Trajectory Execution Research Articles

Haptic Identification of Surfaces as Fields of Force

The ability to discriminate an object's shape and mechanical properties from touch is one of the most fundamental somatosensory functions. When exploring physical properties of an object, such as stiffness and curvature, humans probe the object's surface and obtain information from the many sensory receptors in their upper limbs. This sensory information is critical for the guidance of actions. We studied how humans acquire an internal representation of the shape and mechanical properties of surfaces and how this information affects the execution of trajectories over the surface. Experiments involved subjects executing trajectories while holding a planar manipulandum that renders planar virtual objects with variable shape and mechanical properties. Subjects were instructed to make reaching movements with the hand between points on the boundary of a curved virtual disk of varying stiffness and curvature. The results suggest two classifications of adaptive responses: force perturbations and object boundaries. In the first case, a rectilinear hand movement is enforced by opposing the interaction forces. In the second case, the trajectory conforms to the object boundary so as to reduce interaction forces. While this dichotomy is evident for very rigid and very soft objects, the likelihood of an object boundary classification depended, in a smooth and monotonic way, on the average force experienced during the initial movements. Furthermore, the observed response across a variety of stiffness values lead to a constant average interaction force after adaptation. This suggests that the nervous system may select from the two responses through a mechanism that attempts to establish a constant interaction force.

Optimizing spherical navigator echoes for three‐dimensional rigid‐body motion detection

Spherical navigator (SNAV) echoes show promise in correcting for three-dimensional rigid-body motion. In this paper, several important parameters in the design and performance of the SNAV technique are discussed, including a novel sampling strategy, the optimal k-space radius and sampling density of the navigator, and the execution of the SNAV trajectory by the scanner hardware. A variable-sampling density (VSD) helical-spiral SNAV trajectory, which can acquire data on the entire spherical shell without exceeding the maximum slew rate of the scanner, is presented. To ensure that the VSD SNAV trajectory was properly executed by the scanner hardware, the gradient waveforms were verified using a self-encoding technique. The ability of the VSD SNAV to measure rotational and translational motion was studied with in vitro experiments at various k-space radii and sampling densities. The results of this study show that the best accuracy was attained at k-space radii of 1.4 and 1.6 cm(-1), with 2400 to 4000 samples acquired over the sphere.

Decoding continuous and discrete motor behaviors using motor and premotor cortical ensembles.

Decoding motor behavior from neuronal signals has important implications for the development of a brain-machine interface (BMI) but also provides insights into the nature of different movement representations within cortical ensembles. Motor control can be hierarchically characterized as the selection and planning of discrete movement classes and/or postures followed by the execution of continuous limb trajectories. Based on simultaneous recordings in primary motor (MI) and dorsal premotor (PMd) cortices in behaving monkeys, we demonstrate that an MI ensemble can reconstruct hand or joint trajectory more accurately than an equally sized PMd ensemble. In contrast, PMd can more precisely predict the future occurrence of one of several discrete targets to be reached. This double dissociation suggests that a general-purpose BMI could take advantage of multiple cortical areas to control a wider variety of motor actions. These results also support the hierarchical view that MI ensembles are involved in lower-level movement execution, whereas PMd populations represent the early intention to move to visually presented targets.

Computational Intelligence Based Approach for the Joint Trajectory Generation of Cooperative Robotic Systems

We discuss here the implementation aspects of recently developed tools of computational intelligence as applied to joint trajectory generation of a class of multi-joint cooperative robotic systems. This is an issue closely related to the inverse kinematics problem which usually represents a heavy computational burden on the processing power of any complex robotic structure. High nonlinearities, heavy coupling between the degrees of freedom, and time variant configuration of the robot structure heavily contribute to these difficulties. Soft computing techniques have surged in recent years as effective computational tools for emulating the human capabilities when dealing with complex systems. Some of them are used here to synthesize approaches capable of substantially improving the solving of the inverse kinematics problem for a class of robotic systems and help in generating the joint trajectories in a faster way. Comparative results are provided in terms of accuracy and CPU time required for the execution of different trajectories.

