Motion planning in the presence of movable obstacles

Most motion planning algorithms have dealt with motion in a static workspace, or more recently, with motion in a workspace that changes in a known manner. We consider the problem of finding collision-free motions in a changeable workspace. That is, we wish to find a motion for an object where the object is permitted to move some of the obstacles. In such a workspace, the final positions of the movable obstacles may or may not be part of the goal. In the case where the final positions of the obstacles are specified, the general problem is shown to be PSPACE-hard. In the case where the final positions of the obstacles are unspecified, the motion planning problem is shown to be NP-hard. Algorithms that run inO(n ³) time are presented for the case where there is only one movable obstacle in a polygonal environment withn corners and the object to be moved and the obstacle are convex polygons of constant complexity.     

On-line motion planning: Case of a planar rod

In this paper we develop an algorithm for planning the motion of a planar rod (a line segment) amidst obstacles bounded by simple, closed polygons. The exact shape, number and location of the obstacles are assumed unknown to the planning algorithm, which can only obtain information about the obstacles by detecting points of contact with the obstacles. The ability to detect contact with obstacles is formalized by move primitives that we callguarded moves. We call ours theon-line motion planning problem as opposed to the usualoff-line version. This is a significant departure from the usual setting for motion planning problems. What we demonstrate is that the retraction method can be applied, although new issues arise that have no counterparts in the usual setting. We are able to obtain an algorithm with path complexityO(n ²) guarded moves, wheren is the number of obstacle corners. This matches the known lower bound. The computational complexityO(n ²logn) of our algorithm matches the best known algorithm for the off-line version.This work is supported by NSF grants #DCR-84-01633, #DCR-84-01898 and PSC-CUNY 669287.     

Reactive navigation in dynamic environment using a multisensorpredictor

A reactive navigation system for an autonomous mobile robot in unstructured dynamic environments is presented. The motion of moving obstacles is estimated for robot motion planning and obstacle avoidance. A multisensor-based obstacle predictor is utilized to obtain obstacle-motion information. Sensory data from a CCD camera and multiple ultrasonic range finders are combined to predict obstacle positions at the next sampling instant. A neural network, which is trained off-line, provides the desired prediction on-line in real time. The predicted obstacle configuration is employed by the proposed virtual force based navigation method to prevent collision with moving obstacles. Simulation results are presented to verify the effectiveness of the proposed navigation system in an environment with multiple mobile robots or moving objects. This system was implemented and tested on an experimental mobile robot at our laboratory. Navigation results in real environment are presented and analyzed.     

Obstacle Modelling Oriented to Safe Motion Planning and Control for Planar Rigid Robot Manipulators

Trajectory planning and tracking are crucial tasks in any application using robot manipulators. These tasks become particularly challenging when obstacles are present in the manipulator workspace. In this paper a n-joint planar robot manipulator is considered and it is assumed that obstacles located in its workspace can be approximated in a conservative way with circles. The goal is to represent the obstacles in the robot configuration space. The representation allows to obtain an efficient and accurate trajectory planning and tracking. A simple but effective path planning strategy is proposed in the paper. Since path planning depends on tracking accuracy, in this paper an adequate tracking accuracy is guaranteed by means of a suitably designed Second Order Sliding Mode Controller (SOSMC). The proposed approach guarantees a collision-free motion of the manipulator in its workspace in spite of the presence of obstacles, as confirmed by experimental results.     

A Hierarchical Extension of the <Emphasis Type="Italic">D</Emphasis><Superscript>*</Superscript> Algorithm

In this paper a contribution to the practice of path planning using a new hierarchical extension of the D^* algorithm is introduced. A hierarchical graph is stratified into several abstraction levels and used to model environments for path planning. The hierarchical D^* algorithm uses a down-top strategy and a set of pre-calculated trajectories in order to improve performance. This allows optimality and specially lower computational time. It is experimentally proved how hierarchical search algorithms and on-line path planning algorithms based on topological abstractions can be combined successfully.     

