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The tracking problem for a globally minimum phase nonlinear system is considered. It is assumed that the signal to be tracked is slowly varying and a priori bounds on its magnitude are known. It is shown that if the system has bounded derivatives and exponentially stable zero dynamics then the system admits an output feedback controller which solves the tracking problem.
Closed-form solutions are derived for a class of tracking problems including a linear optimal regulator and a prefilter for a time-invariant plant. The solutions for the prefilter equation and state trajectory coupled by the Riccati equation are exponentially related to the stability matrix of the plant. A computational procedure is presented in recursive form when the desired output state dynamics is assumed linear and time-invariant. Several examples are given for illustration.
General equations for standard deviation, and rms standard deviation of least squares fitted polynomials applied to Apollo tracking problems
A unified treatment of the linear quadratic tracking (LQT) problem, in which a control system's dynamics are modeled by a linear evolution equation with a nonhomogeneous component that is linearly dependent on the control function u, is presented; the treatment proceeds from the theoretical formulation to a numerical approximation framework. Attention is given to two categories of LQT problems in an infinite time interval: the finite energy and the finite average energy. The behavior of the optimal solution for finite time-interval problems as the length of the interval tends to infinity is discussed. Also presented are the formulations and properties of LQT problems in a finite time interval.
An approach using a globally nonsingular representation is proposed for the attitude control problem of a rigid body. The attitude dynamics are described by the nonlinear Euler equation together with the nonlinear kinematic equations which relate a representation of attitude to the angular velocity of the body. When this approach is combined with an energy-motivated Lyapunov function, a large class of globally stable attitude control laws can be derived. This class includes model-independent tracking control, model-dependent tracking control, and adaptive control, allowing tradeoffs between controller complexity, attainable performance, and available model information.
The problem of maneuvering a flexible spacecraft through a large angle while requiring the feedback control system to track a desired output state is considered. The desired output state is assumed to be provided by the corresponding open-loop maneuvering solution for the linear system model. Closed form solutions are provided for the Riccati and prefilter equations defining the optimal control. Example maneuvers are presented where control-rate penalties have been included in the performance index, in order to smooth both the open- and closed-loop control commands.
A single observation station, located at an arbitrary point on the surface of the Earth, can determine only the azimuth and elevation angles of a satellite or ballistic vehicle, and the time at which these observations occur. No information is available about the range or the range-rate of the target. It is shown that five observations of either the elevation or the azimuth, and the time of either set of observations, determine the complete set of orbital elements of the target. The implementation of the theory presented here could provide a great reduction in the hardware costs associated with satellite and reentry vehicle tracking.
The problem of maneuvering a flexible spacecraft through a large-angle while requiring a sub-vector of the terminal state to exactly satisfy a set of terminal constraints is considered. The necessary conditions for this problem lead to three coupled nonlinear Riccati-like differential equations, which are solved in closed form. Example maneuvers are presented where control-rate penalties have been included in the performance index, in order to smooth the closed-loop control commands. Furthermore, example maneuvers are presented for both fixed and free and condition problem.
The STS-78 Space Shuttle Program Mission Report summarizes the Payload activities as well as the Orbiter, External Tank (ET), Solid Rocket Booster (SRB), Reusable Solid Rocket Motor (RSRM), and the Space Shuttle main engine (SSME) systems performance during the seventy-eighth flight of the Space Shuttle Program, the fifty-third flight since the return-to-flight, and the twentieth flight of the Orbiter Columbia (OV-102). In addition to the Orbiter, the flight vehicle consisted of an ET that was designated ET-79; three SSME's that were designated as serial numbers 2041, 2039, and 2036 in positions 1, 2, and 3, respectively; and two SRB's that were designated BI-081. The RSRM's, designated RSRM-55, were installed in each SRB and the individual RSRM's were designated as 360L055A for the left SRB, and 360L055B for the right SRB. The STS-78 Space Shuttle Program Mission Report fulfills the Space Shuttle Program requirement as documented in NSTS 07700, Volume 7, Appendix E. The requirement stated in that document is that each organizational element supporting the Program will report the results of their hardware (and software) evaluation and mission performance plus identify all related in-flight anomalies. The primary objective of this flight was to successfully perform the planned operations of the Life and Microgravity Spacelab experiments. The secondary objectives of this flight were to complete the operations of the Orbital Acceleration Research Experiment (OARE), Biological Research in Canister Unit-Block II (BRIC), and the Shuttle Amateur Radio Experiment II-Configuration C (SAREX-II). The STS-78 mission was planned as a 16-day, plus one day flight plus two contingency days, which were available for weather avoidance or Orbiter contingency operations. The sequence of events for the STS-78 mission is shown in Table 1, and the Space Shuttle Vehicle Management Office Problem Tracking List is shown in Table 2. The Government Furnished Equipment/Flight Crew Equipment (GFE/FCE) Problem Tracking List is shown in Table 3. The Marshall Space Flight Center (MSFC) Problem Tracking List is shown in Table 4. Appendix A lists the sources of data, both formal and informal, that were used to prepare this report. Appendix B provides the definition of acronyms and abbreviations used throughout the report. All times during the flight are given in Greenwich mean time (G.m.t.) and mission elapsed time (MET).