Parametric uncertainty on manipulators dynamics

This paper presents an efficient dynamic formulation for modeling and control of realistic six degrees-of-freedom robot manipulators. The basic dynamic formulation is based upon Kane’s approach. The zero-reference-position method is used to represent the robot and to formulate its governing kinematic equations. Both the inverse dynamics and the direct dynamic problems are discussed. The dynamic system model is controlled by utilizing a sophisticated feedback control scheme. The dynamic behavior of a robot with realistic complexity is examined with a view to investigate the effect of the system model errors on the precision of trajectory execution for the case when a good knowledge of the robot physical parameters may not be available.

Genetic design of dynamically optimal robotic manipulators

This paper presents a procedure for the genetic design of dynamically optimal robotic manipulators. This design procedure is task oriented and minimizes the reaction forces and moments induced by the manipulator during the execution of specific trajectories. These forces and moments are included in an objective function and their reduction is achieved by using genetic algorithms to calculate the balance weight and the associated eccentricity for each link for which the base reaction is minimized. This genetic design technique is illustrated by application to a planar RR manipulator.

Adaptive motor control to aid mobile robot trajectory execution in the presence of changing system parameters

Most of the mobile robot path planning algorithms presented to date, generate intermediate goal coordinates for a mobile robot to pursue, based upon the local environment and the position of the global target. In response to this, we present a general controller for any vehicle which is driven by changing target vectors and show that the restricted speed (or torque) capabilities of the vehicle can be modeled with a nonlinear saturation element. Although the goal attraction path parameters can be optimized so that a vehicle tracks its target in a near time optimal sense, the effect of motor parameter changes or disturbances to the controlled system upon the path of the robot is noted. When the process gain of the robot's motors change, due to temperature changes, run-in time etc., we show that the trajectory of the mobile robot is momentarily affected, before the closed loop control system again places the robot back on to its correct course. A novel method is presented, which manipulates the effective nonlinear speed saturation element, which models the actual speed or torque limitations of any vehicle, in order to remove this problem. Simple modifications can be applied to the derived control system, so that mobile robot adaptive target tracking can take place. The conditions necessary, which can be exploited to allow the response of a mobile robot to be insensitive to changes in motoring parameters are presented, and the method is demonstrated by purposely inducing process gain changes on a real mobile robot.

Time-optimal trajectories for cooperative multi-manipulator systems

We present two schemes for planning the time-optimal trajectory for cooperative multi-manipulator system (CMMS) carrying a common object. We assume that the desired path is given and parameterizable by an arclength variable. Both approaches take into account the dynamics of the manipulators and object. The first approach employs linear programming techniques, and it allows us to obtain the time-optimal execution of the given task utilizing the maximum torque capacities of the joint motors. The second approach is a sub-time-optimal method that is computationally very efficient. In the second approach the given load is divided into a share for each robot in the CMMS in a manner in which the trajectory acceleration/deceleration is maximized, hence the trajectory execution time is minimized. This load distribution approach uses optimization schemes that degenerate to a linear search algorithm for the case of two robots manipulating a common load, and this results in significant reduction of computation time. The load distribution scheme not only enables us to reduce the computation time, but also gives us the possibility of applying this method in real-time planning and control of CMMS. Further, we show that for certain object trajectories the load distribution scheme yields truly time-optimal trajectories.

Human-Machine Collaboration in Robotics: Integrating Virtual Tools with a Collision Avoidance Concept using Conglomerates of Spheres

