inspecting pipes in industrial plants,driving autonomously in off-road and urban envi-ronments, and mowing lawns. Robots are also

interacting with humans in a variety of ways:robots are museum guides, robot pets entertain,and robots assist surgeons in life threatening op-erations. By integrating science, technology, en-gineering, and mathematics (STEM disciplines)in a unique way, the field of robotics studies boththe design of new mechanisms and the algorithmsand frameworks that make robots useful in thephysical world.

This project aims to provide software tools andapplications that will fill some of the existing cur-ricular gaps in college level robotics education.Robotics is not exploited for its fascinating real-world examples and applications in STEM disci-plines. In many high-schools, robotics competi-tions are used to draw students into college andSTEM disciplines. Each year the FIRST compe-titions1 attract hundreds of students from grades1 to 12 who build robots and compete in well-defined contests. Lego MindStorms [1] have pro-vided another appealing entry to the basics ofrobotics in high school and undergraduate edu-cation. Students can quickly assemble a robotusing the basic Lego bricks and special bricks forsensors and actuators. Also, the robot can be pro-grammed through a regular PC. Although studentsspend time calibrating the robots and repeat thedesign-test-modify loop many times to achieve aresult [2], there is no doubt that such efforts haveattracted many students and particularly womento science and engineering. At the freshman levelin colleges, robotics is used to attract studentsto STEM fields. Because of the interdisciplinary

1FIRST (For Inspiration and Recognition of Science andTechnology) http://www.usfirst.org/who/default.aspx?id=34

COMPUTERS IN EDUCATION JOURNAL 1

In: Computers in Education (Special Issue on Novel Approaches to Robotics Education), 20(3):50–59, 2010.

nature of robotics, but also the excitement of build-ing a robot that works and does something useful,colleges across the country strive to have a designclass on robotics to convince students that STEMdisciplines are challenging and fun.A Gap in College-Level Robotics EducationExists After an initial intro-level course onrobotics, students typically have to wait till theirsenior year to take another robotics course. Asa result senior courses are extremely demanding.The reasons are multiple. Robotics offered at thesenior or beginning graduate level tend to includemany topics in an effort to teach the students asmuch as possible about an extremely rich sub-ject. Typically, course instructors are faced withthe difficult task of covering breadth and depthwhile keeping the class manageable and exciting.Robotics textbooks [3–5] cover many topics andchallenge the student and the instructor to keep upwith the material.Goals of this Project This project concentrateson one key concept in robotics: motion planning.Motion planning is a central topic in robotics anddeals with finding feasible collision-free paths thattake a robot from an initial to a final state. Mo-tion capabilities are intrinsically related to robotsand tend to occupy a significant part of upper-level robotics classes. Due to significant advancesover the last decade, motion planning is a verymature field [3–5]. Of the two most recent text-book in robotics, one concentrated entirely onmotion planning [5] and it occupied almost halfof the other book [3]. However, teaching motionplanning is difficult, in part because a consider-able mathematical and algorithmic background isneeded to comprehend critical ideas. As a result,either the module is over by the time students areready for the hands-on experience, or students lackthe the programming background to implementan interesting project.

The project described in this paper aims to fill thegap in robotics curriculum by developing a teach-ing module that includes an extensible softwaretool and related assignments. Also, we aim toengage a broad spectrum of faculty and students,and develop a community focused on motion plan-

ning learning. The effectiveness of our motionplanning curriculum for diverse learners will beassessed at Rice University and other partner in-stitutions. The teaching module’s software tooldescribed in this paper has an easy-to-use interfaceand mitigates many of the problems mentionedabove. A set of assignments is developed, imple-mented and assessed at Rice University and otherinterested partner institutions. A feedback loopwill be implemented to improve the curriculumso that it can be used by other institutions. Also,we aim to engage a broad spectrum of faculty andstudents and promote the growth of a user com-munity that will make the efforts self-sustainablein the long run.

2 BackgroundA Brief History of Motion Planning The gen-eral motion planning problem has been studiedextensively in the past. The classical case is thegeneral mover’s problem, which is posed for poly-hedral robots operating in a polyhedral workspace.This problem was shown to be PSPACE-completein [6]. Advances in robotics and modeling pres-sures the development of practical algorithms forrobots with many degrees of freedom. A newgeneration of sampling-based motion planningalgorithms emerged that preprocesses a robot’sconfiguration space to construct a graph repre-sentation, which approximates the connectivityof the configuration space. See figure 1 for ahigh-level overview of sampling-based planningalgorithms. The predominant family of these al-gorithms was pioneered with the introduction ofthe Probabilistic Roadmap Method (PRM) [7].PRM techniques make some sacrifices over ex-act (exponential-time) algorithms. For example,path non-existence cannot be proven using PRM.However, a weaker completeness result has beenproven: if a path exists then a PRM planner willeventually find it [8].

