Showing papers on "Motion planning published in 1993"

Nonholonomic motion planning: steering using sinusoids

Abstract: Methods for steering systems with nonholonomic c.onstraints between arbitrary configurations are investigated. Suboptimal trajectories are derived for systems that are not in canonical form. Systems in which it takes more than one level of bracketing to achieve controllability are considered. The trajectories use sinusoids at integrally related frequencies to achieve motion at a given bracketing level. A class of systems that can be steered using sinusoids (claimed systems) is defined. Conditions under which a class of two-input systems can be converted into this form are given. >

Simulating humans: computer graphics animation and control

Abstract: 1. Introduction and Historical Background 1.1 Why make human figure models? 1.2 Historical roots 1.3 What is currently possible? 1.4 Manipulation, animation, and simulation 1.5 What did we leave out? 2. Mody Modeling 2.1 Geometric body modeling 2.2 Representing articulated figures 2.3 A flexible torso model 2.4 Shoulder complex 2.5 Clothing models 2.6 The anthropometry database 2.7 The anthropometry spreadsheet 2.8 Strength and torque display 3. Spatial Interaction 3.1 Direct manipulation 3.2 Manipulation with constraints 3.3 Inverse kinematic positioning 4. Behavioral Control of Articulated Figures 4.1 An interactive system for postural control 4.2 Interactive manipulation with behaviors 4.3 The animation interface 4.4 Human figure motions 4.5 Virtual human control 5. Simulation with Societies of Behaviors 5.1 Forward simulation with behaviors 5.2 Locomotion 5.3 Strength guided motion 5.4 Collision-free path and motion planning 5.5 Posture planning 6. Task-level Specifications 6.1 Performance simulation with simple commands 6.2 Natural language expressions of kinematics and space 6.3 Task-level simulation 6.4 A framework for instruction understanding 7. Epilogue 7.1 A road map toward the future 7.2 Conclusion

Elastic bands: connecting path planning and control

Abstract: Elastic bands are proposed as the basis for a framework to close the gap between global path planning and real-time sensor-based robot control. An elastic band is a deformable collision-free path. The initial shape of the elastic is the free path generated by a planner. Subjected to artificial forces, the elastic band deforms in real time to a short and smooth path that maintains clearance from the obstacles. The elastic continues to deform as changes in the environment are detected by sensors, enabling the robot to accommodate uncertainties and react to unexpected and moving obstacles. While providing a tight connection between the robot and its environment, the elastic band preserves the global nature of the planned path. The framework is outlined, and an efficient implementation based on bubbles is discussed. >

Kinodynamic motion planning

Abstract: Kinodynamic planning attempts to solve a robot motion problem subject to simultaneous kinematic and dynamics constraints. In the general problem, given a robot system, we must find a minimal-time trajectory that goes from a start position and velocity to a goal position and velocity while avoiding obstacles by a safety margin and respecting constraints on velocity and acceleration. We consider the simplified case of a point mass under Newtonian mechanics, together with velocity and acceleration bounds. The point must be flown from a start to a goal, amidst polyhedral obstacles in 2D or 3D. Although exact solutions to this problem are not known, we provide the first provably good approximation algorithm, and show that it runs in polynomial time

The applications of harmonic functions to robotics

Abstract: Harmonic functions are solutions to Laplace's equation. Such functions can be used to advantage for potential-field path planning because they do not exhibit spurious local minima. Harmonic functions are shown here to have a number of properties that are essential to robotics applications. Paths derived from harmonic functions are generally smooth. Harmonic functions also offer a complete path-planning algorithm. We show how a harmonic function can be used as the basis for a reactive admittance control. Such schemes allow incremental updating of the environment model. Methods for computing harmonic functions respond well to sensed changes in the environment, and can be used for control while the environment model is being updated.

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

Abstract: 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.

Optimal and Efficient Path Planning for Unknown and Dynamic Environments

Abstract: : The task of planning trajectories for a mobile robot has received considerable attention in the research literature. Algorithms exist for handling a variety of robot shapes, configurations, motion constraints, and environments. Most of the work assumes the robot has a complete and accurate model of its environment before it begins to move; less attention has been paid to the problem of unknown or partially-known environments. This situation occurs for an exploratory robot or one that must move to a goal location without the benefit of a floorplan (indoor) or terrain map (outdoor). Existing approaches plan an initial global path or route based on known information and then modify the plan locally as the robot discovers obstacles with its sensors. While this strategy works well in environments with small, sparse obstacles, it can lead to grossly suboptimal and incomplete results in cluttered spaces. An alternative approach is to replan the global path from scratch each time a new obstacle is discovered.