Acquisition of obstacle motion patterns to improve mobile robot motion planning

Mobile robots for advanced applications have to act in environments which contain moving obstacles (humans). Even though the motions of such obstacles are not precisely predictable, usually they are not completely random; long-term observation of obstacle behavior may thus yield valuable knowledge about prevailing motion patterns. By incorporating such knowledge as statistical data, a new approach called statistical motion planning yields robot motions which are better adapted to the dynamic environment. To put these ideas into practice, an experimental system has been developed. Cameras observe the workspace in order to detect obstacle motion. Statistical data is derived and represented as a set of stochastic trajectories. This data can be directly employed in order to calculate collision probability, i.e. the probability of encountering an obstacle during the robot's motion. Further aspects of motion planning are addressed: path planning which minimizes collision probability, estimation of expected time to reach the goal and reactive planning.     

Obstacle avoidance of redundant manipulators using neural networks based reinforcement learning

This paper proposes a new approach for solving the problem of obstacle avoidance during manipulation tasks performed by redundant manipulators. The developed solution is based on a double neural network that uses Q-learning reinforcement technique. Q-learning has been applied in robotics for attaining obstacle free navigation or computing path planning problems. Most studies solve inverse kinematics and obstacle avoidance problems using variations of the classical Jacobian matrix approach, or by minimizing redundancy resolution of manipulators operating in known environments. Researchers who tried to use neural networks for solving inverse kinematics often dealt with only one obstacle present in the working field. This paper focuses on calculating inverse kinematics and obstacle avoidance for complex unknown environments, with multiple obstacles in the working field. Q-learning is used together with neural networks in order to plan and execute arm movements at each time instant. The algorithm developed for general redundant kinematic link chains has been tested on the particular case of PowerCube manipulator. Before implementing the solution on the real robot, the simulation was integrated in an immersive virtual environment for better movement analysis and safer testing. The study results show that the proposed approach has a good average speed and a satisfying target reaching success rate.     

MRT: A tool developed for predicting the mean message response time of communication channels in sizeable networks exemplified by the Internet

In this paper an algorithm M²RT for predicting the mean message response time (MMRT) of a communication channel is proposed with emphasis on Internet applications. The M²RT development went through four major phases. They include:

(a) Formulating the theoretical foundation with the central limit theorem.

(b) Determining the parameters of the algorithm by simulations.

(c) Performing off-line verification tests for the algorithm with local Internet/Intranet nodes and well-known middleware (MPI and CORBA).

(d) Performing on-line validation of the M²RT over the Internet involving both local and international sites.

The acceptance criteria for the algorithm include:

(a) It must perform efficiently for different conditions of workload, geography, and traffic.

(b) It must perform consistently with the same software entities (e.g., MPI) for similar operations.

(c) It must be able to exist both as an off-line tool and an on-line program object (to be invoked on a real-time basis).

(d) Its computation time should be sufficiently small so that the result actually reflects the current physical conditions.

All the results from simulations, verification tests, and validation experiments have confirmed that the M²RT algorithm indeed meets all the acceptance criteria. In these tests, we also discovered that the algorithm could be developed into a powerful tool for measuring the relative performance between firmware products. This development will be explored in the near future.     

A new efficient motion-planning algorithm for a rod in two-dimensional polygonal space

We present here a new and efficient algorithm for planning collision-free motion of a line segment (a rod or a “ladder”) in two-dimensional space amidst polygonal obstacles. The algorithm uses a different approach than those used in previous motion-planning techniques, namely, it calculates the boundary of the (three-dimensional) space of free positions of the ladder, and then uses this boundary for determining the existence of required motions, and plans such motions whenever possible. The algorithm runs in timeO(K logn) =O(n ² logn) wheren is the number of obstacle corners and whereK is the total number of pairs of obstacle walls or corners of distance less than or equal to the length of the ladder. The algorithm has thus the same complexity as the best previously known algorithm of Leven and Sharir [5], but if the obstacles are not too cluttered together it will run much more efficiently. The algorithm also serves as an initial demonstration of the viability of the technique it uses, which we expect to be useful in obtaining efficient motion-planning algorithms for other more complex robot systems.     

