Showing papers on "Motion planning published in 2007"

Motion Coordination with Distributed Information

Abstract: Motion coordination is a remarkable phenomenon in biological systems and an extremely useful tool for groups of vehicles, mobile sensors, and embedded robotic systems For many applications, teams of mobile autonomous agents need the ability to deploy over a region, assume a specified pattern, rendezvous at a common point, or move in a synchronized manner The objective of this article is to illustrate the use of systems theory to analyze emergent behaviors in animal groups and to design autonomous and reliable robotic networks We present and survey some recently developed theoretical tools for modeling, analysis, and design of motion coordination algorithms in both continuous and discrete time We pay special attention to the distributed character of coordination algorithms, the characterization of their performance, and the development of design methodologies that provide mobile networks with provably correct cooperative strategies

A Human Aware Mobile Robot Motion Planner

Abstract: Robot navigation in the presence of humans raises new issues for motion planning and control when the humans must be taken explicitly into account. We claim that a human aware motion planner (HAMP) must not only provide safe robot paths, but also synthesize good, socially acceptable and legible paths. This paper focuses on a motion planner that takes explicitly into account its human partners by reasoning about their accessibility, their vision field and their preferences in terms of relative human-robot placement and motions in realistic environments. This planner is part of a human-aware motion and manipulation planning and control system that we aim to develop in order to achieve motion and manipulation tasks in the presence or in synergy with humans.

Path Planning for Autonomous Underwater Vehicles

Abstract: Efficient path-planning algorithms are a crucial issue for modern autonomous underwater vehicles. Classical path-planning algorithms in artificial intelligence are not designed to deal with wide continuous environments prone to currents. We present a novel Fast Marching (FM)-based approach to address the following issues. First, we develop an algorithm we call FM* to efficiently extract a 2-D continuous path from a discrete representation of the environment. Second, we take underwater currents into account thanks to an anisotropic extension of the original FM algorithm. Third, the vehicle turning radius is introduced as a constraint on the optimal path curvature for both isotropic and anisotropic media. Finally, a multiresolution method is introduced to speed up the overall path-planning process

Optimal Rough Terrain Trajectory Generation for Wheeled Mobile Robots

Abstract: An algorithm is presented for wheeled mobile robot trajectory generation that achieves a high degree of generality and efficiency. The generality derives from numerical linearization and inversion of forward models of propulsion, suspension, and motion for any type of vehicle. Efficiency is achieved by using fast numerical optimization techniques and effective initial guesses for the vehicle controls parameters. This approach can accommodate such effects as rough terrain, vehicle dynamics, models of wheel-terrain interaction, and other effects of interest. It can accommodate boundary and internal constraints while optimizing an objective function that might, for example, involve such criteria as obstacle avoidance, cost, risk, time, or energy consumption in any combination. The algorithm is efficient enough to use in real time due to its use of nonlinear programming techniques that involve searching the space of parameterized vehicle controls. Applications of the presented methods are demonstrated for planetary rovers.

Planning Paths of Complete Coverage of an Unstructured Environment by a Mobile Robot

Abstract: Abs t rac t Much of the focus of the research effort in path planning for mobile robots has centred on the problem of finding a path from a start location to a goal location, while minimising one or more parameters such as length of path, energy consumption or journey time. A path of complete coverage is a planned path in which a robot sweeps all areas of free space in an environment in a systematic and efficient manner. Possible applications for paths of complete coverage include autonomous vacuum cleaners, lawn mowers, security robots, land mine detectors etc. This paper will present a solution to this problem based upon an extension to the distance transform path planning methodology. The solution has been implemented on the self-contained autonomous mobile robot called the Yamabico.

Manipulation Planning Among Movable Obstacles

Abstract: This paper presents the resolve spatial constraints (RSC) algorithm for manipulation planning in a domain with movable obstacles. Empirically we show that our algorithm quickly generates plans for simulated articulated robots in a highly nonlinear search space of exponential dimension. RSC is a reverse-time search that samples future robot actions and constrains the space of prior object displacements. To optimize the efficiency of RSC, we identify methods for sampling object surfaces and generating connecting paths between grasps and placements. In addition to experimental analysis of RSC, this paper looks into object placements and task-space motion constraints among other unique features of the three dimensional manipulation planning domain.