This paper describes how virtual tools that represent real robot end-effectors are used in conjunction with a generalized conglomerate-of-spheres approach to collision avoidance in such a way that telerobotic trajectory planning can be accomplished using simple gesture phrases such as ‘put that there while avoiding that’. In this concept, an operator (or set of collaborators) need not train for cumbersome telemanipulation on several multiple-link robots, nor do robots need a priori knowledge of operator intent and exhaustive algorithms for evaluating every aspect of a detailed environment model. The human does what humans do best during task specification, while the robot does what machines do best during trajectory planning and execution. Four telerobotic stages were implemented to demonstrate this strategic supervision concept that will facilitate collaborative control between humans and machines. In the first stage, virtual reality tools are selected from a ‘toolbox’ by the operator(s) and then these virtual tools are computationally interwoven into the live video scene with depth correlation. Each virtual tool is a graphic representation of a robot end-effector (gripper, cutter, or other robot tool) that carries tool-use attributes on how to perform a task. An operator uses an instrumented glove to virtually retrieve the disembodied tool, in the shared scene, and place it near objects and obstacles while giving key-point gesture directives, such as ‘cut there while avoiding that’. Collaborators on a network may alter the plan by changing tools or tool positioning to achieve preferred results from their own perspectives. When parties agree, from wherever they reside geographically, the robot(s) create and execute appropriate trajectories suitable to their own particular links and joints. Stage two generates standard joint-interpolated trajectories, and later creates potential field trajectories if necessary. Stage three tests for collisions with obstacles identified by the operator and modeled as conglomerates of spheres. Stage four involves automatic grasping (or cutting etc.) once the robot camera acquires a close-up view of the object during approach. In this paper particular emphasis is placed on the conglomerate-of-spheres approach to collision detection as integrated with the virtual tools concept for a Puma 560 robot by the Virtual Tools and Robotics Group in the Computer Integrated Manufacturing Laboratory at The Pennsylvania State University (Penn State).

Hand acceleration impulse bandwidth during target acquisition: implications for teleoperator bandwidth requirements

The purpose of this experiment was to provide data about bandwidth requirements for teleoperators. During teleoperation, user inputs are changes in forces applied to the master controller arising from changes in hand acceleration during execution of goal-directed trajectories, so human hand acceleration bandwidth sets an upper bound on teleoperator feedforward bandwidth requirements. Participants completed a set of computerized target acquisition tasks using a mouse, and the computer recorded the cursor trajectory. Movement time, positioning error, the number of acceleration-deceleration impulses, impulse bandwidth, impulse amplitude, and impulse period were calculated from the trajectory trace. The results obtained show that to completely capture hand trajectories, master controllers and slave arms must have acceleration bandwidth higher than 9.20 Hz. However, it may be that only the joints closest to the end-effector need to accommodate the highest bandwidths and shoulder joints may only need to accommodate 5.63 Hz acceleration bandwidth. >

Intensified array camera imaging of solid surface combustion aboard the NASA Learjet

An intensified array camera has been used to image weakly luminous flames spreading over thermally thin paper samples in a low-gravity environment aboard the NASA-Lewis Learjet. The aircraft offers 10 to 20 sec of reduced gravity during execution of a Keplerian trajectory and allows the use of instrumentation that is delicate or requires higher electrical power than is available in drop towers. The intensified array camera is a charge intensified device type that responds to light between 400 and 900 nm and has a minimum sensitivity of 10(exp 6) footcandles. The paper sample, either ashless filter paper or a lab wiper, burns inside a sealed chamber which is filled with 21, 18, or 15 pct. oxygen in nitrogen at one atmosphere. The camera views the edge of the paper and its output is recorded on videotape. Flame positions are measured every 0.1 sec to calculate flame spread rates. Comparisons with drop tower data indicate that the flame shapes and spread rates are affected by the residual g level in the aircraft.

Computing the feasible configurations of a 7-DOF arm subject to joint limits

A seven-degree-of-freedom (7-DOF) anthropomorphic arm requires the control of the relative orientation of the elbow to satisfy task, kinematic, and dynamic constraints. While prior work has dealt primarily with iterative repulsive schemes to avoid joint limit stops, a geometric algorithm for explicitly computing the set of feasible configurations of a zero-offset arm at an arbitrary position with respect to the current position is presented. The data facilitates trajectory planning that takes into account a wide range of factors, including the limit stops, rather than reacting to limit stops encountered during trajectory execution. The algorithm was implemented to run on the JIFFE robotics processor. JIFFE computes the feasible configuration set and, mostly for testing, uses the data for inverse kinematics in 10 mu s. >

