Path-planning strategies for a point mobile automaton moving amidst unknown obstacles of arbitrary shape

The problem of path planning for an automaton moving in a two-dimensional scene filled with unknown obstacles is considered. The automaton is presented as a point; obstacles can be of an arbitrary shape, with continuous boundaries and of finite size; no restriction on the size of the scene is imposed. The information available to the automaton is limited to its own current coordinates and those of the target position. Also, when the automaton hits an obstacle, this fact is detected by the automaton's “tactile sensor.” This information is shown to be sufficient for reaching the target or concluding in finite time that the target cannot be reached. A worst-case lower bound on the length of paths generated by any algorithm operating within the framework of the accepted model is developed; the bound is expressed in terms of the perimeters of the obstacles met by the automaton in the scene. Algorithms that guarantee reaching the target (if the target is reachable), and tests for target reachability are presented. The efficiency of the algorithms is studied, and worst-case upper bounds on the length of generated paths are produced.     

Anticipated velocity based guidance strategy for wheeled mobile evader amidst stationary and moving obstacles in bounded environment

This paper is concerned with a class of pursuit‐evasion game problems amidst stationary and moving obstacles in a bounded environment. We concentrate on evader's strategy taking into account the following challenges: (i) pursuer and evader are nonholonomic wheeled mobile robots and the evader is slower than the pursuer; (ii) pursuer follows a proportional navigation law; and (iii) geometry of the environment is not known to the players, a priori. We propose an efficient evader‐centric anticipated velocity based guidance strategy. Pursuer's trajectory is anticipated at each step by the evader using quadratic polynomial interpolation. The aim of the evader is to escape interception with the pursuer for maximum possible time. To deal with static obstacles, a technique based on a well‐known tangent bug algorithm is presented. While dealing with dynamic obstacles, a recently introduced reciprocal orientation method is employed to avoid collision in situations when the dynamic obstacle also cooperates in the process. In case dynamic obstacles do not participate in the process of collision avoidance, a well‐known velocity obstacle method is employed for planning safe collision‐free paths. Efficiency of the proposed algorithms is analyzed with respect to the interception time and the distance traveled by the players. Copyright © 2014 John Wiley & Sons, Ltd.     

On multiple moving objects

This paper explores the motion-planning problem for multiple moving objects. The approach taken consists of assigning priorities to the objects, then planning motions one object at a time. For each moving object, the planner constructs a configuration space-time that represents the time-varying constraints imposed on the moving object by the other moving and stationary objects. The planner represents this space-time approximately, using two-dimensional slices. The space-time is then searched for a collision-free path. The paper demonstrates this approach in two domains. One domain consists of translating planar objects; the other domain consists of two-link planar articulated arms.This report describes research performed at the Artificial Intelligence Laboratory of the Massachusetts Institute of Technology. Michael Erdmann is supported in part by a fellowship from General Motors Research Laboratories. Tomás Lozano-Pérez is supported by an NSF Presidential Young Investigator grant. Support for the Laboratory's Artificial Intelligence research is provided in part by the System Development Foundation, in part by the Office of Naval Research under Office of Naval Research Contract N00014-81-K-0494, and in part by the Advanced Research Projects Agency under Office of Naval Research Contracts N00014-80-C-0505 and N00014-82-K-0344.     

Nonholonomic multibody mobile robots: Controllability and motion planning in the presence of obstacles

We consider mobile robots made of a single body (car-like robots) or several bodies (tractors towing several trailers sequentially hooked). These robots are known to be nonholonomic, i.e., they are subject to nonintegrable equality kinematic constraints involving the velocity. In other words, the number of controls (dimension of the admissible velocity space), is smaller than the dimension of the configuration space. In addition, the range of possible controls is usually further constrained by inequality constraints due to mechanical stops in the steering mechanism of the tractor. We first analyze the controllability of such nonholonomic multibody robots. We show that the well-known Controllability Rank Condition Theorem is applicable to these robots even when there are inequality constraints on the velocity, in addition to the equality constraints. This allows us to subsume and generalize several controllability results recently published in the Robotics literature concerning nonholonomic mobile robots, and to infer several new important results. We then describe an implemented planner inspired by these results. We give experimental results obtained with this planner that illustrate the theoretical results previously developed.This research was partially funded by DARPA contract DAAA21-89-C0002 (Army), CIFE (Center for Integrated Facility Engineering), and Digital Equipment Corporation.     

