Computationally efficient control allocation
10 Aug 2000-Journal of Guidance Control and Dynamics (American Institute of Aeronautics and Astronautics, AIAA)-Vol. 24, Iss: 3, pp 519-524
TL;DR: In this paper, a computationally efficient method for calculating near-optimal solutions to the three-objective, linear control allocation problem is disclosed, which is measured by the number of floating-point operations required for solution.
Abstract: A computationally efficient method for calculating near-optimal solutions to the three-objective, linear control allocation problem is disclosed. The control allocation problem is that of distributing the effort of redundant control effectors to achieve some desired set of objectives. The problem is deemed linear if control effectiveness is affine with respect to the individual control effectors. The optimal solution is that which exploits the collective maximum capability of the effectors within their individual physical limits. Computational efficiency is measured by the number of floating-point operations required for solution. The method presented returned optimal solutions in more than 90% of the cases examined; non-optimal solutions returned by the method were typically much less than 1% different from optimal and the errors tended to become smaller than 0.01% as the number of controls was increased. The magnitude of the errors returned by the present method was much smaller than those that resulted from either pseudo inverse or cascaded generalized inverse solutions. The computational complexity of the method presented varied linearly with increasing numbers of controls; the number of required floating point operations increased from 5.5 i, to seven times faster than did the minimum-norm solution (the pseudoinverse), and at about the same rate as did the cascaded generalized inverse solution. The computational requirements of the method presented were much better than that of previously described facet-searching methods which increase in proportion to the square of the number of controls.
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TL;DR: The major conclusion is that constrained optimization can be performed with computational requirements that fall within an order of magnitude of those of simpler methods.
Abstract: The performanceand computational requirements ofoptimization methodsfor control allocation areevaluated Two control allocation problems are formulated: a direct allocation method that preserves the directionality of the moment and a mixed optimization method that minimizes the error between the desired and the achieved momentsaswellasthecontroleffortTheconstrainedoptimizationproblemsaretransformedinto linearprograms so that they can be solved using well-tried linear programming techniques such as the simplex algorithm A variety of techniques that can be applied for the solution of the control allocation problem in order to accelerate computations are discussed Performance and computational requirements are evaluated using aircraft models with different numbers of actuators and with different properties In addition to the two optimization methods, three algorithms with low computational requirements are also implemented for comparison: a redistributed pseudoinverse technique, a quadratic programming algorithm, and a e xed-point method The major conclusion is that constrained optimization can be performed with computational requirements that fall within an order of magnitude of those of simpler methods The performance gains of optimization methods, measured in terms of the error between the desired and achieved moments, are found to be small on the average but sometimes signie cantAvariety ofissuesthataffecttheimplementation ofthevariousalgorithmsin ae ight-controlsystem are discussed
628 citations
Cites methods from "Computationally efficient control a..."
...In the case of the direct allocation problem, the simplex algorithm applied to the associated LP problem constitutes an alternative to the implementation of [12], with the benefit that it guarantees a solution in a finite period of time....
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...Another fast technique was proposed in [12]....
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...Note that the direct allocation problem may be solved as an LP problem for an arbitrary number of rows in the matrix CB, as opposed to the algorithms proposed earlier [11], [12]....
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TL;DR: In this article, a command filtered backstepping approach is presented that uses adaptive function approximation to control UAVs using three feedback loops, including an inner loop that generates surface position commands.
Abstract: A command filtered backstepping approach is presented that uses adaptive function approximation to control unmanned air vehicles. The controller is designed using three feedback loops. The command inputs to the airspeed and flight-path angle controller are x c , γ c , V c and the bounded first derivatives of these signals. That loop generates comand inputs μ c , α c for a wind-axis angle loop. The sideslip angle command β c is always zero. The wind-axis angle loop generates rate commands P c , Q c , R c for an inner loop that generates surface position commands. The control approach includes adaptive approximation of the aerodynamic force and moment coefficient functions. The approach maintains the stability (in the sense of Lyapunov) of the adaptive function approximation process in the presence of magnitude, rate, and bandwidth limitations on the intermediate states and the surfaces.
330 citations
01 Jan 2003
TL;DR: In this paper, an adaptive backstepping and nonlinear observer design method is proposed for nonlinear control problems in flight control and the results are presented in a general framework and can also be applied to other areas.