基于柱状空间和改进A*算法的无人机规避方法

针对无人机避障问题,提出了基于改进A~*算法和柱状空间的无人机规避方法。首先,根据无人机飞行区域的障碍物分布情况,建立飞行区域的柱状空间;然后将障碍物对无人机的影响引入到估价函数中,重新设计启发函数;最后将基于柱状空间和改进A~*算法的无人机规避方法应用于无人机的规避中,并对规划的路径进行平滑处理。仿真结果表明,该算法能够有效地实现无人机的规避。     

Task Oriented Optimum Positioning of a Mobile Manipulator Base in a Cluttered Environment

A method for generating discrete optimal sequences of base locations for mobile manipulators is presented that considers the task capability of the workspace in a cluttered environment. In implementation, the obstacles and task trajectories are represented by 2ⁿ trees, so that a series of set operations are performed to characterize the manipulators configuration space into topological subspaces. By incorporating trajectory-motion-capable subspaces into the enumeration of the cost function, an optimum search technique is made applicable to the determination of a task feasible location. The method is then extended to a multiple positioning problem by concatenating the single optimization processes into a serial multistage decision making system, for which an optimal set of decisions can be found through a computationally efficient dynamic programming process.The computational paradigm of the present method is coherent with topological workspace analysis, and thus applicable to task trajectories of arbitrary dimensions and shapes. The effectiveness of the presented method is demonstrated through simulation studies performed for a 3-d.o.f. regional manipulator operating under various task conditions.     

A comparison of local parametric C Bézier interpolants for triangular meshes

Parametric curved shape surface schemes interpolating vertices and normals of a given triangular mesh with arbitrary topology are widely used in computer graphics for gaming and real-time rendering due to their ability to effectively represent any surface of arbitrary genus. In this context, continuous curved shape surface schemes using only the information related to the triangle corresponding to the patch under construction, emerged as attractive solutions responding to the requirements of resource-limited hardware environments. In this paper we provide a unifying comparison of the local parametric C⁰ curved shape schemes we are aware of, based on a reformulation of their original constructions in terms of polynomial Bézier triangles. With this reformulation we find a geometric interpretation of all the schemes that allows us to analyse their strengths and shortcomings from a geometrical point of view. Further, we compare the four schemes with respect to their computational costs, their reproduction capabilities of analytic surfaces and their response to different surface interrogation methods on arbitrary triangle meshes with a low triangle count that actually occur in their real-world use.     

Obstacle avoidance for redundant robots using configuration control

The article presents a new and simple solution to the obstacle avoidance problem for redundant robots. In the proposed approach, called configuration control, the redundancy is utilized to configure the robot so as to satisfy a set of kinematic inequality constraints representing obstacle avoidance, while the end-effector is tracking a desired trajectory. The robot control scheme is very simple, and uses on-line adaptation to eliminate the need for the complex dynamic model and parameter values of the robot. Several simulation results for a four-link planar robot are presented to illustrate the versatility of the approach. These include reaching around a stationary obstacle, simultaneous avoidance of two obstacles, robot reconfiguration to avoid a moving obstacle, and avoidance of rectangular obstacles. The simplicity and computational efficiency of the proposed scheme allows on-line implementation with a high sampling rate for real-time obstacle avoidance in a dynamically varying environment.     