We present an online multi-object tracking algorithm to track multiple objects across a large number of image frames. Our work is motivated by the need to study evolution of nanoscale objects by transmission electron microscopy. The proposed approach is based on the existing multi-way data association tracking algorithm that is capable of tracking interacting objects with complex behaviors (i.e., merge, split, overlap, and appearance or disappearance). The multi-way data association is an offline algorithm to associate objects across all image frames at one step with a global optimization, which does not scale very well for large number of image frames. The proposed online tracking algorithm processes image frames as they arrive by detecting all objects in the newly arrived image frame and making the associations of the objects to those detected from the previous frame by the multi-way data association. This frameby-frame association scheme can cause fragmented traces of the objects that are occasionally misdetected for some image frames. We overcome this issue by allowing previously unassociated objects to be associated when the objects reappear within a fixed number of future image frames, namely the frame-delayed association. We combine the multi-way data association with the frame-delayed association to be able to track interacting objects with accurate handling of object disappearance events. The proposed method is validated through applications to simulated multi-object tracking problem and a real multi-object tracking problem. Here, the outcome of the proposed method is compared with four state-of-the-art algorithms.
The STS-77 Space Shuttle Program Mission Report summarizes the Payload activities as well as the: Orbiter, External Tank (ET), Solid Rocket Booster (SRB), Reusable Solid Rocket Motor (RSRM), and the Space Shuttle Main Engine (SSME) systems performance during the seventy-seventh flight of the Space Shuttle Program, the fifty-second flight since the return-to-flight, and the eleventh flight of the Orbiter Endeavour (OV-105). STS-77 was also the last flight of OV-105 prior to the vehicle being placed in the Orbiter Maintenance Down Period (OMDP). In addition to the Orbiter, the flight vehicle consisted of an ET that was designated ET-78; three SSME's that were designated as serial numbers 2037, 2040, and 2038 in positions 1, 2, and 3, respectively; and two SRB's that were designated BI-080. The RSRM's, designated RSRM-47, were installed in each SRB and the individual RSRM's were designated as 360TO47A for the left SRB, and 360TO47B for the right SRB. The STS-77 Space Shuttle Program Mission Report fulfills the Space Shuttle Program requirement as documented in NSTS 07700, Volume VII, Appendix E. The requirement stated in that document is that each organizational element supporting the Program will report the results of their hardware (and software) evaluation and mission performance plus identify all related in-flight anomalies. The primary objectives of this flight were to successfully perform the operations necessary to fulfill the requirements of Spacehab-4, the SPARTAN 207/inflatable Antenna Experiment (IAE), and the Technology Experiments Advancing Missions in Space (TEAMS) payload. Secondary objectives of this flight were to perform the experiments of the Aquatic Research Facility (ARF), Brilliant Eyes Ten-Kelvin Sorption Cryocooler Experiment (BETSCE), Biological Research in Canisters (BRIC), Get-Away-Special (GAS), and GAS Bridge Assembly (GBA). The STS-77 mission was planned as a 9-day flight plus 1 day, plus 2 contingency days, which were available for weather avoidance or Orbiter contingency operations. The sequence of events for the STS-77 mission is shown in Table 1, and the Space Shuttle Vehicle Management Office Problem Tracking List is shown in Table 11. The Government Fumished Equipment/Flight Crew Equipment (GFE/FCE) Problem Tracking List is shown in Table II. Appendix A lists the sources of data, both formal and informal, that were used to prepare this report. Appendix B provides the definition of acronyms and abbreviations used throughout the report. All times during the flight are given in Greenwich mean time (G.m.t.) and mission elapsed time (MET). The six-person crew for STS-77 consisted of John H. Casper, Col., U. S. Air Force, Commander; Curtis L. Brown, Jr., Lt. Col., U. S. Air Force, Pilot; Andrew S. W. Thomas, Civilian, Ph.D., Mission Specialist 1; Daniel W. Bursch, CDR., U. S. Navy, Mission Specialist 2; Mario Runco, Jr., Civilian, Mission Specialist 3; and Marc Gameau, Civilian, PhD, Mission Specialist 4.
In this paper the control of the Lorenz system for both stabilization and tracking problems is studied via feedback linearization and differential flatness. By using the Rayleigh number as the control, only variable physically tunable, a barrier in the controllability of the system is incidentally imposed. This is reflected in the appearance of a singularity in the state transformation. Composite controllers that overcome this difficulty are designed and evaluated. The transition through the manifold defined by such a singularity is achieved by inducing a chaotic response within a boundary layer that contains it. Outside this region, a conventional feedback nonlinear control is applied. In this fashion, the authority of the control is enlarged to the whole. state space and the need for high control efforts is mitigated. In addition, the differential parametrization of the problem is used to track nonlinear functions of one state variable (single tracking) as well as several state variables (cooperative tracking). Control tasks that lead to integrable and non-integrable differential equations for the nominal flat output in steady-state are considered. In particular, a novel numerical strategy to deal with the non-integrable case is proposed. Numerical results validate very well the control design.