PRM provides a good solution to a broad classof motion planning problems where the robot op-erates in a known environment for a good dealof time. Many times one is interested in gettingto the goal as soon as possible without exploring


Figure 1: Sampling-based motion planning. Each red point represents a robot configuration, while the dark grayareas represent ‘forbidden’ areas corresponding to, e.g., collisions. The dimensionality of a robot’s configurationspace is typically much larger than the two shown here (a free moving 3D rigid body already has a 6-dimensionalconfiguration space: 3 for translation and 3 for rotation.) Left: configurations are sampled, checked for collisions, andconnected to nearby other configurations when possible. This results in a graph called the roadmap. Middle: to find apath between two goal configurations, they are first connected to the roadmap, and a path is found through a graphsearch. Right: tree-based algorithms “grow” a tree from the start configuration by iteratively adding tree nodes andedges, often biasing the tree growth towards the goal.

the environment. This led to the development oftree-based planners [9–11]. Tree-based plannersoperate by constructing a tree in the configurationspace. Tree-based methods have some advantagesover a roadmap method: they concentrate on oneor two connected components of the space and pri-marily connect configurations by integrating thecontrols of the system. This novel way of generat-ing configurations and paths is critical in planningfor systems with motion constraints [9, 12, 13].Recent Books In the last few years severalrobotics textbooks have been published [3, 5, 14].These books are currently used in upper level un-dergraduate classes or introductory graduate levelclasses. The first two textbooks cover motion plan-ning extensively. The material is also covered inthe Handbook of Discrete and Computational Ge-ometry [15], the Handbook of Robotics [16], anda recent review article [17].Available Software If students had to write mo-tion planning algorithm implementations fromscratch, much of their time would be spent onwriting the low-level data structures and not onunderstanding the higher-level algorithm. Thereexist a few motion planning software packagessuch the Motion Strategies Library (MSL) [18],the Motion Planning Kit (MPK) [19], and Open-RAVE [20], but they contain only a limited num-ber of algorithms or have not been developed forseveral years (or both). KineoWorks [21] pro-vides commercial motion planning software for

academic research and industrial applications. Re-cently, a new motion planning package calledVizmo++ [22] was introduced for possible educa-tional use, but it appears to have been abandoned(source code or binaries of the software were neverreleased). In 2007, our group released the Object-Oriented Programming System for Motion Plan-ning (OOPSMP) [23]. Although initially releasedas a research tool, through continued developmentit has become viable to use as a teaching tool aswell.

3 Development of Motion PlanningSoftware

3.1 Software Overview

The software used for the teaching module isbased on what is currently offered by the Object-Oriented Programming System for Motion Plan-ning (OOPSMP, http://oopsmp.kavrakilab.org). Itis a software system that provides easy accessto many state-of-the-art sampling-based motionplanning algorithms and underlying data struc-tures. Many motion planning algorithms sharemany similar components, and OOPSMP allowsstudents to quickly design their own planner bycombining existing components. We have spentconsiderable effort in adapting OOPSMP for edu-cational purposes. This is an ongoing process. Wewill first give an overview of existing functional-ity:


Table 1: Motion planning algorithm components. Variants of motion planning algorithms can becomposed by choosing different options in each column.

sampling strategy:• uniform• Gaussian• obstacle-based• bridge test

connection strategy:• random nearest neighbors• approx. nearest neighbors• exact nearest neighbors

path generation:• geodesics (“straight lines”)• best or random control• approx. steer• collision check: incremental,

subdivision

state space:• rotation+translation 2D• rotation+translation 3D• controller: car, diff. drive,

unicycle

• OOPSMP contains implementations of popu-lar motion planning algorithms such as Proba-bilistic Roadmap Methods (PRM) [7], Rapidly-exploring Random Trees (RRT) [13], Expan-sive Spaces Trees (EST) [24], bi-directionaltree planners, and others. There are differentsampling strategies (uniform, Gaussian [25],obstacle-based [26], bridge test [27]) that canbe used with any of the motion planning strate-gies.• Each algorithm can produce solutions for prob-