Generation of configuration space obstacles: The case of moving algebraic curves

We present algebraic algorithms to generate the boundary of planar configuration space obstacles arising from the translatory motion of objects among obstacles. Both the boundaries of the objects and obstacles are given by segments of algebraic plane curves.Research supported in part by NSF Grant MIP-85-21356 and a David Ross Fellowship. An earlier version of this paper appeared in theProceedings of the 1987 IEEE International Conference on Robotics and Automation, pp. 979–984.     

Seeking a path through the crowd: Robot navigation in unknown dynamic environments with moving obstacles based on an integrated environment representation

We present a novel algorithm for collision free navigation of a non-holonomic robot in unknown complex dynamic environments with moving obstacles. Our approach is based on an integrated representation of the information about the environment which does not require to separate obstacles and approximate their shapes by discs or polygons and is very easy to obtain in practice. Moreover, the proposed algorithm does not require any information on the obstacles’ velocities. Under our navigation algorithm, the robot efficiently seeks a short path through the crowd of moving or steady obstacles. A mathematically rigorous analysis of the proposed approach is provided. The performance of the algorithm is demonstrated via experiments with a real robot and extensive computer simulations.     

A visual tool for computer supported learning: The robot motion planning example

We introduce an effective computer aided learning visual tool (CALVT) to teach graph-based applications. We present the robot motion planning problem as an example of such applications. The proposed tool can be used to simulate and/or further to implement practical systems in different areas of computer science such as graphics, computational geometry, robotics and networking. In the robot motion planning example, CALVT enables users to setup the working environment by creating obstacles and a robot of different shapes, specifying starting and goal positions, and setting other path or environment parameters from a user-friendly interface. The path planning system involves several phases. Each of these modules is complex and therefore we provide the possibility of visualizing graphically the output of each phase. Based on our experience, this tool has been an effective one in classroom teaching. It not only cuts down, significantly, on the instructor’s time and effort but also motivates senior/graduate students to pursue work in this specific area of research.     

A local motion planner for car-like robots in a cluttered environment

This paper deals with the motion-planning problem for car-like robots (i.e., a mobile robot with nonholonomic and upper-bounded curvature constraints). In this paper, we propose an efficient planner for a simplified car-like robot model. Our motion planner approximates the derivative of configuration generated by a local holonomic motion planner that ignores motion constrainst, while guaranteeing collision avoidance. Using some simulations, we confirm the validity and efficiency of our algorithm. Presented at the International Symposium on Artificial Life and Robotics, Oita, Japan, February 18–20, 1996     

The complexity of the free space for motion planning amidst fat obstacles

The complexity of motion planning algorithms highly depends on the complexity of the robot's free space, i.e., the set of all collision-free placements of the robot. Theoretically, the complexity of the free space can be very high, resulting in bad worst-case time bounds for motion planning algorithms. In practice, the complexity of the free space tends to be much smaller than the worst-case complexity. Motion planning algorithms with a running time that is determined by the complexity of the free space therefore become feasible in practical situations. We show that, under some realistic assumptions, the complexity of the free space of a robot with any fixed number of degrees of freedom moving around in ad-dimensional Euclidean workspace with fat obstacles is linear in the number of obstacles. The complexity results lead to highly efficient algorithms for motion planning amidst fat obstacles.Research is supported by the Dutch Organization for Scientific Research (NWO) and partially supported by the ESPRIT III BRA Project 6546 (PROMotion).     

Orienting polygonal parts without sensors

In manufacturing it is often necessary to orient parts prior to packing or assembly. We say that a planar part ispolygonal if its convex hull is a polygon. We consider the following problem: given a list ofn vertices describing a polygonal part whose initial orientation is unknown, find the shortest sequence of mechanical gripper actions that is guaranteed to orient the part up to symmetry in its convex hull. We show that such a sequence exists for any polygonal part by giving anO[n ² logn) algorithm for finding the sequence. Since the gripper actions do not require feedback, this result implies that any polygonal part can be orientedwithout sensors.This report describes research conducted in part while the author was a graduate student supported by NSF Grant DMC-8520475 and NASA-Ames Grant NCC 2-463 at the School of Computer Science at Carnegie Mellon University. The author is currently supported by a grant from the Faculty Research Initiation Fund at the University of Southern California.     