The Parti-Game Algorithm for Variable Resolution Reinforcement Learning in Multidimensional State-Spaces

Abstract: Parti-game is a new algorithm for learning feasible trajectories to goal regions in high dimensional continuous state-spaces In high dimensions it is essential that neither planning nor exploration occurs uniformly over a state-space Parti-game maintains a decision-tree partitioning of state-space and applies techniques from game-theory and computational geometry to efficiently and adaptively concentrate high resolution only on critical areas The current version of the algorithm is designed to find feasible paths or trajectories to goal regions in high dimensional spaces Future versions will be designed to find a solution that optimizes a real-valued criterion Many simulated problems have been tested, ranging from two-dimensional to nine-dimensional state-spaces, including mazes, path planning, non-linear dynamics, and planar snake robots in restricted spaces In all cases, a good solution is found in less than ten trials and a few minutes

Flatness, motion planning and trailer systems

Abstract: A solution of the motion planning without obstacles for the standard a-trailer system is proposed This solution relies basically on the fact that the system is flat with the Cartesian coordinates of the last trailer as a linearizing output The Frenet formulae are used to simplify the calculations and permit to deal with angle constraints The general 1-trailer system, where the trailer is not directly hitched to the car at the center of the rear axle, is also flat The geometric construction used for the standard 1-trailer system can be extended to this more realistic system MATLAB simulations illustrate this method >

Real-time collision avoidance in teleoperated whole-sensitive robot arm manipulators

Abstract: The problem of generating collision-free motion in an operator-assisted teleoperated robot arm manipulator system is discussed. The concentration is on several system requirements: a real real-time operation, a guarantee of collision-free motion for the entire body of the arm manipulator, and an ability to handle obstacles of arbitrary shapes. The suggested methodology draws on recent work on motion planning with incomplete information for whole-sensitive robots. >

A Differential Geometric Approach to Motion Planning

Abstract: We propose a general strategy for solving the motion planning problem for real analytic, controllable systems without drift. The procedure starts by computing a control that steers the given initial point to the desired target point for an extended system, in which a number of Lie brackets of the system vector fields are added to the right-hand side. The main point then is to use formal calculations based on the product expansion relative to a P. Hall basis, to produce another control that achieves the desired result on the formal level. It then turns out that this control provides an exact solution of the original problem if the given system is nilpotent. When the system is not nilpotent, one can still produce an iterative algorithm that converges very fast to a solution. Using the theory of feedback nilpotentization, one can find classes of non-nilpotent systems for which the algorithm, in cascade with a precompensator, produces an exact solution in a finite number of steps. We also include results of simulations which illustrate the effectiveness of the procedure.

Motion planning in dynamic environments using the relative velocity paradigm

Abstract: A simple and efficient approach to the computation of avoidance maneuvers among moving obstacles is presented. The method is discussed for the case of a single maneuvering object avoiding several obstacles moving on known linear trajectories. The original dynamic problem is transformed into several static problems using the relative velocity between the maneuvering object and each obstacle. The static problems are converted into a single problem by means of a vector transformation, and the set of velocity vectors guaranteeing the avoidance of all the obstacles is computed. Within this set, the best maneuver for the particular approach can be selected. The geometric background of this approach is developed for both 2-D and 3-D cases, and the method is applied to an example of a 3-D avoidance maneuver. >

Trajectory generation for the N-trailer problem using Goursat normal form

Abstract: Shows how the machinery of exterior differential systems can be used to help solve nonholonomic motion planning problems. Since the Goursat normal form, for exterior differential systems is dual to chained form for vector fields, the authors solve the problem of steering a mobile robot with N trailers by converting the system into chained form, doing the path-planning in the chained form coordinates, and converting the path back into the original coordinates. Simulations of the N-trailer system parallel parking and backing into a loading dock are included. >

Controllability of a multibody mobile robot

Abstract: This paper presents a proof of controllability for a multibody mobile robot (e.g., a car pulling and pushing trailers like a luggage carrier in an airport). Such systems appear as canonical systems to illustrate the tools from differential geometric control theory required by nonholonomic motion planning. Three modeling steps are considered: geometric, differential, and control steps. The author derives the kinematic equations for four distinct multibody mobile robot systems: a convoy driven by 1) a unicycle, 2) a two-driving wheels vehicle, 3) a real car and 4) the first two bodies. He shows that these four control systems correspond to the same differential model, which is then used to give the same proof of controllability. Previous work proved the controllability of two-body systems and three-body systems. The main result of this paper is prove the controllability for a general n-body system. >

On the Dynamics of Space Manipulators Using the Virtual Manipulator, with Applications to Path Planning

Abstract: Robotic manipulators carried by future spacecraft are expected to perform important tasks in space, such as the servicing of satellites. However, the performance of these systems could be severely degraded by dynamic disturbances to the spacecraft caused by manipulator motions. This paper presents a method for representing the dynamics of space manipulator systems using the recently developed Virtual Manipulator (VM) concept. This representation is then applied to develop algorithms which can be used to plan manipulator motions that minimize disturbances of the spacecraft.

