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This paper presents a unified and efficient method of solving the inverse kinematics for 6 d.o.f. serial connections of two 3 d.o.f. serial and parallel manipulators.
Techniques for improving the performance of robotic-manipulator path-control systems comprising independent SISO feedback controllers for each joint are discussed and illustrated with block diagrams, reviewing the results of recent analytical investigations. Topics examined include the servo design for a single link, the equations of motion for manipulators, SISO servo design for multiple links, inverse methods, pole placement with compensation of the gravity terms, linear state-feedback control based on the perturbation equations, and adaptive control methods. Consideration is given to variable-structure systems, suboptimal controllers, and the optimal-design-strategy approach.
The authors present a new scheme for the adaptive control of mechanical manipulators along with proof of convergence. Difficulties encountered in the input-error type adaptive controller are remedied by combining an explicit identifier with discrete time updates of the parameter values along with a computed torque type control law. The new scheme requires no matrix inversion with its consequent drain on the computational power of the controller. A discussion is presented of the dynamic model of a manipulator, a computed torque adaptive scheme, an input error identifier, and a hybrid identifier.
A simple direct stress analysis method is proposed for a laminate with a clearance-fit fastener subjected to combined bearing and bypass loads in tension or compression, including bearing and bypass loads on bolt-hole contact and local stresses. The approach uses a linear-elastic finite element analysis with an inverse formulation; conditions along the bolt-hole interface are specified by constraint equations that limit nodal displacements to a circular arc corresponding to the bolt diameter. The application of the method to the analysis of the effects of bearing-bypass loading on bolt-hole contact angles and local stresses, with the plate material properties representing a quasi-isotropic T300/5208 graphite/epoxy laminate, is discussed.
This paper presents the complete forward and inverse kinematics solutions for control of the three degree-of-freedom (DOF) double octahedral variable geometry truss (VGT) module as an extensible gimbal. A VGT is a truss structure partially comprised of linearly actuated members. A VGT can be used as joints in a large, lightweight, high load-bearing manipulator for earth- and space-based remote operations, plus industrial applications. The results have been used to control the NASA VGT hardware as an extensible gimbal, demonstrating the capability of this device to be a joint in a VGT-based manipulator. This work is an integral part of a VGT-based manipulator design, simulation, and control tool.
Symbolic inversion of the Jacobian matrix for spherical wrist arms is investigated. It is shown that, taking advantage of the simple geometry of these arms, the closed-form solution of the system Q = J-1X, representing a transformation from task space to joint space, can be obtained very efficiently. The solutions for PUMA, Stanford, and a six-revolute-joint coplanar arm, along with all singular points, are presented. The solution for each joint variable is found as an explicit function of the singular points which provides a better insight into the effect of different singular points on the motion and force exertion of each individual joint. For the above arms, the computation cost of the solution is on the same order as the cost of forward kinematic solution and it is significantly reduced if forward kinematic solution is already obtained. A comparison with previous methods shows that this method is the most efficient to date.
Superconducting quantum interference device (SQUID) microscopes are a new generation of instruments that map magnetic fields with unprecedented spatial resolution and moment sensitivity. Unlike standard rock magnetometers, SQUID microscopes map magnetic fields rather than measuring magnetic moments such that the sample magnetization pattern must be retrieved from source model fits to the measured field data. In this paper, we presented the first direct comparison between paleomagnetic analyses on natural samples using joint measurements from SQUID microscopy and moment magnetometry. We demonstrated that in combination with apriori geologic and petrographic data, SQUID microscopy can accurately characterize the magnetization of lunar glass spherules and Hawaiian basalt. The bulk moment magnitude and direction of these samples inferred from inversions of SQUID microscopy data match direct measurements on the same samples using moment magnetometry. In addition, these inversions provide unique constraints on the magnetization distribution within the sample. These measurements are among the most sensitive and highest resolution quantitative paleomagnetic studies of natural remanent magnetization to date. We expect that this technique will be able to extend many other standard paleomagnetic techniques to previously inaccessible microscale samples.
Energy efficient, lightweight robot arms for space applications have considerable structural flexibility. For large and fast motions, both the nonlinear coupled dynamics and the elastic behavior of the robots must be considered in control system designs. This paper presents an approach to the control of a class of flexible robotic systems. A control law is derived which decouples the joint-angle motion from the flexible motion and asymptotically decomposes the elastic dynamics into two subsystems, representing the transverse vibrations of the elastic link in two orthogonal planes. This decomposition allows the design of an elastic mode stabilizer independently based on lower order models representing structural flexibility. The closed-loop system is shown to be globally asymptotically stable and robust to uncertainty in system parameters. Simulation results are presented to show that large, fast control of joint angles can be performed in spite of space vehicle motion and uncertainty in the payload.
