Steven Lavalle - Academia.edu (original) (raw)

Papers by Steven Lavalle

Automation and Control Engineering, 2006

Springer Tracts in Advanced Robotics, 2009

This paper introduces a problem in which an agent (robot, human, or animal) travels among obstacl... more This paper introduces a problem in which an agent (robot, human, or animal) travels among obstacles and binary detection beams. The task is to determine the possible agent path based only on the binary sensor data. This is a basic filtering problem encountered in many settings, which may arise from physical sensor beams or virtual beams that are derived from other sensing modalities. Methods are given for three alternative representations: 1) the possible sequences of regions visited, 2) path descriptions up to homotopy class, and 3) numbers of times winding around obstacles. The solutions are adapted to the minimal sensing setting; therefore, precise estimation, distances, and coordinates are replaced by topological expressions. Applications include sensor-based forensics, assisted living, security, and environmental monitoring.

2010 IEEE International Conference on Robotics and Automation, 2010

We present exploration and mapping strategies for a mobile robot moving among a finite collection... more We present exploration and mapping strategies for a mobile robot moving among a finite collection of convex obstacles in the plane. The obstacles are unknown to the robot, which does not have access to coordinates and cannot measure distances or angles. The robot has a unique sensor, called the gap sensor, that tracks the direction of the depth discontinuities in

The proliferation of embedded computing and wireless communication technologies are opening up tr... more The proliferation of embedded computing and wireless communication technologies are opening up tremendous possibilities for designing systems with unprecedented capabilities, in fields ranging from air and ground transportation, to law enforcement and homeland security, manufacturing, medical devices, environmental control, and energy management. The shift from human-controlled systems to highly automated systems in safety-critical applications places an enormous burden on the certification of new systems, as new types of failure modes are potentially introduced.

Abstract: Within the popular probabilistic roadmap (PRM)framework for motion planning, we challen... more Abstract: Within the popular probabilistic roadmap (PRM)framework for motion planning, we challenge the use of randomization.By applying quasi-random sampling techniques, we illustrateboth experimental and theoretical advantages of using deterministicsamples. Two quasi-random variants of PRM-based planners areproposed: 1) a classical PRM with quasi-random sampling, and 2)a quasi-random lattice-based Lazy roadmap. Both have been implemented,and are shown through experiments to oer some...

Proceedings of International Conference on Robotics and Automation, 1997

We introduce the problem of computing robot motion strategies that maintain visibility of a movin... more We introduce the problem of computing robot motion strategies that maintain visibility of a moving target in a cluttered workspace. Both motion constraints (as considered in standard motion planning) and visibility constraints (as considered in visual tracking) must be satisfied. Additional criteria, such as the total distance traveled, can be optimized. The general problem is divided into two categories, on

Springer Tracts in Advanced Robotics, 2005

In this paper, we discuss the field of sampling-based motion planning. In contrast to methods tha... more In this paper, we discuss the field of sampling-based motion planning. In contrast to methods that construct boundary representations of configuration space obstacles, sampling-based methods use only information from a collision detector as they search the configuration space. The simplicity of this approach, along with increases in computation power and the development of efficient collision detection algorithms, has resulted in the introduction of a number of powerful motion planning algorithms, capable of solving challenging problems with many degrees of freedom. First, we trace how samplingbased motion planning has developed. We then discuss a variety of important issues for sampling-based motion planning, including uniform and regular sampling, topological issues, and search philosophies. Finally, we address important issues regarding the role of randomization in sampling-based motion planning.

International Journal of Robotic Research, 2005

ABSTRACT. We consider coordination of multiple robots in a common environment, each robot having,... more ABSTRACT. We consider coordination of multiple robots in a common environment, each robot having,its own,(distinct) roadmap.,Our primary,contribution is a classification of and exact algorithm,for computing,vector-valued,— or Pareto — optima,for collision-free coordination. We indicate the utility of new,geometric techniques,from CAT(0) geometry,and,give an argument,that curvature,bounds,are the key distinguishing feature between,systems,for which,the classification is finite and for those in which it is not.