Randomization for robot tasks: Using dynamic programming in the space of knowledge states

This paper explores the use of randomization as a primitive action in the solution of robot tasks. An example of randomization is the strategy of shaking a bin containing a part in order to orient the part in a desired stable state with some high probability. Further examples include tapping, vibrating, twirling, and random search. For instance, it is sometimes beneficial for a system to execute random motions purposefully when the precise motions required to perform an operation are unknown, as when they lie below the available sensor resolution.The purpose of this paper is to provide a theoretical framework for the planning and execution of randomized strategies for robot tasks. This framework is built on the standard backchaining approach of dynamic programming. Specifically, a randomizing planner backchains from the goal in a state space whose states describe the knowledge available to the system at run-time. By choosing random actions in a principled manner at run-time, a system can sometimes obtain a probabilistic strategy for accomplishing a task even when no guaranteed strategy exists for accomplishing that task. In other cases, the system may be able to obtain a speedup over an existing guaranteed strategy.The main result of this paper consists of two examples. One example shows that randomization can sometimes speed up task completion from exponential time to polynomial time. The other example shows that such a speedup is not always possible.The author is now with the School of Computer Science and the Robotics Institute at Carnegie-Mellon University. The work reported here was performed while at the MIT Artificial Intelligence Laboratory. This work was supported in part by the Office of Naval Research under the University Research Initiative Program through Contract N00014-86-K-0685, by an NSF Presidential Young Investigator Award to Tomás Lozano-Pérez, by a fellowship from NASA's Jet Propulsion Laboratory, and by the Advanced Research Projects Agency of the Department of Defense under Office of Naval Research Contract N00014-85-K-0124. Additional support at CMU was provided under NSF grant IRI-9010686.     

Motion coordination for industrial robotic systems with redundant degrees of freedom

This work investigates how to distribute in an optimum fashion the desired movement of the end-effector of an industrial robot with respect to the workpiece, when there are redundant degrees of freedom, such as a positioning table. The desired motion is given as a series of acceleration functions in respective time intervals. The constraints of the optimisation are the available acceleration limit of axes, such as the table axes, the upper bounds to velocity and displacement of each axis and the avoidance of singular point areas of the robot, as defined by its manufacturer. The optimisation criterion is minimum total work for the motion. A genetic algorithm was used to solve the problem. The fitness function of the genetic algorithm calls a kinematics and dynamics simulation model of the robotic installation constructed in Matlab™, in order to compute the work consumed and to check possible violation of constraints. Examples of straight line and circular movement are given to prove the concept. Results are encouraging, yet demand on computing power is high.     

A learning fuzzy algorithm for motion planning of mobile robots

A sensor-based fuzzy algorithm is proposed to navigate a mobile robot in a 2-dimensional unknown environment filled with stationary polygonal obstacles. When the robot is at the starting point, vertices of the obstacles that are visible from the robot are scanned by the sensors and the one with the highest priority is chosen. Here, priority is an output fuzzy variable whose value is determined by fuzzy rules. The robot is then navigated from the starting point to the chosen vertex along the line segment connecting these two points. Taking the chosen vertex as the new starting point, the next navigation decision is made. The navigation process will be repeated until the goal point is reached.In implementation of fuzzy rules, the ranges of fuzzy variables are parameters to be determined. In order to evaluate the effect of different range parameters on the navigation algorithm, the total traveling distance of the robot is defined as the performance index first. Then a learning mechanism, which is similar to the simulated annealing method in the neural network theory, is presented to find the optimal range parameters which minimize the performance index. Several simulation examples are included for illustration.     

Low-level flexible planning for mobile manipulators: a distributed perception approach

The paper proposes a method to improve flexibility of the motion planning process for mobile manipulators. The approach is based on the exploitation of perception data available only from simple proximity sensors distributed on the robot. Such data are used to correct pre-planned motions to cope with uncertainties and dynamic changes of the scene at execution time. The algorithm computes robot motion commands aimed at fulfilling the mission by combining two tasks at the same time, i.e. following the planned end-effector path and avoiding obstacles in the environment, by exploiting robot redundancy as well as handling priorities among tasks. Moreover, a technique to smoothly switch between the tasks is presented. To show the effectiveness of the method, four experimental case studies have been presented consisting in a place task executed by a mobile manipulator in an increasingly cluttered scene.     