Multipartite RRTs for Rapid Replanning in Dynamic Environments

Abstract: The rapidly-exploring random tree (RRT) algorithm has found widespread use in the field of robot motion planning because it provides a single-shot, probabilistically complete planning method which generalizes well to a variety of problem domains. We present the multipartite RRT (MP-RRT), an RRT variant which supports planning in unknown or dynamic environments. By purposefully biasing the sampling distribution and re-using branches from previous planning iterations, MP-RRT combines the strengths of existing adaptations of RRT for dynamic motion planning. Experimental results show MP-RRT to be very effective for planning in dynamic environments with unknown moving obstacles, replanning in high-dimensional configuration spaces, and replanning for systems with space time constraints.

Construction and optimal search of interpolated motion graphs

Abstract: Many compelling applications would become feasible if novice users had the ability to synthesize high quality human motion based only on a simple sketch and a few easily specified constraints. We approach this problem by representing the desired motion as an interpolation of two time-scaled paths through a motion graph. The graph is constructed to support interpolation and pruned for efficient search. We use an anytime version of A* search to find a globally optimal solution in this graph that satisfies the user's specification. Our approach retains the natural transitions of motion graphs and the ability to synthesize physically realistic variations provided by interpolation. We demonstrate the power of this approach by synthesizing optimal or near optimal motions that include a variety of behaviors in a single motion.

An Efficient Localization Scheme for a Differential-Driving Mobile Robot Based on RFID System

Abstract: This paper presents an efficient localization scheme for an indoors mobile robot using Radio-Frequency IDentification (RFID) systems. The mobile robot carries an RFID reader at the bottom of the chassis, which reads the RFID tags on the floor to localize the mobile robot. Each of the RFID tags stores its own absolute position, which is used to calculate the position, orientation, and velocity of the mobile robot. However, a localization system based on RFID technology inevitably suffers from an estimation error. In this paper, a new triangular pattern of arranging the RFID tags on the floor has been proposed to reduce the estimation error of the conventional square pattern. In addition, the motion-continuity property of the differential-driving mobile robot has been utilized to improve the localization accuracy of the mobile robot. According to the conventional approach, two readers are necessary to identify the orientation of the mobile robot. Therefore, this new approach, based on the motion-continuity property of the differential-driving mobile robot, provides a cheap and fast estimation of the orientation. The proposed algorithms used to raise the accuracy of the robot localization are successfully verified through experiments.

Where's Waldo? Sensor-Based Temporal Logic Motion Planning

Abstract: Given a robot model and a class of admissible environments, this paper provides a framework for automatically and verifiably composing controllers that satisfy high level task specifications expressed in suitable temporal logics. The desired task specifications can express complex robot behaviors such as search and rescue, coverage, and collision avoidance. In addition, our framework explicitly captures sensor specifications that depend on the environment with which the robot is interacting, resulting in a novel paradigm for sensor-based temporal logic motion planning. As one robot is part of the environment of another robot, our sensor-based framework very naturally captures multi-robot specifications. Our computational approach is based on first creating discrete controllers satisfying so-called general reactivity formulas. If feasible, the discrete controller is then used in order to guide the sensor-based composition of continuous controllers resulting in a hybrid controller satisfying the high level specification, but only if the environment is admissible.

Capturing robot workspace structure: representing robot capabilities

Abstract: Humans have at some point learned an abstraction of the capabilities of their arms. By just looking at the scene they can decide which places or objects they can easily reach and which are difficult to approach. Possessing a similar abstraction of a robot arm's capabilities in its workspace is important for grasp planners, path planners and task planners. In this paper, we show that robot arm capabilities manifest themselves as directional structures specific to workspace regions. We introduce a representation scheme that enables to visualize and inspect the directional structures. The directional structures are then captured in the form of a map, which we name the capability map. Using this capability map, a manipulator is able to deduce places that are easy to reach. Furthermore, a manipulator can either transport an object to a place where versatile manipulation is possible or a mobile manipulator or humanoid torso can position itself to enable optimal manipulation of an object.

Multi-Robot Area Patrol under Frequency Constraints

Abstract: This paper discusses the problem of generating patrol paths for a team of mobile robots inside a designated target area. Patrolling requires an area to be visited repeatedly by the robot(s) in order to monitor its current state. First, we present frequency optimization criteria used for evaluation of patrol algorithms. We then present a patrol algorithm that guarantees maximal uniform frequency, i.e., each point in the target area is covered at the same optimal frequency. This solution is based on finding a circular path that visits all points in the area, while taking into account terrain directionality and velocity constraints. Robots are positioned uniformly along this path, using a second algorithm. Moreover, the solution is guaranteed to be robust in the sense that uniform frequency of the patrol is achieved as long as at least one robot works properly.

