Circular Guidance Laws With and Without Terminal Velocity Direction Constraints
18 Aug 2008-
TL;DR: In this paper, two circular guidance laws have been developed based on a 3D vector approach: one circular guidance law without terminal velocity direction constraint and the other one with terminal velocity directional constraint.
Abstract: Two circular guidance laws have been developed based on a 3-D vector approach: one circular guidance law without terminal velocity direction constraint and the other circular guidance law with terminal velocity direction constraint. Both approaches can be implemented easily with predictable time to go and trajectory. They are effective for both stationary and moving targets.
Citations
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TL;DR: In this article, an extended trajectory shaping guidance (ETSG) law is proposed under the assumption that the missile-target relative velocity is constant and the line of sight angle is small.
Abstract: To control missile’s miss distance as well as terminal impact angle, by involving the time-to-go-nth power in the cost function, an extended optimal guidance law against a constant maneuvering target or a stationary target is proposed using the linear quadratic optimal control theory. An extended trajectory shaping guidance (ETSG) law is then proposed under the assumption that the missile-target relative velocity is constant and the line of sight angle is small. For a lag-free ETSG system, closed-form solutions for the missile’s acceleration command are derived by the method of Schwartz inequality and linear simulations are performed to verify the closed-form results. Normalized adjoint systems for miss distance and terminal impact angle error are presented independently for stationary targets and constant maneuvering targets, respectively. Detailed discussions about the terminal misses and impact angle errors induced by terminal impact angle constraint, initial heading error, seeker zero position errors and target maneuvering, are performed.
21 citations
TL;DR: In this paper, the Radau pseudospectral method was used to discretize the differential equations expressed by control variables and state variables with multiple constraints into series algebraic equations, only expressed by state variables.
Abstract: A new algorithm was developed for the initial parameters optimization of guided projectiles with multiple constraints. Due to the relationship between the analytical guidance logic and state variables of guided projectiles, the Radau pseudospectral method was used to discretize the differential equations expressed by control variables and state variables with multiple constraints into series algebraic equations, only expressed by state variables. The initial parameter optimization problem was transformed to a nonlinear programming problem, and the sequential quadratic programming algorithm was used to obtain the optimal combinations of initial height and range to target, and make the final velocity of guided projectiles maximum with constraints. Comparing with the appropriate initial conditions solved by Monte Carlo method and the flight characteristics solved by integrating the original differential equations in the optimal initial parameters computed by the new algorithm, the feasibility of new algorithm was validated.
5 citations
Cites background from "Circular Guidance Laws With and Wit..."
...Presently, several studies are conducted for developing the guidance logic withmultiple constraints [1, 2] and searching the launch acceptable region (LAR) of a guided bomb, while the initial conditions are known [3, 4]....
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TL;DR: In this paper, an existing circular guidance law developed for missile guidance is modified to be applied for the fine braking phase of lunar powered descent, and a simple compensation scheme based on comparison of actual velocity from sensors and expected velocity from the algorithm is also proposed to take care of the variation in gravity and initial mass estimate.
Abstract: Augmented design of a guidance algorithm previously developed for intercepting target in a missile-target engagement scenario, but catering to powered descent soft landing on lunar surface is the main focus of this paper. When it comes to lunar soft landing guidance formulation, it is required that the Lander reach the desired position with terminal velocity constraints. An existing circular guidance law developed for missile guidance is modified to be applied for the fine braking phase of lunar powered descent. Presently in the algorithm, at the beginning of each guidance cycle, there will be an assumed varying circular path from missile to target and the guidance solution lies in finding the acceleration towards the centre of the circle so that the missile moves towards the target. The design augmentation proposed for lunar landing introduces a quadratic acceleration term opposite to the instantaneous tangential velocity vector to ensure terminal conditions. Coefficients of the quadratic acceleration profile are determined by the length of the circle as well as the magnitude of instantaneous tangential velocity. Finally a simple compensation scheme based on comparison of actual velocity from sensors and expected velocity from the algorithm is also proposed to take care of the variation in gravity and error in initial mass estimate.
5 citations
TL;DR: In this article, the Radau pseudospectral method was used to discretize the differential equations including control variables and state variables with multiple constraints into series algebraic equations that were expressed only by state variables.
Abstract: A new algorithm was developed for the initial parameters optimization of guided projectiles with multiple constraints. Due to the relationship between the analytic guidance logic and state variables of guided projectiles, the Radau pseudospectral method was used to discretize the differential equations including control variables and state variables with multiple constraints into series algebraic equations that were expressed only by state variables. The initial parameter optimization problem was transformed to a nonlinear programming problem, and the sequential quadratic programming algorithm was used to obtain the optimal combinations of initial height and range to target for the final velocity of guided projectiles maximum with constraints. Comparing with the appropriate initial conditions solved by Monte Carlo method and the flight characteristics solved by integrating the original differential equations in the optimal initial parameters computed by the new algorithm, the feasibility of new algorithm was validated.
2 citations
08 Jun 2010
TL;DR: In this paper, a guidance law with the terminal angle restraint is proposed, which is given by establishing the right Hamiltonian, and the practical application in Engineering is also given in this paper.
Abstract: This paper investigates a new concept of “overhead-attack”. Firstly, a guidance law with the terminal angle restraint proposed, which is given by establishing the right Hamiltonian. Furthermore the practical application in Engineering is also given in this paper. The guidance law provides a trajectory scheme with terminal angle restraint, which is efficient for penetration bombs or missiles. Simulations show that the guidance law is effective for overhead-attack, which requires higher overload for the bomb as the increase of the terminal angle. Secondly, this paper investigates four important factors for penetration bombs: the guidance system, the homing head, the range, and the maneuverability. The analyses of those four factors are also given. It has been proven that this guidance law works effectively for a bomb that needs to attack an “overhead” target. It confirms that the method works in practical application.