Many microgravity space-science experiments require vibratory acceleration levels that are unachievable without active isolation. The Boeing Corporation's active rack isolation system (ARIS) employs a novel combination of magnetic actuation and mechanical linkages to address these isolation requirements on the International Space Station. Effective model-based vibration isolation requires: (1) An isolation device, (2) an adequate dynamic; i.e., mathematical, model of that isolator, and (3) a suitable, corresponding controller. This Technical Memorandum documents the validation of that high-fidelity dynamic model of ARIS. The verification of this dynamics model was achieved by utilizing two commercial off-the-shelf (COTS) software tools: Deneb's ENVISION(registered trademark), and Online Dynamics Autolev(trademark). ENVISION is a robotics software package developed for the automotive industry that employs three-dimensional computer-aided design models to facilitate both forward and inverse kinematics analyses. Autolev is a DOS-based interpreter designed, in general, to solve vector-based mathematical problems and specifically to solve dynamics problems using Kane's method. The simplification of this model was achieved using the small-angle theorem for the joint angle of the ARIS actuators. This simplification has a profound effect on the overall complexity of the closed-form solution while yielding a closed-form solution easily employed using COTS control hardware.
A Space Robot Simulator Vehicle (SRSV) was constructed to model a free-flying robot capable of doing construction, manipulation and repair work in space. The SRSV is intended as a test bed for development of dynamic and static control methods for space robots. The vehicle is built around a two-foot-diameter air-cushion vehicle that carries batteries, power supplies, gas tanks, computer, reaction jets and radio equipment. It is fitted with one or two two-link manipulators, which may be of many possible designs, including flexible-link versions. Both the vehicle body and its first arm are nearly complete. Inverse dynamic control of the robot's manipulator has been successfully simulated using equations generated by the dynamic simulation package SDEXACT. In this mode, the position of the manipulator tip is controlled not by fixing the vehicle base through thruster operation, but by controlling the manipulator joint torques to achieve the desired tip motion, while allowing for the free motion of the vehicle base. One of the primary goals is to minimize use of the thrusters in favor of intelligent control of the manipulator. Ways to reduce the computational burden of control are described.
Control for the bracing strategy is being examined. It was concluded earlier that trajectory planning must be improved to best achieve the bracing motion. Very interesting results were achieved which enable the inverse dynamics of flexible arms to be calculated for linearized motion in a more efficient manner than previously published. The desired motion of the end point beginning at t=0 and ending at t=t sub f is used to calculate the required torque at the joint. The solution is separated into a causal function that is zero for t is less than 0 and an accusal function which is zero for t is greater than t sub f. A number of alternative end point trajectories were explored in terms of the peak torque required, the amount of anticipatory action, and other issues. The single link case is the immediate subject and an experimental verification of that case is being performed. Modeling with experimental verification of closed chain dynamics continues. Modeling effort has pointed out inaccuracies that result from the choice of numerical techniques used to incorporate the closed chain constraints when modeling our experimental prototype RALF (Robotic Arm Large and Flexible). Results were compared to TREETOPS, a multi body code. The experimental verification work is suggesting new ways to make comparisons with systems having structural linearity and joint and geometric nonlinearity. The generation of inertial forces was studied with a small arm that will damp the large arm's vibration.
Future manned space operations for Space Station Freedom will call for a variety of carefully planned multimedia digital communications, including full-frame-rate color video, to support remote operations of scientific experiments. This paper presents the results of an investigation to determine if video compression is a viable solution to transmission bandwidth constraints. It reports on the impact of different levels of compression and associated calculational parameters on image acceptability to investigators in life-sciences research at ARC. Three nonhuman life-sciences disciplines (plant, rodent, and primate biology) were selected for this study. A total of 33 subjects viewed experimental scenes in their own scientific disciplines. Ten plant scientists viewed still images of wheat stalks at various stages of growth. Each image was compressed to four different compression levels using the Joint Photographic Expert Group (JPEG) standard algorithm, and the images were presented in random order. Twelve and eleven staffmembers viewed 30-sec videotaped segments showing small rodents and a small primate, respectively. Each segment was repeated at four different compression levels in random order using an inverse cosine transform (ICT) algorithm. Each viewer made a series of subjective image-quality ratings. There was a significant difference in image ratings according to the type of scene viewed within disciplines; thus, ratings were scene dependent. Image (still and motion) acceptability does, in fact, vary according to compression level. The JPEG still-image-compression levels, even with the large range of 5:1 to 120:1 in this study, yielded equally high levels of acceptability. In contrast, the ICT algorithm for motion compression yielded a sharp decline in acceptability below 768 kb/sec. Therefore, if video compression is to be used as a solution for overcoming transmission bandwidth constraints, the effective management of the ratio and compression parameters according to scientific discipline and experiment type is critical to the success of remote experiments.