Abstract: In this thesis we study a number of nonlinear control problems motivated by their appearance in flight control. The results are presented in a general framework and can also be applied to other areas. The two main topics are backstepping and control allocation.Backstepping is a nonlinear control design method that provides an alternative to feedback linearization. Here, backstepping is used to derive robust linear control laws for two nonlinear systems, related to angle of attack control and flight path angle control, respectively. The resulting control laws require less modeling information than corresponding designs based on feedback linearization, and achieve global stability in cases where feedback linearization can only be performed locally. Further, a method for backstepping control of a rigid body is developed, based on a vector description of the dynamics. We also discuss how to augment an existing nonlinear controller to suppress constant input disturbances. Two methods, based on adaptive backstepping and nonlinear observer design, are proposed.Control allocation deals with actuator utilization for overactuated systems. In this thesis we pose the control allocation problem as a constrained least squares problem to account for actuator position and rate constraints. Efficient solvers based on active set methods are developed with similar complexity to existing, approximate, pseudoinverse methods. A method for dynamic control allocation is also proposed which enables a frequency dependent control distribution among the actuators to be designed. Further, the relationship between control allocation and linear quadratic control is investigated. It is shown that under certain circumstances, the two techniques give the same freedom in distributing the control effort among the actuators. An advantage of control allocation, however, is that since the actuator constraints are considered, the control capabilities of the actuator suite can be fully exploited.
305 citations
TL;DR: Constrained control allocation is studied, and it is shown how an explicit piecewise linear representation of the optimal solution can be computed numerically using multiparametric quadratic programming.
Abstract: Constrained control allocation is studied, and it is shown how an explicit piecewise linear representation of the optimal solution can be computed numerically using multiparametric quadratic programming. Practical benefits of the approach include simple and efficient real-time implementation that permits software verifiability. Furthermore, it is shown how to handle control deficiency, reconfigurability, and flexibility to incorporate, for example, rate constraints. The algorithm is demonstrated on several overactuated aircraft control configurations, and the computational complexity is compared to other explicit approaches from the literature. The applicability of the method is further demonstrated using overactuated marine vessel dynamic position experiments on a scale model in a basin.
122 citations
Dissertation•
01 Jan 2003
TL;DR: In this article, the authors proposed a method for better compensation of the second type of disturbances, slowly-varying forces, by introducing feedback from measured acceleration, which was shown theoretically and through model experiments that positioning performance can be improved without compromising on thruster usage.
Abstract: This dissertation contains new results on the design of dynamic positioning (DP) systems for marine surface vessels A positioned ship is continuously exposed to environmental disturbances, and the objective of the DP system is to maintain the desired position and heading by applying adequate propeller thrust The disturbances can be categorized into three classes First, there are stationary forces mainly due to wind, ocean currents, and static wave drift Secondly, there are slowly-varying forces mainly due to wave drift, a phenomenon experienced in irregular seas Finally there are rapid, zero mean linear wave loads causing oscillatory motion with the same frequency as the incoming wave train The main contribution of this dissertation is a method for better compensation of the second type of disturbances, slowly-varying forces, by introducing feedback from measured acceleration It is shown theoretically and through model experiments that positioning performance can be improved without compromising on thruster usage The specific contributions are: • Observer design: Two observers with wave filtering capabilities was developed, analyzed, and tested experimentally Both of them incorporate position and, if available, velocity and acceleration measurements Filtering out the rapid, zero mean motion induced by linear wave loads is particularly important whenever measured acceleration is to be used by the DP controller, because in an acceleration signal, the high frequency contributions from the linear wave loads dominate • Controller design: A low speed tracking controller has been developed The proposed control law can be regarded as an extension of any conventional PID-like design, and stability was guaranteed for bounded yaw rate A method for numerically calculating this upper bound was proposed, and for most ships the resulting bound will be higher than the physical limitation For completeness, the missing nonlinear term that, if included in the controller, would ensure global exponential stability was identified The second contribution of this dissertation is a new method for mapping controller action into thruster forces A low speed control allocation method for overactuated ships equipped with propellers and rudders was derived Active use of rudders, together with propeller action, is advantageous in a DP operation, because the overall fuel consumption can be reduced A new model ship, Cybership II, together with a low-cost position reference system was developed with the aim of testing the proposed concepts The acceleration experiments were carried out at the recently developed Marine Cybernetics Laboratory, while the control allocation experiment was carried out at the Guidance, Navigation and Control Laboratory The main results of this dissertation have been published or are still under review for publication in international journals and at international conferences
119 citations
References
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TL;DR: In this article, the problem of the allocation of several airplane flight controls to the generation of specified body-axis moments is addressed, and a direct method of allocating these several controls is presented that guarantees the maximum possible moment can be generated within the constraints of the controls.