A Cartesian-space position/force controller is presented for redundant robots. The proposed control structure partitions the control problem into a nonredundant position/force trajectory tracking problem and a redundant mapping problem between Cartesian control input F is a set member of the set R(sup m) and robot actuator torque T is a set member of the set R(sup n) (for redundant robots, m is less than n). The underdetermined nature of the F yields T map is exploited so that the robot redundancy is utilized to improve the dynamic response of the robot. This dynamically optimal F yields T map is implemented locally (in time) so that it is computationally efficient for on-line control; however, it is shown that the map possesses globally optimal characteristics. Additionally, it is demonstrated that the dynamically optimal F yields T map can be modified so that the robot redundancy is used to simultaneously improve the dynamic response and realize any specified kinematic performance objective (e.g., manipulability maximization or obstacle avoidance). Computer simulation results are given for a four degree of freedom planar redundant robot under Cartesian control, and demonstrate that position/force trajectory tracking and effective redundancy utilization can be achieved simultaneously with the proposed controller.
Theoretical aspects of radar tracking problem and design criteria for radar tracking systems
The design of a microwave landing system (MLS) aircraft receiver, capable of optimal performance in multipath environments found in air terminal areas, is reported. Special attention was given to the angle tracking problem of the receiver and includes tracking system design considerations, study and application of locally optimum estimation involving multipath adaptive reception and then envelope processing, and microcomputer system design. Results show processing is competitive in this application with i-f signal processing performance-wise and is much more simple and cheaper. A summary of the signal model is given.
The STS-46 Space Shuttle Program Mission Report contains a summary of the Orbiter, External Tank (ET), Solid Rocket Booster/Redesigned Solid Rocket Motor (SRB/RSRM), and the Space Shuttle main engine (SSME) subsystem performance during the forty-ninth flight of the Space Shuttle Program, and the twelfth flight of the Orbiter vehicle Atlantis (OV-104). In addition to the Atlantis vehicle, the flight vehicle consisted of the following: an ET, designated ET-48 (LWT-41); three SSME's, which were serial numbers 2032, 2033, and 2027 in positions 1, 2, and 3, respectively; and two SRB's which were designated BI-052. The lightweight/redesigned SRM's that were installed in each SRB were designated 360W025A for the left RSRM and 360L025B for the right RSRM. The primary objective of this flight was to successfully deploy the European Retrievable Carrier (EURECA) payload and perform the operations of the Tethered Satellite System-1 (TSS-1) and the Evaluation of Oxygen Interaction with Material 3/Thermal Energy Management Processes 2A-3 (EOIM-3/TEMP 2A-3). The secondary objectives of this flight were to perform the operations of the IMAX Cargo Bay Camera (ICBC), Consortium for Material Development in Space Complex Autonomous Payload-2 and 3 (CONCAP-2 and CONCAP-3), Limited Duration Space Environment Candidate Materials Exposure (LDCE), Pituitary Growth Hormone Cell Function (PHCF), and Ultraviolet Plume Instrumentation (UVPI). In addition to summarizing subsystem performance, this report also discusses each Orbiter, ET, SSME, SRB, and RSRM in-flight anomaly in the applicable section of the report. Also included in the discussion is a reference to the assigned tracking number as published on the Problem Tracking List. All times are given in Greenwich mean time (G.m.t.) as well as mission elapsed time (MET).
An adaptive control technique to improve the flying qualities of an aircraft in turbulence was investigated. The approach taken was to obtain maximum likelihood estimates of the unknown coefficients of the aircraft system and then, using these estimates along with the separation principle, to define the stochastic optimal control. The maximum likelihood estimation technique that accounted for the effects of turbulence provided good estimates of the unknown coefficients and of the turbulence. The assessment of the stochastic optimal control based on the maximum likelihood estimates showed that the desired effects were attained for the regulator problem of minimizing pitch angle and the tracking problem of requiring normal acceleration to follow the pilot input.
1) The pilot study provided meaningful conclusions that are generally consistent with the earlier Test Effectiveness work done between 1992 and 1994: a) Analysis of pre-launch problem/failure reports is consistent with earlier work. b) Analysis of post-launch early mission anomaly reports indicates that there are more software issues in newer missions, and the no-test category for identification of post-launch failures is more significant than in the earlier analysis. 2) Future work includes understanding how differences in Missions effect these analyses: a) There are large variations in the number of problem reports and issues that are documented by the different Projects/Missions. b) Some missions do not have any reported environmental test anomalies, even though environmental tests were performed. 3) Each project/mission has different standards and conventions for filling out the PFR forms, the industry may wish to address this issue: a) Existing problem reporting forms are to document and track problems, failures, and issues (etc.) for the projects, to ensure high quality. b) Existing problem reporting forms are not intended for data mining.