Blending reactivity and goal-directedness in a fuzzy controller

Abstract: Controlling the movement of an autonomous mobile robot requires the ability to pursue strategic goals in a highly reactive way. The authors describe a fuzzy controller for such a mobile robot that can take abstract goals into consideration. Through the use of fuzzy logic, reactive behavior, e.g., avoiding obstacles on the way, and goal-oriented behavior, e.g., trying to reach a given location, are smoothly blended into one sequence of control actions. The technique proposed has been implemented in the SRI mobile robot Flakey, resulting in extremely smooth and reliable movement. >

Exploration and model building in mobile robot domains

Abstract: The first results on COLUMBUS, an autonomous mobile robot, are presented. COLUMBUS operates in initially unknown structured environments. Its task is to explore and model the environment efficiently while avoiding collisions with obstacles. COLUMBUS uses an instance-based learning technique for modeling its environment. Real-world experiences are generalized via two artificial neural networks that encode the characteristics of the robot's sensors, as well as the characteristics of typical environments which the robot is assumed to face. Once trained, these networks allow for the transfer of knowledge across different environments the robot will face over its lifetime. Exploration is achieved by navigating to low confidence regions. A dynamic programming method is employed in background to find minimal-cost paths that, when executed by the robot, maximize exploration. >

Computation of configuration-space obstacles using the fast Fourier transform

Abstract: This paper presents a new method for computing the configuration-space map of obstacles that is used in motion-planning algorithms. The method derives from the observation that, when the robot is a rigid object that can only translate, the configuration space is a convolution of the workspace and the robot. This convolution is computed with the use of the fast Fourier transform (FFT) algorithm. The method is particularly promising for workspaces with many and/or complicated obstacles, or when the shape of the robot is not simple. It is an inherently parallel method that can significantly benefit from existing experience and hardware on the FFT. >

Primitives for smoothing mobile robot trajectories

Abstract: Clothoids are very useful for smoothing the motion of a mobile robot moving along a trajectory. This paper addresses the problem of smoothing mobile robot motions when cusps, i.e., changes of motion direction along the trajectory, are imposed. We pinpoint some special curves (that we call "anticlothoids") and we discuss how they can be used together with clothoids in order to smooth a predefined trajectory. >

Fast path planning using modified A* method

Abstract: An algorithm is presented for planning the path of an object (robot) through an obstacle cluttered space by using a modified A* method for searching through the free space. The A* method can be extremely slow for large numbers of cells to be searched. The alternative presented is to use trial vectors that span several cells to aid in the planning. The fine resolution of the obstacle mapping is maintained. A loose search is performed on the fine grid. The paths that are found using this method are slightly sub-optimal. The speed of the searching algorithm is significantly increased. Solution times for three-dimensional problems are typically below 100 milliseconds, while the traditional A* search for the same problem is several minutes. The trade-off is a large speed increase for a slight degradation in path length optimality. Two-dimensional problems are solved very quickly. >

Motion Planning amidst Fat Obstacles

Abstract: The complexity of exact 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. In practice, the complexity of the free space tends to be much smaller. We show that, under some realistic assumptions, the complexity of the free space of a robot moving amidst fat obstacles is linear in the number of obstacles. The complexity results lead to efficient algorithms for motion planning amidst fat obstacles: we show that the motion planning algorithm by Schwartz and Sharir runs in time if the obstacles are fat. Finally, we modify the algorithm to improve the running time to

The "Ariadne's clew" algorithm: global planning with local methods

Abstract: The goal of the work described is to build a path planner able to drive a robot in a dynamic environment where the obstacles are moving. In order to do so, the authors propose a method, called Ariadne's clew algorithm, to build a global path planner based on the combination of two local planning algorithms: an explore algorithm and a search algorithm. The purpose of the explore algorithm is to collect information about the environment with an increasingly fine resolution by placing landmarks in the searched space. The goal of the search algorithm is to opportunistically check if the target can be easily reached from any given placed landmark. The Ariadne's clew algorithm is shown to be very fast is most cases, allowing planning in dynamic environment. It is shown to be complete, which means that it is sure to find a path when one exists. A massively parallel implementation of this algorithm is described.

System for obstacle avoidance path planning for multiple-degree-of-freedom mechanism

Abstract: In a system for obstacle avoidance path finding for a multiple-degree-of-freedom mechanism such as a mobile robot moving from a starting point to a goal while avoiding obstacles. Obstacles are defined to be a virtual space having a continuous drag coefficient that increases with increasing proximity to the obstacles. A path is determined on the basis of the variational principle as the extreme for a functional such as time required for the mobile robot's movement. Since the viscous drag coefficient is greatest at the obstacles, the determined path does not go through the obstacles thereby avoiding the obstacles. Moreover, since the path is determined on the variational principle, the time required for the movement is adopted as the functional, the determined path will locally be that of minimum time.

