Solving Fuel-optimal Impulsive Rendezvous Problem Using Primer Vector Theory and Real Algebraic Geometry
نویسندگان
چکیده
Abstract. In this paper, the optimal fuel impulsive time-fixed rendezvous problem is considered. Under some simplifying assumptions, this problem may be recast as a non convex polynomial optimization problem. A numerical solving algorithm using a convex relaxation based on sum-of-squares representation of positive polynomials is proposed. Numerical results are evaluated on two examples and checked with a more classical numerical approach based on homotopy continuation for solving polynomial equation systems.
منابع مشابه
Using polynomial optimization to solve the fuel-optimal impulsive rendezvous problem
The optimal fuel impulsive time-fixed rendezvous problem is reviewed. In a linear setting, it may be reformulated as a nonconvex polynomial optimization problem for a pre-specified fixed number of velocity increments. A numerical algorithm using a convex relaxation based on a sum-of-squares representation of positive polynomials is first proposed. Its numerical efficiency is assessed using a cl...
متن کاملA New Mixed Iterative Algorithm to Solve the Fuel-Optimal Linear Impulsive Rendezvous Problem
The optimal fuel impulsive time-fixed rendezvous problem is reviewed. In a linear setting, it may be reformulated as a non convex polynomial optimization problem for a pre-specified fixed number of velocity increments. Relying on variational results previously published in the literature, an improved mixed iterative algorithm is defined to address the issue of optimization over the number of im...
متن کاملUsing polynomial optimization to solve the fuel-optimal linear impulsive rendezvous problem
Nomenclature a = semi-major axis ; e = eccentricity ; ν = true anomaly ; φ(ν) = fundamental matrix of relative motion ; B(ν) = input matrix in the dynamic model of relative motion ; R(ν) = φ(ν)B(ν) = φ(ν)B(ν) = primer vector evolution matrix ; uf = φ(νf )Xf − φ(ν1)X1 6= 0 = boundary conditions ; N = number of velocity increments ; νi, ∀ i = 1, · · · , N = impulses application times ; ∆vi = impu...
متن کاملFuel-Optimal Spacecraft Rendezvous with Hybrid On–Off Continuous and Impulsive Thrust
J = cost function N = number of impulses NLT = number of low-thrust-independent thrusters p = primer-vector magnitude p = primer vector pm = primer-vector absolute maximum r = relative position vector rj = space collocation of the jth impulse tf = final time tint = intermediate time tj = time instant of the jth impulse application tm = midcourse time corresponding to the primer absolute maximum...
متن کاملSymmetry Properties of Optimal Space Trajectories
The determination of minimum-fuel or minimum-time space trajectories has been pursued for decades, using different methods of solution. This work illustrates some symmetry properties that hold for optimal space trajectories and can considerably simplify their determination. The existence of symmetry properties is demonstrated in the presence of certain boundary conditions for the problem of int...
متن کامل