Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userBranch-and-Bound Method for Just-in-Time Optimization of Radar Search Patterns
79
0
0.0
(
0
)
Added by
Damien Chablat
Publication date
2020
fields
Informatics Engineering
and research's language is
English
Ask ChatGPT about the research
No Arabic abstract
Electronic phased-array radars offer new possibilities for radar search pattern optimization by using bi-dimensional beam-forming and beam-steering. Radar search pattern optimization can be approximated as a set cover problem and solved using integer programming, while accounting for localized clutter and terrain masks in detection constraints. We present a set cover problem approximation for time-budget minimization of radar search patterns, under constraints of range, detection probability and direction-specific scan update rates. Branch&Bound is a classical optimization procedure for solving combinatorial problems. It is known mainly as an exact algorithm, but features interesting characteristics, making it particularly fit for solving optimization problems in real-time applications and producing just-in-time solutions.
rate research
Read More
Quasi branch and bound is a recently introduced generalization of branch and bound, where lower bounds are replaced by a relaxed notion of quasi-lower bounds, required to be lower bounds only for sub-cubes containing a minimizer. This paper is devoted to studying the possible benefits of this approach, for the problem of minimizing a smooth function over a cube. This is accomplished by suggesting two quasi branch and bound algorithms, qBnB(2) and qBnB(3), that compare favorably with alternative branch and bound algorithms. The first algorithm we propose, qBnB(2), achieves second order convergence based only on a bound on second derivatives, without requiring calculation of derivatives. As such, this algorithm is suitable for derivative free optimization, for which typical algorithms such as Lipschitz optimization only have first order convergence and so suffer from limited accuracy due to the clustering problem. Additionally, qBnB(2) is provably more efficient than the second order Lipschitz gradient algorithm which does require exact calculation of gradients. The second algorithm we propose, qBnB(3), has third order convergence and finite termination. In contrast with BnB algorithms with similar guarantees who typically compute lower bounds via solving relatively time consuming convex optimization problems, calculation of qBnB(3) bounds only requires solving a small number of Newton iterations. Our experiments verify the potential of both these methods in comparison with state of the art branch and bound algorithms.
With the development of robotics, there are growing needs for real time motion planning. However, due to obstacles in the environment, the planning problem is highly non-convex, which makes it difficult to achieve real time computation using existing non-convex optimization algorithms. This paper introduces the convex feasible set algorithm (CFS) which is a fast algorithm for non-convex optimization problems that have convex costs and non-convex constraints. The idea is to find a convex feasible set for the original problem and iteratively solve a sequence of subproblems using the convex constraints. The feasibility and the convergence of the proposed algorithm are proved in the paper. The application of this method on motion planning for mobile robots is discussed. The simulations demonstrate the effectiveness of the proposed algorithm.
In this paper, we have developed a parallel branch and bound algorithm which computes the maximal structured singular value $mu$ without tightly bounding $mu$ for each frequency and thus significantly reduce the computational complexity.
In this paper, we propose multi-input multi-output (MIMO) beamforming designs towards joint radar sensing and multi-user communications. We employ the Cramer-Rao bound (CRB) as a performance metric of target estimation, under both point and extended target scenarios. We then propose minimizing the CRB of radar sensing while guaranteeing a pre-defined level of signal-to-interference-plus-noise ratio (SINR) for each communication user. For the single-user scenario, we derive a closed form for the optimal solution for both cases of point and extended targets. For the multi-user scenario, we show that both problems can be relaxed into semidefinite programming by using the semidefinite relaxation approach, and prove that the global optimum can always be obtained. Finally, we demonstrate numerically that the globally optimal solutions are reachable via the proposed methods, which provide significant gains in target estimation performance over state-of-the-art benchmarks.
This paper studies existing direct transcription methods for trajectory optimization applied to robot motion planning. There are diverse alternatives for the implementation of direct transcription. In this study we analyze the effects of such alternatives when solving a robotics problem. Different parameters such as integration scheme, number of discretization nodes, initialization strategies and complexity of the problem are evaluated. We measure the performance of the methods in terms of computational time, accuracy and quality of the solution. Additionally, we compare two optimization methodologies frequently used to solve the transcribed problem, namely Sequential Quadratic Programming (SQP) and Interior Point Method (IPM). As a benchmark, we solve different motion tasks on an underactuated and non-minimal-phase ball-balancing robot with a 10 dimensional state space and 3 dimensional input space. Additionally, we validate the results on a simulated 3D quadrotor. Finally, as a verification of using direct transcription methods for trajectory optimization on real robots, we present hardware experiments on a motion task including path constraints and actuation limits.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