Design and motion planning of a mechanical snake

Abstract: The paper presents the design and motion planning for a mechanical snake robot that was built at the University of Michigan. The structure of the robot enables it to move without wheels. It is constructed of a series of articulated links, each one with a motor and linear solenoid. Although each link has only one motor, this structure allows the body configuration to be easily controlled thereby enabling the robot to move in very cluttered environments. The motion planning system provides the robot with a basic motion pattern that can be easily modified for different tasks and environments. The mechanical snake does not avoid obstacles on its way, but rather "accommodates" them by continuing its motion towards the target while in contact with the obstacles. With the authors' design and motion planning, each link has a different number of degrees-of-freedom in each motion stage, providing the robot with great adaptability even during contact with obstacles in a cluttered environment. >

A global approach to path planning for redundant manipulators

Abstract: This paper presents a new approach to path planning for redundant manipulators. The path planning problem is posed as a finite time nonlinear control problem which can be solved by a Newton-Raphson type algorithm together with an exterior penalty function method. This technique is capable of handling various goal task definitions as well as incorporating both joint and task space constraints. The algorithm has shown promising results in planning joint path sequences to meet Cartesian goal planning and path following. In contrast to local approaches, this algorithm is less prone to problems such as singularities and local minima. Applications to planar 3R and 4R arms, cooperating 3R arms and a spatial 9 DOF arm are included. >

Dynamic trajectory planning with dynamic constraints: A 'state-time space' approach

Abstract: This paper address dynamic trajectory planning, which is defined as trajectory planning for a robot subject to dynamic constraints and moving in a dynamic workspace, i.e., with moving obstacles. The authors propose the concept of state-time space as a tool to formulate dynamic trajectory planning problems. The state-time space of a robot is its state space augmented by the time dimension. The constraints imposed by both the moving obstacles and the dynamic constraints can be represented by static forbidden regions of state-time space. Since a trajectory maps to a curve in state-time space, dynamic trajectory planning simply consists in finding a curve in state-time space. This concept is used to determine a time-optimal trajectory for a car-like robot subject to dynamic constraints and moving along a given path on a dynamic planar workspace.

On the dynamics of contact between space robots and configuration control for impact minimization

Abstract: Contact between free-flying space robots, and the minimization of the impulse at contact are studied. A general approach for modeling systems with a moving base is presented. In particular, the formulation of the dynamical equations of motion for a space-based manipulator system with external applied forces are considered. The new equation of motion is then used to derive a dynamical contact model. Unlike previous approaches, the analysis takes into account both relative translational and rotational motions between contacting bodies. An analysis of the dynamical contact model reveals that the impulse at contact could be minimized by the optimization of a scalar cost function. Two approaches to the Cartesian space planning problem for space-based systems are discussed. A joint space planning strategy that achieves both trajectory tracking and impact minimization is proposed. Simulation results for a fifteen-degree-of-freedom (DOF) space robot are presented. >

Further progress in robot juggling: the spatial two-juggle

Abstract: A spatial two-juggle is discussed. The device has the ability to bat two freely falling balls into stable periodic vertical trajectories with a single three degree-of-freedom robot arm using a real-time stereo camera system for sensory input. After a brief review of a previously-reported one-juggle, the author's initial approach to the two-juggle planning and control problem is described. A number of important refinements to their initial strategy are given. Data from typical two-juggle runs in the laboratory are given. >

The complexity of the free space for a robot moving amidst fat obstacles

Abstract: We propose a new definition of fatness of geometric objects and compare it with alternative definitions. We show that, under some realistic assumptions, the complexity of the free space for a robot, with any fixed number of degrees of freedom moving in a d-dimensional Euclidean workspace with fat obstacles, is linear in the number of obstacles. The complexity of motion planning algorithms depends on the complexity of the robot's free space, and theoretically, the complexity of the free space can be very high. Thus, our result opens the way to devising provable efficient motion planning algorithms in certain realistic settings.

Event-based planning and control for multi-robot coordination

Abstract: A planning and control scheme for multi-robot coordination is presented. An event-based motion reference that drives the system to achieve the best possible coordination is introduced. The general task space is combined with the nonlinear feedback technique to design hybrid position/force controllers. To improve the force control performance, the dynamics of joint motors are taken into account. For a given task, a task projection operator can be found for each robot, with consideration of redundancy management. A distributed computing architecture is proposed for parallel implementation of this scheme. The event-based coordination scheme was experimentally implemented and tested for the coordinated control of two six-degree-of-freedom PUMA 560 robots with very good results. >