Given a collection of robots sharing a common environment, assume that each possesses an individu... more Given a collection of robots sharing a common environment, assume that each possesses an individual roadmap for its C-space and a cost function for attaining a goal. Vector-valued (or Pareto) optima for collision-free coordination are by no means unique: in fact, continua of optimal coordinations are possible. However, for cylindrical obstacles (those defined by pairwise interactions), we prove a finite

Computing optimal paths for mobile robots is an interesting and important problem. This paper pre... more Computing optimal paths for mobile robots is an interesting and important problem. This paper presents a method to compute the shortest path for a differential-drive mobile robot, which is a disc, among piecewise smooth and convex obstacles. We consider all trajectories that are composed of a finite number of subpaths inside the free space and on the boundary of obstacle

Proceedings 2001 ICRA. IEEE International Conference on Robotics and Automation (Cat. No.01CH37164), 2001

We address an on-line version of the visibility-based pursuit-evasion problem. We take a minimali... more We address an on-line version of the visibility-based pursuit-evasion problem. We take a minimalist approachinmodelingthecapabilitiesofapursuerrobot. Apointpursuermovesinanunknown,simply- connected, piecewise-smooth planar environment, and is given the task of locating any unpredictable, movingevadersthathaveunboundedspeed. Theevadersareassumedtobepointsthatmovecontinuously. To solve the problem, the pursuer must for each target have an unobstructed view of it at some time during execution. The pursuer is equipped with a range sensor

... Citations. 1696, Robot Motion Planning – Latombe - 1991. ... 146, Rapidly-Exploring Random Tr... more ... Citations. 1696, Robot Motion Planning – Latombe - 1991. ... 146, Rapidly-Exploring Random Trees: A New Tool for Path Planning – LaValle - 1998. ... 124, Nonholonomic multibody mobile robots : Controllability and motion planning in the presence of obstacles – Latombe - 1991. ...

Proceedings of the 2005 IEEE International Conference on Robotics and Automation, 2005

Sampling-based planners have solved difficult problems in many applications of motion planning in... more Sampling-based planners have solved difficult problems in many applications of motion planning in recent years. In particular, techniques based on the Rapidly-exploring Random Trees (RRTs) have generated highly successful singlequery planners. Even though RRTs work well on many problems, they have weaknesses which cause them to explore slowly when the sampling domain is not well adapted to the problem.

IEEE International Conference on Robotics and Automation, 2004. Proceedings. ICRA '04. 2004, 2004

This paper addresses the problem of generating uniform deterministic samples over the spheres and... more This paper addresses the problem of generating uniform deterministic samples over the spheres and the three-dimensional rotation group, SO(3). The target applications include motion planning, optimization, and verification problems in robotics and in related areas, such as graphics, control theory and computational biology. We introduce an infinite sequence of samples that is shown to achieve: 1) low-dispersion, which aids in the development of resolution complete algorithms, 2) lattice structure, which allows easy neighbor identification that is comparable to what is obtained for a grid in R d , and 3) incremental quality, which is similar to that obtained by random sampling. The sequence is demonstrated in a samplingbased motion planning algorithm.

2007 46th IEEE Conference on Decision and Control, 2007

Abstract—We consider finding a time-optimal trajectory for an airplane from some starting point a... more Abstract—We consider finding a time-optimal trajectory for an airplane from some starting point and orientation to some final point and orientation. Our model extends the Dubins car [15] to have altitude, which leads to Dubins airplane. We assume that the system has ...

Robotics Research, 1998

Autonomous Observers are mobile robots that cooperativelyperform vision tasks. Their designraises... more Autonomous Observers are mobile robots that cooperativelyperform vision tasks. Their designraises new issues in motion planning, where visibilityconstraints and motion obstructions mustbe simultaneously taken into account. This paperpresents the concept of an Autonomous Observerand its applications. It discusses three problems inmotion planning with visibility constraints: modelbuilding, target finding, and target tracking.1 IntroductionWe are interested in mobile robots which...