Spatial operators have been used to analyze the dynamics of robotic multibody systems and to develop novel computational dynamics algorithms. Mass matrix factorization, inversion, diagonalization, and linearization are among several new insights obtained using such operators. While initially developed for serial rigid body manipulators, the spatial operators and the related mathematical analysis have been shown to extend very broadly including to tree and closed topology systems, to systems with flexible joints, links, etc. This work uses concepts from graph theory to explore the mathematical foundations of spatial operators. The goal is to study and characterize the properties of the spatial operators at an abstract level so that they can be applied to a broader range of dynamics problems. The rich mathematical properties of the kinematics and dynamics of robotic multibody systems has been an area of strong research interest for several decades. These properties are important to understand the inherent physical behavior of systems, for stability and control analysis, for the development of computational algorithms, and for model development of faithful models. Recurring patterns in spatial operators leads one to ask the more abstract question about the properties and characteristics of spatial operators that make them so broadly applicable. The idea is to step back from the specific application systems, and understand more deeply the generic requirements and properties of spatial operators, so that the insights and techniques are readily available across different kinematics and dynamics problems. In this work, techniques from graph theory were used to explore the abstract basis for the spatial operators. The close relationship between the mathematical properties of adjacency matrices for graphs and those of spatial operators and their kernels were established. The connections hold across very basic requirements on the system topology, the nature of the component bodies, the indexing schemes, etc. The relationship of the underlying structure is intimately connected with efficient, recursive computational algorithms. The results provide the foundational groundwork for a much broader look at the key problems in kinematics and dynamics. The properties of general graphs and trees of nodes and edge were examined, as well as the properties of adjacency matrices that are used to describe graph connectivity. The nilpotency property of such matrices for directed trees was reviewed, and the adjacency matrices were generalized to the notion of block weighted adjacency matrices that support block matrix elements. This leads us to the development of the notion of Spatial Kernel Operator SKO kernels. These kernels provide the basis for the development of SKO resolvent operators.
This paper is concerned with the implementation and assessment of joint motion management strategies for kinematically redundant robotic manipulators operating in the micro-gravity environment of Space Station. These robots must be capable of conducting experiments and manufacturing processes without disturbing the micro-gravity environment through base reactions/motions. The redundant degrees of freedom of the manipulator permit the inverse kinematic problem to be solved simultaneously with the minimization of a cost function. The cost function in this case is the weighted sum of the squares of the base forces and moments and is minimized over discrete time segments. The Generalized Inverse Method and Rayleigh Ritz technique are used to solve the combined optimization/inverse kinematics problem. Numerical examples include various robotic configurations and degrees of manipulator redundancy.
This paper describes the algorithm used to point the high gain antennae on NASA/JPL's Mars Exploration Rovers. The gimballed antennae must track the Earth as it moves across the Martian sky during communication sessions. The algorithm accounts for (1) gimbal range limitations, (2) obstructions both on the rover and in the surrounding environment, (3) kinematic singularities in the gimbal design, and (4) up to two joint-space solutions for a given pointing direction. The algorithm computes the intercept-times for each of the occlusions and chooses the jointspace solution that provides the longest track time before encountering an occlusion. Upon encountering an occlusion, the pointing algorithm automatically switches to the other joint-space solution if it is not also occluded. The algorithm has successfully provided flop-free pointing for both rovers throughout the mission.