Abstract: This paper addresses the problem of the allocation of several airplane flight controls to the generation of specified body-axis moments. The number of controls is greater than the number of moments being controlled, and the ranges of the controls are constrained to certain limits. They are assumed to be individually linear in their effect throughout their ranges of motion and independent of one another in their effects. The geometries of the subset of the constrained controls and of its image in moment space are examined. A direct method of allocating these several controls is presented that guarantees the maximum possible moment can be generated within the constraints of the controls. It is shown that no single generalized inverse can yield these maximum moments everywhere without violating some control constraint. A method is presented for the determination of a generalized inverse that satisfies given specifications which are arbitrary but restricted in number. We then pose and solve a minimization problem that yields the generalized inverse that best approximates the exact solutions. The results are illustrated at each step by an example problem involving three controls and two moments.
527 citations
10 Aug 1998
TL;DR: The control allocation problem is defined in terms of solving or approximately solving a system of linear equations subject to constraints for redundant actuator control variable commands as mentioned in this paper, where the constraints arise from actuation rate and position limits.
Abstract: The control allocation problem is defined in terms of solving or approximately solving a system of linear equations subject to constraints for redundant actuator control variable commands. There is one equation for each controlled axis. The constraints arise from actuation rate and position limits. An axis priority weighting is introduced when the equations cannot be solved exactly because of the constraints. A actuator command preference weighting and preferred values are introduced to uniquely solve the equations when there are more unknowns than equations. Several approaches to this problem are discussed. The approaches are broadly grouped into linear and quadratic programming approaches. While the linear programming approach is well suited to solving the general problem a computationally faster but approximate solution was found with the quadratic programming approach. Example results based on tailless aircraft flight control are presented to illustrate the key aspects of the approaches to control allocation. Conclusions and recommendations are stated relative to the various approaches.
218 citations
TL;DR: In this paper, a method for the solution of the constrained control allocation problem for the case of three moments is presented, in which the number of controls is greater than the total number of moments being controlled, and the ranges of the controls are constrained to certain limits.
Abstract: This paper presents a method for the solution of the constrained control allocation problem for the case of three moments. The control allocation problem is to find the "best" combination of several flight control effectors for the generation of specified body-axis moments. The number of controls is greater than the number of moments being controlled, and the ranges of the controls are constrained to certain limits. The controls are assumed to be individually linear in their effect throughout their ranges of motion and complete in the sense that they generate moments in arbitrary combinations. The best combination of controls is taken to be an apportioning of the controls that yields the greatest total moment in a specified ratio of moments without exceeding any control constraint. The method of solving the allocation problem is presented as an algorithm and is demonstrated for a problem of seven aerodynamic controls on an F-18 airplane.
208 citations
TL;DR: This paper describes the results of recent research into the problem of allocating several flight control effectors to generate moments acting on a flight vehicle using various generalized inverse solutions and a hybrid solution utilizing daisy chaining.
Abstract: This paper describes the results of recent research into the problem of allocating several flight control effectors to generate moments acting on a flight vehicle. The results focus on the use of various generalized inverse solutions and a hybrid solution utilizing daisy chaining. In this analysis, the number of controls is greater than the number of moments being controlled, and the ranges of the controls are constrained to certain limits. The control effectors are assumed to be individually linear in their effects throughout their ranges of motion and independent of one another in their effects. A standard of comparison is developed based on the volume of moments or moment coefficients a given method can yield using admissible control deflections. Details of the calculation of the various volumes are presented. Results are presented for a sample problem involving 10 flight control effectors. The effectivenesses of the various allocation schemes are contrasted during an aggressive roll about the velocity vector at low dynamic pressure. The performance of three specially derived generalized inverses, a daisy-chaining solution, and direct control allocation are compared.
141 citations
Patent•
16 Jul 1996TL;DR: In this paper, a region is repeatedly scanned providing a plurality of images or data sets having points corresponding to ojbects in the region to be tracked, and an M-dimensional combinatorial optimization assignment problem is formulated using the points from M-1 of the images or datasets, wherein each point is preferably used in extending at most one track.
Abstract: A method and system for real-time tracking of objects is disclosed. A region is repeatedly scanned providing a plurality of images or data sets having points corresponding to ojbects in the region to be tracked. Given a previously determined track for each object in the region, an M-dimensional combinatorial optimization assignment problem is formulated using the points from M-1 of the images or data sets, wherein each point is preferably used in extending at most one track. The M-dimensional problem is subsequently solved for an optimal or near-optimal assignment of the points to the tracks, extending the tracking of the objects so that a response to each object can be initiated by the system in real-time. Speed and accuracy is provided by an iterative Lagrangian Relaxation technique wherein a plurality of constraint dimensions are relaxed simultaneously to yield a reduced dimensional optimization problem whose solution is used to formulate an assignment problem of dimensionality less than M. The iterative reducing of dimensions terminates when exact solutions are determined for two-dimensional cases. A recovery procedure is used for determining a higher dimensional assignment problem solution from a problem having one less dimension. The procedure is useful when the reduced dimensional optimizational problem has two constraint dimensions.
137 citations