Journal of image guided surgery, 1995

The computer-assisted spine surgery system presented in this paper follows the basic ideas which ... more The computer-assisted spine surgery system presented in this paper follows the basic ideas which have been developed for computer-assisted medical interventions (CAMI) in our lab since 1985. There are three steps to insert a linear tool inside vertebral pedicles. First, the surgeon defines an optimal trajectory on pre-operative computed tomography. Second, this trajectory is reported in the operating room coordinate system using an intra-operative sensor and a registration algorithm. Third, a guiding system helps the surgeon follow the selected trajectory. In this paper, we present an implementation of this method that uses only a 3-dimensional optical localizer. Results on cadaver specimens and on the first seven patients are presented.

Proceedings 2007 IEEE International Conference on Robotics and Automation, 2007

This paper characterizes the information space of a robot moving in the plane with limited sensin... more This paper characterizes the information space of a robot moving in the plane with limited sensing. The robot has a landmark detector, which provides the cyclic order of the landmarks around the robot, and it also has a touch sensor, that indicates when the robot is in contact with the environment boundary. The robot cannot measure any precise distances or

Contemporary Mathematics, 2007

This paper considers a robot that moves in the plane and is only able to sense the cyclic order o... more This paper considers a robot that moves in the plane and is only able to sense the cyclic order of landmarks with respect to its current position. No metric information is available regarding the robot or landmark positions; moreover, the robot does not have a compass or odometers (e.g., coordinates). We carefully study the information space of the robot, and establish its capabilities in terms of mapping the environment and accomplishing tasks, such as navigation and patrolling. The information space can be nicely characterized using the notion of order type, which provides information powerful enough to determine which points lie inside the convex hulls of subsets of landmarks. An extension to this work using braid groups is briefly discussed at the end of the paper.

Automation and Control Engineering, 2006

Springer Tracts in Advanced Robotics, 2009

This paper introduces a problem in which an agent (robot, human, or animal) travels among obstacl... more This paper introduces a problem in which an agent (robot, human, or animal) travels among obstacles and binary detection beams. The task is to determine the possible agent path based only on the binary sensor data. This is a basic filtering problem encountered in many settings, which may arise from physical sensor beams or virtual beams that are derived from other sensing modalities. Methods are given for three alternative representations: 1) the possible sequences of regions visited, 2) path descriptions up to homotopy class, and 3) numbers of times winding around obstacles. The solutions are adapted to the minimal sensing setting; therefore, precise estimation, distances, and coordinates are replaced by topological expressions. Applications include sensor-based forensics, assisted living, security, and environmental monitoring.

2010 IEEE International Conference on Robotics and Automation, 2010

We present exploration and mapping strategies for a mobile robot moving among a finite collection... more We present exploration and mapping strategies for a mobile robot moving among a finite collection of convex obstacles in the plane. The obstacles are unknown to the robot, which does not have access to coordinates and cannot measure distances or angles. The robot has a unique sensor, called the gap sensor, that tracks the direction of the depth discontinuities in

The proliferation of embedded computing and wireless communication technologies are opening up tr... more The proliferation of embedded computing and wireless communication technologies are opening up tremendous possibilities for designing systems with unprecedented capabilities, in fields ranging from air and ground transportation, to law enforcement and homeland security, manufacturing, medical devices, environmental control, and energy management. The shift from human-controlled systems to highly automated systems in safety-critical applications places an enormous burden on the certification of new systems, as new types of failure modes are potentially introduced.