lems involving one or multiple robots. Eachrobot can rotate and translate, but a user canalso impose constraints on the kinematics anddynamics that restrict the possible motions.OOPSMP implements several kinodynamicmodels of cars, differential drives, and unicy-cles, and makes it easy to add new models ofdifferent robotic systems.• OOPSMP also contains many general purpose

functions and data structures for:Linear algebra: low-dimensional vector andmatrix operations.Topology: rigid body topology in 2D and 3D,such as SO(2) and SE(3) (rotations in 3D asquaternions).Numerical integration: several fixed-step andadaptive-step methods up to 8th order.Data structures and algorithms: sets, disjointsets, update-able heaps, graphs, depth-firstsearch, breadth-first search, Dijkstra’s shortestpath, A∗ search.Proximity algorithms: nearest neighbors formetric spaces.• OOPSMP can be run as command line tool or

run interactively with a simple graphical inter-face. Figure 2 shows some example problems

in 2D and 3D, along with solution paths. It runson Microsoft Windows, Linux, and Mac OS X.

OOPSMP implements motion planners in amodular, and objected-oriented fashion. This isdone in a plug-and-play fashion: users can eas-ily create new components as plugins and havetheir functionality immediately available at run-time without having to recompile any part ofOOPSMP. Table 1 gives an overview of the com-mon components of a motion planning algorithmand which options are available for each compo-nent in OOPSMP. Each motion-planning compo-nent (data structures and low-level algorithms)can be combined and plugged into each motionplanner giving rise to a combinatorially large num-ber of possibilities. This provides a great degreeof flexibility in evaluating the impact of differ-ent components and comparing different motionplanners.

Figure 2: Screenshots of the graphical version ofOOPSMP.


robot OOPSMP console window

OOPSMP motion planning queriesSolution to a selected query

Figure 3: The SketchUp interface to the OOPSMP software.

3.2 Education-Focused Software Develop-ment

We have developed a new graphical user interfaceto OOPSMP that relies on Google Sketchup, apopular, free 3D modeling program. This makesthe tool more accessible to students with little pro-gramming experience, but—just as importantly—it also allows students to explore the high-level be-havior of different motion planning algorithms ondifferent problems without getting bogged downin writing low-level code. Through a plugin forSketchUp a student can define and solve motionplanning programs using OOPSMP. The plugingenerates the input files for OOPSMP, runs theOOPSMP program in the background, and readsback the output. Instead of running OOPSMPinside SketchUp, one can also export motion plan-ning problems and run the OOPSMP program out-side of SketchUp. This is useful for more complexproblems that may take a long time to solve. TheSketchUp plugin makes it much easier to try outdifferent planning algorithms and see the effect ofchanging algorithm parameters. Figure 3 showsthe interface of the SketchUp plugin. For a “robot”in the form of a free-flying L-shaped block sev-eral motion planning queries have been defined.

Each query consists of a start and goal pose. Af-ter OOPSMP has been called from SketchUp tosolve the queries, the solutions can be shown inanimation. SketchUp provides access to the on-line Google 3D Warehouse, a repository wherepeople around the world deposit geometric mod-els of everything ranging from simple householdobjects to realistic car models to complete build-ings. This makes it very simple to create realisticenvironments and robots to test motion planningalgorithms. The significance of this is not to be un-derestimated. In the past, many motion planningalgorithms could only be demonstrated on simpletoy examples, because it would take an inordinateamount of effort to create complex environments.

4 Motion Planning CurriculumDevelopment

We have developed a series of assignments thatgradually introduce students to motion planningalgorithms. The lecture material necessary to com-plete these assignments is described in at least tworobotics textbooks currently on the market [3, 5].The assignments will be given to students takingrobotics courses at Rice. Formal assessment willbe done and feedback will be solicited from the in-


structors and the students to continuously improvethe assignments which will use OOPSMP. Sincethe courses will be taught several times, laying thebasis for correct assessment is important for thesuccess of this project.

With the enhancements described above, it willbe possible to cover a broad range of problems inassignments. For instance, in a robotics class thatis more tailored towards mechanical engineeringstudents, example exercises can be used that em-phasize control aspects of motion planning. Forcomputer science students assignments can focuson the complexity of motion planning for high-dimensional systems.