The stochastic motion roadmap: A sampling framework for planning with Markov motion uncertainty

Abstract: We present a new motion planning framework that explicitly considers uncertainty in robot motion to maximize the probability of avoiding collisions and successfully reaching a goal. In many motion planning applications ranging from maneuvering vehicles over unfamiliar terrain to steering flexible medical needles through human tissue, the response of a robot to commanded actions cannot be precisely predicted. We propose to build a roadmap by sampling collision-free states in the configuration space and then locally sampling motions at each state to estimate state transition probabilities for each possible action. Given a query specifying initial and goal configurations, we use the roadmap to formulate a Markov Decision Process (MDP), which we solve using Infinite Horizon Dynamic Programming in polynomial time to compute stochastically optimal plans. The Stochastic Motion Roadmap (SMRM) thus combines a sampling-based roadmap representation of the configuration space, as in PRM's, with the well-established theory of MDP's. Generating both states and transition probabilities by sampling is far more flexible than previous Markov motion planning approaches based on problem-specific or grid-based discretizations. In this paper, we formulate SMRM and demonstrate it by generating non-holonomic plans for steerable needles, a new class of medical needles that follow curved paths through soft tissue and can be modeled as a variant of a Dubins car. Using randomized simulations, we show that SMRM is computationally faster than a previously reported MDP method and confirm that SMRM generates motion plans with a significantly higher probability of success compared to shortest-path plans.

Particle RRT for Path Planning with Uncertainty

Abstract: This paper describes a new extension to the rapidly-exploring random tree (RRT) path planning algorithm. The particle RRT algorithm explicitly considers uncertainty in its domain, similar to the operation of a particle filter. Each extension to the search tree is treated as a stochastic process and is simulated multiple times. The behavior of the robot can be characterized based on the specified uncertainty in the environment, and guarantees can be made as to the performance under this uncertainty. Extensions to the search tree, and therefore entire paths, may be chosen based on the expected probability of successful execution. The benefit of this algorithm is demonstrated in the simulation of a rover operating in rough terrain with unknown coefficients of friction

Dynamic window based approach to mobile robot motion control in the presence of moving obstacles

Abstract: This paper presents a motion control method for mobile robots in partially unknown environments populated with moving obstacles. The proposed method is based on the integration of focused D* search algorithm and dynamic window local obstacle avoidance algorithm with some adaptations that provide efficient avoidance of moving obstacles. The moving obstacles are modelled as moving cells in the occupancy grid map and their motion is predicted by applying a procedure similar to the dynamic window approach. The collision points of the robot predicted trajectory and moving cells predicted trajectories form the new active obstacles in the environment, which should be avoided. The algorithms are implemented and verified using a Pioneer 3DX mobile robot equipped with laser range finder.

Classic and Heuristic Approaches in Robot Motion Planning A Chronological Review

Abstract: This paper reviews the major contributions to the Motion Planning (MP) field throughout a 35-year period, from classic approaches to heuristic algorithms Due to the NP-Hardness of the MP problem, heuristic methods have outperformed the classic approaches and have gained wide popularity After surveying around 1400 papers in the field, the amount of existing works for each method is identified and classified Especially, the history and applications of numerous heuristic methods in MP is investigated The paper concludes with comparative tables and graphs demonstrating the frequency of each MP method’s application, and so can be used as a guideline for MP researchers Keywords—Robot motion planning, Heuristic algorithms

Affective State Estimation for Human–Robot Interaction

Abstract: In order for humans and robots to interact in an effective and intuitive manner, robots must obtain information about the human affective state in response to the robot's actions. This secondary mode of interactive communication is hypothesized to permit a more natural collaboration, similar to the "body language" interaction between two cooperating humans. This paper describes the implementation and validation of a hidden Markov model (HMM) for estimating human affective state in real time, using robot motions as the stimulus. Inputs to the system are physiological signals such as heart rate, perspiration rate, and facial muscle contraction. Affective state was estimated using a two- dimensional valence-arousal representation. A robot manipulator was used to generate motions expected during human-robot interaction, and human subjects were asked to report their response to these motions. The human physiological response was also measured. Robot motions were generated using both a nominal potential field planner and a recently reported safe motion planner that minimizes the potential collision forces along the path. The robot motions were tested with 36 subjects. This data was used to train and validate the HMM model. The results of the HMM affective estimation are also compared to a previously implemented fuzzy inference engine.