Manipulator Inverse Kinematics for Untimed End-Effector Trajectories With Ordinary Singularities

This article addresses the following inverse kinematics problem: given an untimed spatial end-effector trajectory, determine joint trajectories that are consistent with its execution. An algorithm for the continuous iterative solution of this problem for six-degree-of-freedom manipulators of arbitrary structure is presented. The main idea of this algorithm is that it converges with equal ease at both regular configurations and certain ( "or dinary ") singularities. Ordinary singularities (herein defined) depend on the given end-effector trajectory, as well as the ma nipulator configuration, and represent "dead points" where the end effector (but not the manipulator) must pause during trajectory execution. The algorithm is based on the predictor-corrector method of path following using (1) a newly developed second-order predictor, (2) a first-order Newton method corrector, and (3) the idea of including the end effector's position (along its trajec tory) as a dependent (rather than independent) variable in the formulation. Both the predictor and the corrector are derived from Taylor series expansion of the 4 x 4 matrix equation of closure and require only the solution of linear systems of equations. Examples are given that demonstrate the algorithm's ability to pass through ordinary singularities to determine alternate joint trajectories for the same end-effector trajectory. These examples also show how ordinary singularities can be included in manipulator motions that are similar to a boxer's jab or a runner's kick.

An Object-Directed Pathplanning System for Multiple Robots with Singularity-Coping Properties

The design of trajectory planning concepts for the realtime control of multirobot systems still deserves attention due to unsolved problems that arise, if manipulators work together cooperatively. Coordinated operation of robots is an efficient approach to perform tasks, which require the handling of large, heavy or sensitive loads. In order to take full advantage of the inherent multirobot capabilities, the variety of tasks ranges from independent operation of individual robots to the execution of tasks with several manipulators working together cooperatively. The object-oriented concept presented here offers a uniform approach for the trajectory planning of both individual and coordinated robot movements. The basic concept of trajectory planning had to be extended systematically to provide all the functionality necessary for cooperative tasks. As dynamic limitations of individual robots due to the approaching to singular configurations are of increasing importance in the case of coordinated operation, algorithms which are able to cope with singularities in multirobot systems have been implemented. The algorithm presented here supports teleoperation by means of six dimensional sensor balls and automatic execution of paths as well. Due to the pathtracking properties of the algorithm, deviations from the desired trajectory can be avoided. This ensures the accurate execution of trajectories generated offline with the help of CAD-tools. Integrating this method into the hierarchical trajectory planning system offers both userconformable and safe operation taking automatically account of the kinematic restrictions imposed by the load. This approach has been experimentally verified in the scope of the CIROS-project (Control of Intelligent Robots in Space) where a concept for space automation with the aid of robotics has been elaborated and exemplarily realized. The entire system contains components for man-machine- interaction, planning, world modeling, simulation, coordinated operation and collision avoidance which cooperate in several time spheres on different levels of abstraction. By means of a tool exchange facility two robots with seven degrees of freedom each are equipped with appropriate endeffectors to perform a wide range of handling tasks. This paper concentrates on the aspect of multirobot control as a part of work in the field of coordinated operation, where independent and coordinated operation as well as the modes of automatic pathplanning and teleoperation have been implemented to provide the functionality required for the control of robots in the CIROS project.

Constraint Generation for Trajectory Planning Systems

In this paper we formulate the problem of determining constraints in the parameter space used for planning reference trajectories for tracking systems. The objective is to obtain parameter constraints which allow a maximal amount of maneuverability while assuring that operatmg limits will not be violated and that the system can execute the prescribed reference trajectory within a given error tolerance. We present a numerical algorithm for generating the parameter constrants based on previously computed constraints in the space of the continuous-time trajectory and its derivatives. A simplicial approximation method is used to generate a polyhedral approximation to a maximal set of parameters corresponding to executable trajectories. Supervisory planning and control can then be carried out in the reference trajectory parameter space without detailed simulation of the underlying system dynamics. We illustrate the computational algorithm and its application to trajectory planning for a two-axis CNC cutting tool.