4.1 Assignments

The assignments are set up so that each assign-ment builds on the previous assignment, but with-out directly depending on it. Furthermore, foreach assignment we have developed several ver-sions that vary in depth. By varying the depth ofeach assignment and the number of assignmentsinstructors can adjust the assignments to the levelof the students and the amount of time they wantto allocate to the motion planning module in theirrobotics class. We have initially divided the as-signments into four initial categories:Getting familiar with motion planning algo-rithms The students will use the self-paced tuto-rials from the OOPSMP handbook to get familiarwith the basic workflow of solving motion plan-ning problems: (a) define an environment, (b)define a robot, (c) define motion planning queriesby specifying pairs of start/goal configurations,(d) select a motion planning algorithm and its pa-rameters, and (e) solve the problem by runningthe algorithm. This assignment can be completedusing the SketchUp interface to OOPSMP.Develop a ‘naıve’ motion planning algorithmIn these assignments students have to write somecode that implements a simplified version of oneof the algorithms contained in OOPSMP. In oneassignment a code template is given and studentshave to “fill in the blanks.” This will teach stu-

dents the basic code structure. OOPSMP consistsof thousands of lines of C++ code. This can beoverwhelming at first, so an assignment that illus-trates which classes need to be implemented andhow they are connected is useful. A subsequent as-signment will ask the students to implement a vari-ant of an algorithm that already exists in OOPSMP.An important part of this assignment is the perfor-mance evaluation of an algorithm. It is not alwayseasy to decide which algorithm is better. Run-time matters, but the number of vertices and edgescreated in the roadmap or tree are also importantsince they can indicate how the algorithm perfor-mance would scale to more complex problems.Many motion planning algorithms rely on randomsampling, so runs need to be repeated to obtaina reliable estimate of expected performance. An-other complication in performance measurementis that there really is no standard benchmark prob-lem. Any algorithm needs to be evaluated on a setof various benchmarks to get an understanding ofits strengths and weaknesses.Comparison of algorithms The comparison ofmotion planning algorithms requires critical think-ing. Students learn that determining which algo-rithm is ‘better’ is non-trivial. Besides run-time,many other performance metrics are important,such as the number of collision checks or the mem-ory use. The selection of good test cases is alsocritical. Considering both performance metricsand problem selection will help students general-ize specific results and evaluate which algorithmsare more likely to scale up to more complex sys-tems.Replace a core component with an alternativeimplementation This assignment will help stu-dents acquire a deeper understanding of the nutsand bolts of motion planning. At Rice Univer-sity, where OOPSMP has already been used in arobotics class taught by Kavraki, students couldchoose projects such as: (a) implement a bettercollision checker, (b) write a different proximitydata structure, or (c) implement a new motionplanning algorithm that is not a simple variant ofwhat is available in OOPSMP.


Open-ended projects At Rice, we have also de-veloped several ideas for projects that can beimplemented at varying levels of difficulty. Ex-amples include path optimization (of, e.g., pathlength, smoothness, energy consumption, etc.),path clustering, dynamic manipulation with a pla-nar manipulator (with kinodynamic constraintsand possibly under-actuated joints), and forma-tion planning.

4.2 Documentation

To complete the assignments students need docu-mentation that explains in detail what functional-ity is available and how to use it. Currently, thedocumentation consists of a high-level descrip-tion of the code structure, basic usage instruc-tions as well as a large collection of linked webpages that are automatically extracted from theextensive comments in the code. As part of thisproject we will develop a comprehensive referencemanual that provides the background and concep-tual framework that undergraduates for a roboticscourse are expected to have. To get started withOOPSMP, though, a reference manual is not al-ways what the students need most. Initially, theywill need a handbook that explains at a high levelhow all the pieces of the program fit together andincludes tutorials with worked-out examples andscreencasts. Such a handbook is virtually non-existent at this point. We will also link the lec-ture material to assignments by inserting refer-ences to a robotics textbook [3] in all documenta-tion. This book is used in many robotics classesaround the country (see the web site for the bookat http://motionplanning.com).

We have a developed a tutorial for OOPSMPthat consists of slides, movies, and code. Thetutorial materials are available online at http://www.kavrakilab.org/OOPSMPtutorial. The tuto-rial was held in September 2008 at the IEEE/RSJInternational Conference on Intelligent Robotsand Systems, one of the major conferences inrobotics. Faculty can use the tutorial as-is, or justuse selected material in their own slides.