Abstract: Within the popular probabilistic roadmap (PRM)framework for motion planning, we challen... more Abstract: Within the popular probabilistic roadmap (PRM)framework for motion planning, we challenge the use of randomization.By applying quasi-random sampling techniques, we illustrateboth experimental and theoretical advantages of using deterministicsamples. Two quasi-random variants of PRM-based planners areproposed: 1) a classical PRM with quasi-random sampling, and 2)a quasi-random lattice-based Lazy roadmap. Both have been implemented,and are shown through experiments to oer some...

Proceedings of International Conference on Robotics and Automation, 1997

We introduce the problem of computing robot motion strategies that maintain visibility of a movin... more We introduce the problem of computing robot motion strategies that maintain visibility of a moving target in a cluttered workspace. Both motion constraints (as considered in standard motion planning) and visibility constraints (as considered in visual tracking) must be satisfied. Additional criteria, such as the total distance traveled, can be optimized. The general problem is divided into two categories, on

Springer Tracts in Advanced Robotics, 2005

In this paper, we discuss the field of sampling-based motion planning. In contrast to methods tha... more In this paper, we discuss the field of sampling-based motion planning. In contrast to methods that construct boundary representations of configuration space obstacles, sampling-based methods use only information from a collision detector as they search the configuration space. The simplicity of this approach, along with increases in computation power and the development of efficient collision detection algorithms, has resulted in the introduction of a number of powerful motion planning algorithms, capable of solving challenging problems with many degrees of freedom. First, we trace how samplingbased motion planning has developed. We then discuss a variety of important issues for sampling-based motion planning, including uniform and regular sampling, topological issues, and search philosophies. Finally, we address important issues regarding the role of randomization in sampling-based motion planning.

International Journal of Robotic Research, 2005

ABSTRACT. We consider coordination of multiple robots in a common environment, each robot having,... more ABSTRACT. We consider coordination of multiple robots in a common environment, each robot having,its own,(distinct) roadmap.,Our primary,contribution is a classification of and exact algorithm,for computing,vector-valued,— or Pareto — optima,for collision-free coordination. We indicate the utility of new,geometric techniques,from CAT(0) geometry,and,give an argument,that curvature,bounds,are the key distinguishing feature between,systems,for which,the classification is finite and for those in which it is not.

Given a collection of robots sharing a common environment, assume that each possesses an individu... more Given a collection of robots sharing a common environment, assume that each possesses an individual roadmap for its C-space and a cost function for attaining a goal. Vector-valued (or Pareto) optima for collision-free coordination are by no means unique: in fact, continua of optimal coordinations are possible. However, for cylindrical obstacles (those defined by pairwise interactions), we prove a finite

Computing optimal paths for mobile robots is an interesting and important problem. This paper pre... more Computing optimal paths for mobile robots is an interesting and important problem. This paper presents a method to compute the shortest path for a differential-drive mobile robot, which is a disc, among piecewise smooth and convex obstacles. We consider all trajectories that are composed of a finite number of subpaths inside the free space and on the boundary of obstacle

Proceedings 2001 ICRA. IEEE International Conference on Robotics and Automation (Cat. No.01CH37164), 2001

We address an on-line version of the visibility-based pursuit-evasion problem. We take a minimali... more We address an on-line version of the visibility-based pursuit-evasion problem. We take a minimalist approachinmodelingthecapabilitiesofapursuerrobot. Apointpursuermovesinanunknown,simply- connected, piecewise-smooth planar environment, and is given the task of locating any unpredictable, movingevadersthathaveunboundedspeed. Theevadersareassumedtobepointsthatmovecontinuously. To solve the problem, the pursuer must for each target have an unobstructed view of it at some time during execution. The pursuer is equipped with a range sensor

... Citations. 1696, Robot Motion Planning – Latombe - 1991. ... 146, Rapidly-Exploring Random Tr... more ... Citations. 1696, Robot Motion Planning – Latombe - 1991. ... 146, Rapidly-Exploring Random Trees: A New Tool for Path Planning – LaValle - 1998. ... 124, Nonholonomic multibody mobile robots : Controllability and motion planning in the presence of obstacles – Latombe - 1991. ...