Torque-limited path following by online trajectory time scaling

A feedback scheme for path following by trajectory time scaling is presented. The scheme is used in execution of fast trajectories along a geometric path, where the motion is limited by torque constraints. The time scaling is done by using a secondary controller that modifies a nominal trajectory during motion. The nominal, high-performance trajectory typically leads to torques that are at the limits, which leaves no control authority to compensate for modeling errors and disturbances. By modifying the time scaling of the nominal trajectory when the torques saturate, closed-loop action is possible. A key idea is that a scalar quantity (the path acceleration) is modified, resulting in coordinated adjustment of the individual joint motions. Two algorithms for online trajectory scaling are presented. One is based on online bounds on path acceleration, and one is designed to handle nominal minimum time trajectories. The functionality of the secondary controller is verified by simulations and experiments.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Evaluation and Time-Scaling of Trajectories for Wheeled Mobile Robots

A method is presented for evaluating the feasibility of trajectories generated by path-planning systems for wheeled mobile robots (WMRs). Constraints that limit the class of executable trajectories for a given WMR are classified as path constraints, kinematic constraints, and dynamic constraints. Path constraints, which are limits on the path geometry, are a function of the wheelbase configuration and steering mechanism. Limits that involve only functions of velocities and accelerations are termed kinematic constraints. Dynamic constraints refer to limits on force/torque inputs and frictional force constraints which must be satisfied for a trajectory to be feasible. We show that when path constraints are violated the path must be modified to achieve feasibility, while violations of kinematic and dynamic constraints can be eliminated by time scaling so that the same path is followed at a slower speed. The concepts are developed and illustrated in the context of a model for the dynamics of conventionally steered vehicle.

A vectorized Monte Carlo code to simulate charged-particle motion within crystals

A new Monte Carlo method for the calculation of blocking patterns in single crystals is described. Vectorized execution and use of the same trajectories to simulate many different processes substantially reduce computing time.

High Speed Optical Scanning Techniques for Dimensional Measurement

Recently, human–robot cooperation (HRC) research activities have focused on the development of new methodologies for the generation of safe robot trajectories. However, the applicability of such methodologies in a real context is limited due to the inherent uncertainty of robot trajectory execution time (i.e. the robot can avoid the worker by modifying its velocity along the path). This paper proposes an approach to estimate a confidence interval on robot trajectory execution time for scenarios in which human–robot space sharing is required. First, human arm movements are studied for a given set of assembly collaborative tasks: worker occupancy volumes and occupancy volume probabilities are derived. Then, a finite number of alternative robot trajectories, crossing human occupancy volumes with different occupancy probabilities, are generated. It is therefore possible to estimate a probability for the robot to reduce its velocity, and a confidence interval on the robot execution time. The application on a real assembly case is discussed.

Planning and Execution of Straight Line Manipulator Trajectories

Recently developed manipulator control languages typically specify motions as sequences of points through which a tool affixed to the end of the manipulator is to pass. The effectiveness of such motion specification formalisms is greatly increased if the tool moves in a straight line between the user-specified points. This paper describes two methods for achieving such straight line motions. The first method is a refinement of one developed in 1974 by R. Paul. Intermediate points are interpolated along the Cartesian straight line path at regular intervals during the motion, and the manipulator's kinematic equations are solved to produce the corresponding intermediate joint parameter values. The path interpolation functions developed here offer several advantages, including less computational cost and improved motion characteristics. The second method uses a motion planning phase to precompute enough intermediate points so that the manipulator may be driven by interpolation of joint parameter values while keeping the tool on an approximately straight line path. This technique allows a substantial reduction in real time computation and permits problems arising from degenerate joint alignments to be handled more easily. The planning is done by an efficient recursive algorithm which generates only enough intermediate points to guarantee that the tool's deviation from a straight line path stays within prespecified error bounds.