Reducing the Complexity of Robot's Scene for Faster Collision Detection

In many real-life industrial applications such as welding and painting, the hand tip of a robot manipulator must follow a desired Cartesian curve while its body avoids collisions with obstacles in its environment. Collision detection is an absolutely essential task for any robotic manipulators in order to operate safely and effectively in cluttered environments. A significant factor that influences the complexity of the collision detection problem is the obstacles' density, i.e., the total number of obstacles in the robot's environment.In this paper, a heuristic algorithm for approximating the collision detection problem into a simpler one is presented. The algorithm reduces the number of obstacles that must be examined during the robot's motion by applying efficient techniques from computational geometry. The algorithm runs in time O(max(n ² log m, n m)) , and uses O(n ² + m n) space; with n being the number of obstacles in the robot's workspace, and m the total number of obstacles' vertices. Both costs are worst-case bounds.     

Step sequence planning for a biped robot by means of a cylindrical shape model and a high-resolution 2.5D map

A novel step sequence planning (SSP) method for biped-walking robots is presented. The method adopts a free space representation custom-designed for efficient biped robot motion planning. The method rests upon the approximation of the robot shape by a set of 3D cylindrical solids. This feature allows efficient determination of feasible paths in a 2.5D map, comprising stepping over obstacles and stair climbing. A SSP algorithm based on A^∗-search is proposed which uses the advantages of the aforementioned environment representation. The efficiency of the proposed approach is evaluated by a series of simulations performed for eight walking scenarios.     

An obstacle avoidance algorithm for robot manipulators based on decision-making force

Obstacle avoidance is a significant skill not only for mobile robots but also for robot manipulators working in unstructured environments. Various algorithms have been proposed to solve off-line planning and on-line adaption problems. However, it is still not able to ensure safety and flexibility in complex scenarios. In this paper, a novel obstacle avoidance algorithm is proposed to improve the robustness and flexibility. The method contains three components: A closed-loop control system is used to filter the preplanned trajectory and ensure the smoothness and stability of the robot motion; the dynamic repulsion field is adopted to fulfill the robot with primitive obstacle avoidance capability; to mimic human’s complex obstacle avoidance behavior and instant decision-making mechanism, a parametrized decision-making force is introduced to optimize all the feasible motions. The algorithms were implemented in planar and spatial robot manipulators. The comparative results show the robot can not only track the task trajectory smoothly but also avoid obstacles in different configurations.     

Collision-avoidance for redundant robots through control of the self-motion of the manipulator

A new method to on-line collision-avoidance of the links of redundant robots with obstacles is presented. The method allows the use of redundant degrees of freedom such that a manipulator can avoid obstacles while tracking the desired end-effector trajectory. It is supposed that the obstacles in the workspace of the manipulator are presented by convex polygons. The recognition of collisions of the links of the manipulator with obstacles results on-line through a nonsensory method. For every link of the redundant manipulator and every obstacle a boundary ellipse is defined in workspace such that there is no collision if the robot joints are outside these ellipses. In case a collision is imminent, the collision-avoidance algorithm compute the self-motion movements necessary to avoid the collision. The method is based on coordinate transformation and inverse kinematics and leads to the favorable use of the abilities of redundant robots to avoid the collisions with obstacles while tracking the end-effector trajectory. This method has the advantage that the configuration of the manipulator after collision-avoidance can be influenced by further requirements such as avoidance of singularities, joint limits, etc. The effectiveness of the proposed method is discussed by theoretical considerations and illustrated by simulation of the motion of three-and four-link planar manipulators between obstacles.     

空间机械臂在线实时避障路径规划研究

针对目前空间机械臂避障路径规划算法计算量大难以达到在线实时规划的缺点,对空间机械臂的在线实时避障路径规划问题进行了研究和探讨。采用规则体的包络对障碍物进行建模,并借助C空间法的思想,把障碍物和机械臂映射到两个相互垂直的平面内,将机械臂工作空间的三维问题转化为二维问题,并结合二岔树逆向寻优的方法进行路径搜索,从而大大减少了计算量,达到了在线实时规划的要求。最后在空间机器人仿真系统上对其进行了仿真研究,验证了该方法的可行性。