Task Sequencing for High-Level Sensor-Based Control

Abstract: Classical sensor-based approaches tend to constrain all the degrees of freedom of a robot during the execution of a task. In this paper, a new solution is proposed. The key idea is to divide the global full-constraining task into several subtasks, which can be applied or inactivated to take into account potential constraints of the environment. Far from any constraint, the robot moves according to the full task. When it comes closer to a configuration to avoid, a higher level controller removes one or several subtasks, and activates them again when the constraint is avoided. The last controller ensures the convergence at the global level by introducing some look-ahead capabilities when a local minimum is reached. The robot accomplishes the global task by automatically sequencing sensor-based tasks, obstacle avoidance, and short deliberative phases. In this paper, a complete solution to implement this idea is proposed, along with several experiments that prove the validity of this approach

Modular Self-reconfigurable Robot Systems: Challenges and Opportunities for the Future

Abstract: T he field of modular self-reconfigurable robotic systems addresses the design, fabrication , motion planning, and control of autonomous kinematic machines with variable morphology. Beyond conventional actuation, sensing, and control typically found in fixed-morphology robots, self-reconfigurable robots are also able to deliberately change their own shape by rearranging the connectivity of their parts in order to adapt to new circumstances, perform new tasks, or recover from damage. Over the last two decades, the field of modular robotics has advanced from proof-of-concept systems to elaborate physical implementations and simulations. The goal of this article is to outline some of this progress and identify key challenges and opportunities that lay ahead. Modular robots are usually composed of multiple building blocks of a relatively small repertoire, with uniform docking interfaces that allow transfer of mechanical forces and moments, electrical power, and communication throughout the robot. The modular building blocks often consist of some primary structural actuated unit and potentially some additional specialized units such as grippers, feet, wheels, cameras, payload, and energy storage and generation units. Figure 1 illustrates such a system in the context of a potential application. Modular self-reconfigurable robotic systems can be generally classified into several architectural groups by the geometric arrangement of their units. Several systems exhibit hybrid properties. ◆ Lattice Architectures: Lattice architectures have units that are arranged and connected in some regular, three-dimensional pattern, such as a simple cubic or hexagonal grid. Control and motion can be executed in parallel. Lattice architectures usually offer simpler reconfiguration, as modules move to a discrete set of neighboring locations in which motions can be made open-loop. The computational representation can also be more easily scaled to more complex systems. ◆ Chain/Tree Architectures: Chain/tree architectures have units that are connected together in a string or tree topology. This chain or tree can fold up to become space filling, but the underlying architecture is serial. Through articulation, chain architectures can potentially reach any point or orientation in space, and are therefore more versatile but computationally more difficult to represent and analyze and more difficult to control. ◆ Mobile Architectures: Mobile architectures have units that use the environment to maneuver around and can either hook up to form complex chains or lattices or form a number of smaller robots that execute coordinated movements and together form a larger " virtual " network. Control of all three types of modular systems can be centralized …

A Fuzzy-Logic-Based Approach for Mobile Robot Path Tracking

Abstract: One important problem in autonomous robot navigation is the effective following of an unknown path traced in the environment in compliance with the kinematic limits of the vehicle, i.e., bounded linear and angular velocities and accelerations. In this case, the motion planning must be implemented in real-time and must be robust with respect to the geometric characteristics of the unknown path, namely curvature and sharpness. To achieve good tracking capability, this paper proposes a path following approach based on a fuzzy-logic set of rules which emulates the human driving behavior. The input to the fuzzy system is represented by approximate information concerning the next bend ahead the vehicle; the corresponding output is the cruise velocity that the vehicle needs to attain in order to safely drive on the path. To validate the proposed algorithm two completely different experiments have been run: in the first experiment, the vehicle has to perform a lane-following task acquiring lane information in real-time using an onboard camera; in the second, the motion of the vehicle is obtained assigning in real-time a given time law. The obtained results show the effectiveness of the proposed method