Optimal and suboptimal motion planning for collision avoidance of mobile robots in non-stationary environments

An optimal control formulation of the problem of collision avoidance of mobile robots moving in terrains containingmoving obstacles is presented. A dynamic model of the mobile robot and the dynamic constraints are derived. Collision avoidance is guaranteed if the minimum distance between the robot and the objects is nonzero. A nominal trajectory is assumed to be known from off-line planning. The main idea is to change the velocity along the nominal trajectory so that collisions are avoided. Furthermore, time consistency with the nominal plan is desirable. Two solutions are obtained: (1) A numerical solution of the optimization problem and a perturbation type of control to update the optimal plan and (2) A computationally efficient method giving near optimal solutions. Simulation results verify the value of the proposed strategies and allow for comparisons.     

A configuration deactivation algorithm for boosting probabilistic roadmap planning of robots

We present a method to improve the execution time used to build the roadmap in probabilistic roadmap planners. Our method intelligently deactivates some of the configurations during the learning phase and allows the planner to concentrate on those configurations that are most likely going to be useful when building the roadmap. The method can be used with many of the existing sampling algorithms. We ran tests with four simulated robot problems typical in robotics literature. The sampling methods applied were purely random, using Halton numbers, Gaussian distribution, and bridge test technique. In our tests, the deactivation method clearly improved the execution times. Compared with pure random selections, the deactivation method also significantly decreased the size of the roadmap, which is a useful property to simplify roadmap planning tasks.     

Fuzzy Logic Based Behavior Fusion for Navigation of an Intelligent Mobile Robot

This paper presents a new method for behavior fusion control of a mobile robot in uncertain environments.Using behavior fusion by fuzzy logic,a mobile robot is able to directly execute its motion according to range information about environments,acquired by ultrasonic sensors,without the need for trajectory planning.Based on low-level behavior control,an efficient strategy for integrating high-level global planning for robot motion can be formulated,since,in most applications,some information on environments is prior knowledge.A global planner,therefore,only to generate some subgoal positions rather than exact geometric paths.Because such subgoals can be easily removed from or added into the plannes,this strategy reduces computational time for global planning and is flexible for replanning in dynamic environments.Simulation results demonstrate that the proposed strategy can be applied to robot motion in complex and dynamic environments.     

Path-based approach to integrated planning and control for robotic systems: A path-based approach provides an analytical integration of robot planning and control. As a result, the task level control can be achieved, and the system is capable of coping with unexpected or uncertain events

Our newly developed event-based planning and control theory is applied to robotic systems. It Introduces a suitable action or motion reference variable other than time, but directly related to the desired and measurable systems output, called event. Here the event is the length of the path tracked by a robot. It enables the construction of an integrated planning and control system where planning becomes a real-time closed-loop process. The path-based integration planning and control scheme is exemplified by a single-arm tracking problem. Time and energy optimal motion plans combined with nonlinear feedback control are derived in closed form. To the best of our knowledge, this closed-form solution was not obtained before. The equivalence of path-based and time-based representations of nonlinear feedback control is shown, and an overall system stability criterion has also been obtained. The application of event-based integrated planning and control provides the robotic systems the capability to cope with unexpected and uncertain events in real time, without the need for replanning. The theoretical results are illustrated and verified by experiments.     

An autonomous mobile robot with a 3D laser range finder for 3D exploration and digitalization of indoor environments

Digital 3D models of the environment are needed in rescue and inspection robotics, facility managements and architecture. This paper presents an automatic system for gaging and digitalization of 3D indoor environments. It consists of an autonomous mobile robot, a reliable 3D laser range finder and three elaborated software modules. The first module, a fast variant of the Iterative Closest Points algorithm, registers the 3D scans in a common coordinate system and relocalizes the robot. The second module, a next best view planner, computes the next nominal pose based on the acquired 3D data while avoiding complicated obstacles. The third module, a closed-loop and globally stable motor controller, navigates the mobile robot to a nominal pose on the base of odometry and avoids collisions with dynamical obstacles. The 3D laser range finder acquires a 3D scan at this pose. The proposed method allows one to digitalize large indoor environments fast and reliably without any intervention and solves the SLAM problem. The results of two 3D digitalization experiments are presented using a fast octree-based visualization method.