2 citations
Cites background from "Circular Guidance Laws With and Wit..."
...When the homing head is locking on the target, there should be a big frame angle for the homing head to lock on steadily [14]....
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References
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TL;DR: In this paper, a geodesic and normal curvatures of the trajectory of a single-missile trajectory on the surface generated by the line of sight were derived from a simple criterion for optimum navigation to the line-of-sight motion.
Abstract: Following a brief comparison of three collision‐seeking types of navigation—pure pursuit, constant‐bearing collision, and proportional navigation—the usual definition of planar proportional navigation is extended to three dimensions. Based upon a simple criterion for optimum navigation to the line‐of‐sight motion, a proper formulation is found in terms of the geodesic and normal curvatures of the missile path on the surface generated by the line of sight. By a suitable choice of a reference coordinate system, the missile‐target kinematic relationships are then linearized, assuming relatively small deviations of the missile from a collision course. Upon combining these ``geometry feedback'' equations with the equations of guidance, the missile trajectory is found to be given in terms of two independent linear differential equations of identical form and of one higher order than the missile transfer function. Typical solutions are found for some simple cases. The character of the trajectory is shown to depend on an ``effective navigation constant'' proportional to the missile navigation constant (or gain) and the ratio of missile speed to closing speed; a value of this parameter greater than two is found to be necessary to insure finite terminal missile acceleration. Two example trajectories are calculated from both the exact and the linearized trajectory equations to indicate the accuracy of the linearization.
174 citations
"Circular Guidance Laws With and Wit..." refers methods in this paper
...The most widely used is proportional navigation guidance [Adler, 1956]....
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TL;DR: In this paper, the authors proposed a new guidance law termed generalized vector explicit guidance (GENEX), which can simultaneously achieve design specifications on miss distance and final missile-target relative orientation.
Abstract: This paper proposes and evaluates a new guidance law termed generalized vector explicit guidance (GENEX). This guidance law can simultaneously achieve design specifications on miss distance and final missile-target relative orientation. The latter may be used to enhance the performance of warheads the effectiveness of which is influenced by the terminal encounter geometry. The GENEX guidance law is parameterized in terms of a design coefficient that determines the degree of curvature in the trajectory. Feasibility of GENEX guidance was demonstrated by its application to two weapon scenarios. The first was an air-to-air missile terminal homing scenario. Assuming ideal sensor information and a single-lag missile response model, the guidance was shown to perform well against an air target performing evasive maneuvers. A specified zero-aspect terminal encounter angle was achieved while simultaneously minimizing miss distance. The second application involved an air-to-surface munition released from an unmanned air vehicle. The GENEX guidance law was able to produce trajectories satisfying a terminal impact angle constraint. In addition, an engagement region of sufficient size was shown to be achievable using guidance gains scheduled with target location and weapon release altitude.
158 citations
10 Dec 2002
TL;DR: In this paper, the authors presented a precision guidance law with impact angle constraint for a two-dimensional planar intercept, based on the principle of following a circular arc to the target, hence the name "circular navigation guidance".
Abstract: Presents a precision guidance law with impact angle constraint for a two-dimensional planar intercept. It is based on the principle of following a circular arc to the target, hence the name "circular navigation guidance" (CNG). This law is shown mathematically to be successful over a wide range of initial conditions. Computer simulations show that CNG performs much better than an equivalent law from the literature, and that it outperforms the standard proportional navigation guidance law in terms of miss distance. A simplified law is presented that can be used without range-to-target information.
102 citations
15 Aug 2005
TL;DR: Two time-to-go closed-form solutions were developed and will be discussed here, one of which provides an accurate time- to-go for a missile using true proportional navigation guidance.
Abstract: Time-to-go is the time when the missile will arrive at the point of closest approach to the target. A good time-to-go estimate is important for the guidance laws that depend explicitly on the time-to-go. Two time-to-go closed-form solutions were developed and will be discussed here. One time-to-go estimate accounts for the missile-to-target accelerations. It provides an accurate time-to-go estimate if the missile and target accelerations are constants, or average missile and target accelerations for the flight can be estimated. The other time-to-go estimate accounts for future true proportional navigation acceleration. It provides an accurate time-to-go for a missile using true proportional navigation guidance. Both time-to-go estimates are very simple to implement.
17 citations
Additional excerpts
...TGO1 is the typical time-to-go estimate based on the following definition [Lam 2005]: v v v x ˆ ˆ ˆ ˆ ⋅ ⋅ − = τ , (5....
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TL;DR: In this paper, a simple acceleration-compensated zero-effort-miss guidance law has been derived, which does take advantage of the knowledge of target acceleration, and it is shown that this new guidance law will outperform proportional navigation guidance, even when the target acceleration is not perfectly known.
Abstract: This paper shows that true proportional navigation guidance can be derived directly from a zero-effort-miss guidance law, and explains why the augmented proportional navigation guidance law does not take full advantage of the knowledge of target acceleration A simple acceleration-compensated zero-effortmiss guidance law has been derived, which does take advantage of the knowledge of target acceleration This paper also demonstrates that this new guidance law will outperform proportional navigation guidance and augmented proportional navigation guidance, even when the target acceleration is not perfectly known
13 citations
"Circular Guidance Laws With and Wit..." refers background in this paper
...Another guidance law is the zero-effortmiss guidance law [Lam, 2007]....
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