Grasp planning in complex scenes

Abstract: This paper combines grasp analysis and manipulation planning techniques to perform fast grasp planning in complex scenes In much previous work on grasping, the object being grasped is assumed to be the only object in the environment Hence the grasp quality metrics and grasping strategies developed do not perform well when the object is close to obstacles and many good grasps are infeasible We introduce a framework for finding valid grasps in cluttered environments that combines a grasp quality metric for the object with information about the local environment around the object and information about the robot's kinematics We encode these factors in a grasp-scoring function which we use to rank a precomputed set of grasps in terms of their appropriateness for a given scene We show that this ranking is essential for efficient grasp selection and present experiments in simulation and on the HRP2 robot

Creating High-quality Paths for Motion Planning

Abstract: Many algorithms have been proposed that create a path for a robot in an environment with obstacles. Most methods are aimed at finding a solution. However, for many applications, the path must be of a good quality as well. That is, a path should be short and should keep some amount of minimum clearance to the obstacles. Traveling along such a path reduces the chances of collisions due to the difficulty of measuring and controlling the precise position of the robot. This paper reports a new technique, called Partial shortcut, which decreases the path length. While current methods have difficulties in removing all redundant motions, the technique efficiently removes these motions by interpolating one degree of freedom at a time. Two algorithms are also studied that increase the clearance along paths. The first one is fast but can only deal with rigid, translating bodies. The second algorithm is slower but can handle a broader range of robots, including three-dimensional free-flying and articulated robots, which may reside in arbitrary high-dimensional configuration spaces. A big advantage of these algorithms is that clearance along paths can now be increased efficiently without using complex data structures and algorithms. Finally, we combine the two criteria and show that high-quality paths can be obtained for a broad range of robots.

A Resource Allocation Algorithm for Multivehicle Systems With Nonholonomic Constraints

Abstract: This paper is about the allocation of tours of m targets to n vehicles. The motion of the vehicles satisfies a nonholonomic constraint (i.e., the yaw rate of the vehicle is bounded). Each target is to be visited by one and only one vehicle. Given a set of targets and the yaw rate constraints on the vehicles, the problem addressed in this paper is 1) to assign each vehicle a sequence of targets to visit, and 2) to find a feasible path for each vehicle that passes through the assigned targets with a requirement that the vehicle returns to its initial position. The heading angle at each target location may not be specified. The objective function is to minimize the sum of the distances traveled by all vehicles. A constant factor approximation algorithm is presented for the above resource allocation problem for both the single and the multiple vehicle case. Note to Practitioners-The motivation for this paper stems from the need to develop resource allocation algorithms for unmanned aerial vehicles (UAVs). Small autonomous UAVs are seen as ideal platforms for many applications, such as searching for targets, mapping a given area, traffic surveillance, fire monitoring, etc. The main advantage of using these small autonomous vehicles is that they can be used in situations where a manned mission is dangerous or not possible. Resource allocation problems naturally arise in these applications where one would want to optimally assign a given set of vehicles to the tasks at hand. The feature that differentiates these resource allocation problems from similar problems previously studied in the literature is that there are constraints on the motion of the vehicle. This paper addresses the constraint that captures the inability of a fixed wing aircraft to turn at any arbitrary yaw rate. The basic problem addressed in this paper is as follows: Given n vehicles and m targets, find a path for each vehicle satisfying yaw rate contraints such that each target is visited exactly once by a vehicle and the total distance traveled by all vehicles is minimized. We assume that the targets are at least 2r apart, where r is the minimum turning radius of the vehicle. This is a reasonable assumption because the sensors on these vehicles can map or see an area whose width is at least 2r. We give an algorithm to solve this problem by combining ideas from the traveling salesman problem and the path planning literature. We also show how these algorithms perform in the worst-case scenario

Path planning and collision avoidance for movement of instruments in a radiation therapy environment

Abstract: A patient positioning system for use with a radiation therapy system that monitors the location of fixed and movable components and pre-plans movement of the movable components so as to inhibit movement if a collision would be indicated. The positioning system can also coordinate movement of multiple movable components for reduced overall latency in registering a patient. The positioning system includes external measurement devices which measure the location and orientation of objects, including components of the radiation therapy system, in space and can also monitor for intrusion into the active area of the therapy system by personnel or foreign objects to improve operational safety of the radiation therapy system.