4.3 Assessment

Systematic, formal outcomes assessment will beconducted to evaluate the effectiveness of the tech-nical, curricular and community building activi-ties. Both formative and summative evaluationmethods are included. For example, the new tech-nology will be pilot-tested with undergraduatesand the feedback used to inform design decisionson critical components and functionality. Also,evidence of student learning outcomes will be col-lected at Rice University and other partner institu-tions on an ongoing basis, strengths and weaknessidentified, and the results used to improve curricu-lum materials and teaching methods. In contrast,the project’s success will be determined at theend of the study by evaluating the overall level ofachievement attained by student participants. Inaddition, student and instructor surveys designedto capture quantitative data (e.g., the amount of in-dependent exploration) and qualitative data (e.g.,student suggestions for ways to improve the cur-riculum or technology) will augment measures ofstudent learning. An independent expert will behired 1–2 weeks each year to analyze and helpevaluate the results.

5 Dissemination

Our work can be used to broaden the dialog be-tween students and faculty and beyond institu-tional boundaries by creating a worldwide com-munity of OOPSMP users. In the long run, weaim for the OOPSMP project to be self-sustaining.Over 200 people from around the world have al-ready registered as OOPSMP users. We currentlyhave an official mailing list for users to discussOOPSMP. This is mostly used for announcements.Since many people are already inundated withemail these days, we therefore plan to make of-ficial announcements available through both ablog/RSS feed and the mailing list.

Our work can also be used to form partnershipswith faculty members who are planning to use ourteaching module in their classes. In exchange forfaculty and student participation in surveys, we


would be able to assist in the design and selectionof assignments tailored for the specific needs of aclass. Anyone can download and use the teachingmodule without this additional overhead. We willkeep track of the number of instructors includingthis module in their courses. The growth and en-gagement of the OOPSMP user community into acollaborative educational resource will be trackedthrough the project’s blog/RSS feed and emaillist. User community responses to a brief onlineuser registration form and basic web analytics willdocument community size and user characteris-tics, along with the development of communitycollaborative activities.

6 Conclusion

This project aspires to transform how college stu-dents learn robotics by offering a motion planningcurriculum that enhances deep learning and issupported by an integrated software environment.Students are challenged to work on real-worldrobotics problems, and develop deeper knowledgeby reflecting on and formally evaluating their re-sults. We scaffold learning by freeing students oftedious details and heavy programming and helpthem to develop critical thinking within and out-side robotics through a hands-on problem-basedlearning approach. In the long run, the productsof this project can strengthen other courses incomputer science and engineering, and motivateyounger students to pursue STEM careers. Thework will be widely disseminated through the Na-tional Science Digital Library (NSDL).

Acknowledgements

This project is funded by NSF CCLI 0920721.The authors are indebted to Kostas Bekris, ErionPlaku and the other members of the Kavraki Labfor developing the initial version of OOPSMP.They are also grateful for the work done by NickBridle and Nicholas Feltman that resulted in theOOPSMP plugin for Google SketchUp.

References

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Biographical Information

Mark Moll is a research scientist in the Physicaland Biological Computing group at Rice Univer-sity. Previously, he has was a research scientistat the Information Sciences Institute at the Uni-versity of Southern California. Before that, hewas a post-doctoral research associate at Rice Uni-versity in the Physical and Biological ComputingGroup. He a obtained a Ph.D. degree in Com-puter Science from Carnegie Mellon Universityin 2002 and a M.S. degree in Computer Sciencefrom the University of Twente in the Netherlandsin 1995. His current research interests include mo-tion planning, and geometric problems in roboticsand computational structural biology.

Janice Bordeaux, Associate Dean of theGeorge R. Brown School of Engineering and aLicensed Psychologist, is an expert on learning inhigher education, educational program improve-ment processes, and outcomes assessment. Inthe last nine years Bordeaux has collaborated onnumerous federally and privately funded educa-


tional projects including interdisciplinary, multi-institutional, and web-based initiatives for educa-tional communities.

Lydia E. Kavraki received the Ph.D. degree incomputer science from Stanford University, Stan-ford, CA, U.S.A. She is currently the Noah Hard-ing Professor of computer science and bioengi-neering with Rice University, Houston, TX. Sheis the author or coauthor of more than 150 tech-nical papers and a robotics textbook: Principlesof Robot Motion (MIT Press, 2005). Her currentresearch interests include motion planning for con-tinuous and hybrid systems, connection of formalmethods and task planning with motion planning,manipulation, networked multiagent systems, andapplications of robotics methods to biology.

Prof. Kavraki is a Fellow of the Associationfor the Advancement of Artificial Intelligence andthe American Institute for Medical and BiologicalEngineering. She is the recipient of the Associ-ation for Computing Machinery Grace MurrayHopper Award and the Early Academic CareerAward from the IEEE Robotics and AutomationSociety. Information about her work can be foundat http://www.kavrakilab.org.


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