Proceedings of the 2005 IEEE International Conference on Robotics and Automation, 2005

Sampling-based planners have solved difficult problems in many applications of motion planning in... more Sampling-based planners have solved difficult problems in many applications of motion planning in recent years. In particular, techniques based on the Rapidly-exploring Random Trees (RRTs) have generated highly successful singlequery planners. Even though RRTs work well on many problems, they have weaknesses which cause them to explore slowly when the sampling domain is not well adapted to the problem.

IEEE International Conference on Robotics and Automation, 2004. Proceedings. ICRA '04. 2004, 2004

This paper addresses the problem of generating uniform deterministic samples over the spheres and... more This paper addresses the problem of generating uniform deterministic samples over the spheres and the three-dimensional rotation group, SO(3). The target applications include motion planning, optimization, and verification problems in robotics and in related areas, such as graphics, control theory and computational biology. We introduce an infinite sequence of samples that is shown to achieve: 1) low-dispersion, which aids in the development of resolution complete algorithms, 2) lattice structure, which allows easy neighbor identification that is comparable to what is obtained for a grid in R d , and 3) incremental quality, which is similar to that obtained by random sampling. The sequence is demonstrated in a samplingbased motion planning algorithm.

2007 46th IEEE Conference on Decision and Control, 2007

Abstract—We consider finding a time-optimal trajectory for an airplane from some starting point a... more Abstract—We consider finding a time-optimal trajectory for an airplane from some starting point and orientation to some final point and orientation. Our model extends the Dubins car [15] to have altitude, which leads to Dubins airplane. We assume that the system has ...

Robotics Research, 1998

Autonomous Observers are mobile robots that cooperativelyperform vision tasks. Their designraises... more Autonomous Observers are mobile robots that cooperativelyperform vision tasks. Their designraises new issues in motion planning, where visibilityconstraints and motion obstructions mustbe simultaneously taken into account. This paperpresents the concept of an Autonomous Observerand its applications. It discusses three problems inmotion planning with visibility constraints: modelbuilding, target finding, and target tracking.1 IntroductionWe are interested in mobile robots which...

Journal of image guided surgery, 1995

The computer-assisted spine surgery system presented in this paper follows the basic ideas which ... more The computer-assisted spine surgery system presented in this paper follows the basic ideas which have been developed for computer-assisted medical interventions (CAMI) in our lab since 1985. There are three steps to insert a linear tool inside vertebral pedicles. First, the surgeon defines an optimal trajectory on pre-operative computed tomography. Second, this trajectory is reported in the operating room coordinate system using an intra-operative sensor and a registration algorithm. Third, a guiding system helps the surgeon follow the selected trajectory. In this paper, we present an implementation of this method that uses only a 3-dimensional optical localizer. Results on cadaver specimens and on the first seven patients are presented.

Proceedings 2007 IEEE International Conference on Robotics and Automation, 2007

This paper characterizes the information space of a robot moving in the plane with limited sensin... more This paper characterizes the information space of a robot moving in the plane with limited sensing. The robot has a landmark detector, which provides the cyclic order of the landmarks around the robot, and it also has a touch sensor, that indicates when the robot is in contact with the environment boundary. The robot cannot measure any precise distances or

Contemporary Mathematics, 2007

This paper considers a robot that moves in the plane and is only able to sense the cyclic order o... more This paper considers a robot that moves in the plane and is only able to sense the cyclic order of landmarks with respect to its current position. No metric information is available regarding the robot or landmark positions; moreover, the robot does not have a compass or odometers (e.g., coordinates). We carefully study the information space of the robot, and establish its capabilities in terms of mapping the environment and accomplishing tasks, such as navigation and patrolling. The information space can be nicely characterized using the notion of order type, which provides information powerful enough to determine which points lie inside the convex hulls of subsets of landmarks. An extension to this work using braid groups is briefly discussed at the end of the paper.