Task constrained motion planning in robot joint space

Abstract: We explore global randomized joint space path planning for articulated robots that are subject to task space constraints. This paper describes a representation of constrained motion for joint space planners and develops two simple and efficient methods for constrained sampling of joint configurations: Tangent Space Sampling (TS) and First-Order Retraction (FR). Constrained joint space planning is important for many real world problems involving redundant manipulators. On the one hand, tasks are designated in work space coordinates: rotating doors about fixed axes, sliding drawers along fixed trajectories or holding objects level during transport. On the other, joint space planning gives alternative paths that use redundant degrees of freedom to avoid obstacles or satisfy additional goals while performing a task. In simulation, we demonstrate that our methods are faster and significantly more invariant to problem/algorithm parameters than existing techniques.

Omnidirectional Vision Based Topological Navigation

Abstract: In this work we present a novel system for autonomous mobile robot navigation. With only an omnidirectional camera as sensor, this system is able to build automatically and robustly accurate topologically organised environment maps of a complex, natural environment. It can localise itself using such a map at each moment, including both at startup (kidnapped robot) or using knowledge of former localisations. The topological nature of the map is similar to the intuitive maps humans use, is memory-efficient and enables fast and simple path planning towards a specified goal. We developed a real-time visual servoing technique to steer the system along the computed path. A key technology making this all possible is the novel fast wide baseline feature matching, which yields an efficient description of the scene, with a focus on man-made environments.

Efficient planning of informative paths for multiple robots

Abstract: In many sensing applications, including environmental monitoring, measurement systems must cover a large space with only limited sensing resources. One approach to achieve required sensing coverage is to use robots to convey sensors within this space. Planning the motion of these robots - coordinating their paths in order to maximize the amount of information collected while placing bounds on their resources (e.g., path length or energy capacity) - is aNP-hard problem. In this paper, we present an efficient path planning algorithm that coordinates multiple robots, each having a resource constraint, to maximize the "informativeness" of their visited locations. In particular, we use a Gaussian Process to model the underlying phenomenon, and use the mutual information between the visited locations and remainder of the space to characterize the amount of information collected. We provide strong theoretical approximation guarantees for our algorithm by exploiting the submodularity property of mutual information. In addition, we improve the efficiency of our approach by extending the algorithm using branch and bound and a region-based decomposition of the space. We provide an extensive empirical analysis of our algorithm, comparing with existing heuristics on datasets from several real world sensing applications.

Theta*: any-angle path planning on grids

Abstract: Grids with blocked and unblocked cells are often used to represent terrain in computer games and robotics However, paths formed by grid edges can be sub-optimal and unrealistic looking, since the possible headings are artificially constrained We present Theta*, a variant of A*, that propagates informati on along grid edges without constraining the paths to grid edges Theta* is simple, fast and finds short and realistic looking paths We compare Theta* against both Field D*, the only other variant of A* that propagates information along grid edges without constraining the paths to grid edges, and A* with post-smoothed paths Although neither path planning method is guaranteed to find shortest paths, we show experimentally that Theta* finds shorter and more realistic looking paths than either of these existing techniques

Manipulation Planning for Deformable Linear Objects

Abstract: Research on robotic manipulation has mainly focused on manipulating rigid objects so far. However, many important application domains require manipulating deformable objects, especially deformable linear objects (DLOs), such as ropes, cables, and sutures. Such objects are far more challenging to handle, as they can exhibit a much greater diversity of behaviors, and their manipulation almost inevitably requires two robotic arms, or more, performing well-coordinated motions. This paper describes a new motion planner for manipulating DLOs and tying knots (both self-knots and knots around simple static objects) using two cooperating robotic arms. This planner blends new ideas with preexisting concepts and techniques from knot theory, robot motion planning, and computational modeling. Unlike in traditional motion planning problems, the goal to be achieved by the planner is a topological state of the world, rather than a geometric one. To search for a manipulation path, the planner constructs a topologically biased probabilistic roadmap in the configuration space of the DLO. During roadmap construction, it uses inverse kinematics to determine the successive robot configurations implied by the DLO configurations and tests their feasibility. Also, inspired by the real life, the planner uses static ldquoneedlesrdquo (by analogy to the needles used in knitting) for maintaining the stability of the DLO during manipulation and to make the resulting manipulation plan robust to imperfections in the physical model of the DLO. The implemented planner has been tested both in graphic simulation and on a dual-PUMA-560 hardware platform to achieve various knots, like bowline, neck-tie, bow (shoe-lace), and stun-sail.