The COMEX (CO2 and MEthane eXperiment) campaign supports the mission definition of CarbonSat and HyspIRI (Hyperspectral Infrared Imager) by providing representative airborne remote sensing data ‐ MAMAP (Methane Airborne MAPper) for CarbonSat; the Airborne Visual InfraRed Imaging Spectrometer (Classic & Next Generation) AVIRIS‐C/AVIRIS‐NG for HyspIRI ‐ as well as ground-based and airborne in‐situ data. The objectives of the COMEX campaign activities are (see Campaign Implementation Plan (RD‐4)): 1. Investigate spatial/spectral resolution trade‐offs for CH4 anomaly detection and flux inversion by comparison of MAMAP‐derived emission estimates with AVIRIS/AVIRIS‐NG derived data. 2. Evaluate sun‐glint observation geometry on CH4 retrievals for marine sources. 3. Characterize the effect of Surface Spectral Reflectance (SSR) heterogeneity on trace gas retrievals of CO2 and CH4 for medium and low‐resolution spectrometry. 4. Identify benefits from joint SWIR/TIR (ShortWave InfraRed/Thermal InfraRed ) data for trace gas detection and retrieval by comparison of MAMAP and AVIRIS/AVIRIS‐NG NIR/SWIR data with MAKO (Aerospace Corp.)TIR data. The ability to derive emission source strength for a range of strong emitting targets by remote sensing will be evaluated from combined AVIRIS‐NG and MAMAP data, adding significant value to the HyspIRI campaign AVIRIS‐NG dataset. The data will be used to quantify anomalies in atmospheric CO2 and CH4 from strong local greenhouse gas sources e.g. localized industrial complexes, landfills, etc. and to derive CO2 and CH4 emissions estimates from atmospheric gradient measurements. The original campaign concept was developed by University of Bremen and BRI. The COMEX campaign is funded bilaterally by NASA and ESA (European Space Agency). Whereas NASA funds the US part of the project via a contract with Dr. Ira Leifer, BRI (Bubbleology Research International), the contribution of MAMAP to the COMEX campaign is funded by ESA within the COMEX‐E project and NASA with respect to a 50 percent contribution to the flight-related costs of flying MAMAP on a US aircraft. The Data Acquisition Report (RD‐9) describes the instrumentation used, the measurements made by the team during the COMEX campaign in May/June 2014 and August/September 2014 in California, and an initial assessment of the data quality.
An efficient, adaptive neural learning paradigm for addressing the inverse kinematics of redundant manipulators is presented. The proposed methodology exploits the infinite local stability of terminal attractors - a new class of mathematical constructs which provide unique information processing capabilities to artificial neural systems. For robotic applications, synaptic elements of such networks can rapidly acquire the kinematic invariances embedded within the presented samples. Subsequently, joint-space configurations, required to follow arbitrary end-effector trajectories, can readily be computed. In a significant departure from prior neuromorphic learning algorithms, this methodology provides mechanisms for incorporating an in-training skew to handle kinematics and environmental constraints.
Cooperative research in microwave remote sensing between the Hydrological Sciences Branch of the NASA Goddard Space Flight Center and the Earth Sciences Faculty of the Vrije Universiteit Amsterdam began with the Botswana Water and Energy Balance Experiment and has continued through a series of highly successful International Research Programs. The collaboration between these two research institutions has resulted in significant scientific achievements, most notably in the area of satellite-based microwave remote sensing of soil moisture. The Botswana Program was the first joint research initiative between these two institutions, and provided a unique data base which included historical data sets of Scanning Multifrequency Microwave Radiometer (SN4NM) data, climate information, and extensive soil moisture measurements over several large experimental sites in southeast Botswana. These data were the basis for the development of new approaches in physically-based inverse modelling of soil moisture from satellite microwave observations. Among the results from this study were quantitative estimates of vegetation transmission properties at microwave frequencies. A single polarization modelling approach which used horizontally polarized microwave observations combined with monthly composites of Normalized Difference Vegetation Index was developed, and yielded good results. After more precise field experimentation with a ground-based radiometer system, a dual-polarization approach was subsequently developed. This new approach realized significant improvements in soil moisture estimation by satellite. Results from the Botswana study were subsequently applied to a desertification monitoring study for the country of Spain within the framework of the European Community science research programs EFEDA and RESMEDES. A dual frequency approach with only microwave data was used for this application. The Microwave Polarization Difference Index (MPDI) was calculated from 37 GHz data and used to derive the one-way canopy transmissivity. Using a simple radiative transfer model, this information was combined with horizontally polarized 6.6 GHz SMMR observations to derive a 9-year time series of soil moisture for all of Spain at a one quarter degree spatial scale. Both day and night SMMR observations were used independently, in order to check the consistency of the results. A first order Fourier Transform was performed on the mean monthly soil moisture values to identify major characteristics of time series such as trend, amplitude, and phase shift.