Unscented MPSP for Optimal Control of a Class of Uncertain Nonlinear Dynamic Systems

A new computationally efficient nonlinear optimal control synthesis technique, named as unscented model predictive static programming (U-MPSP), is presented in this paper that is applicable to a class of problems with uncertainties in time-invariant system parameters and/or initial conditions. This new technique is a fusion of two recent ideas, namely MPSP and Riemann-Stieltjes optimal control problems. First, unscented transform is utilized to construct a low-dimensional finite number of deterministic problems. The philosophy of MPSP is utilized next so that the solution can be obtained in a computational efficient manner. The control solution not only ensures that the terminal constraint is met accurately with respect to the mean value, but it also ensures that the associated covariance matrix (i.e., the error ball) is minimized. Significance of U-MPSP has been demonstrated by successfully solving two benchmark problems, namely the Zermelo problem and inverted pendulum problem, which contain parametric and initial condition uncertainties

Optimally allocated nonlinear robust control of a reusable launch vehicle during re-entry

A nonlinear robust control design approach is presented in this paper for a prototype reusable launch vehicle (RLV) during the critical re-entry phase where the margin for error is small. A nominal control is designed following the dynamic inversion philosophy for the reaction control system (RCS) and optimal dynamic inversion philosophy for the aerodynamic control actuation. This nominal controller is augmented next with a barrier Lyapunov function based neuro-adaptive control in the inner loop, which enforces the body rates of the actual system i.e. in presence of uncertainties to track the closed-loop body rates of the nominal plant. A fusion logic is also presented for fusing the RCS and aerodynamic control. The control design approach presented here assures robust tracking of the guidance commands despite the presence of uncertainties in the plant model. Extensive nonlinear six degree-of-freedom (DoF) simulation study, which embeds additional practical constraints such as actuator delay in the aerodynamic control actuation and constraints related to the RCS, shows that the proposed design approach has both good command following as well as robustness characteristics

Desensitized Optimal Trajectory for Multi-phase Lunar Landing

Lunar landing problem has been formulated as desensitized optimal control problem and solved by Legendre Pseudospectral method. The problem has been split into three phases to account for mission constraints, namely the braking with rough navigation stage (from 18km to 7km), attitude hold stage (holding the attitude for 35sec) for a typical mission scenario. In presence of uncertainties, following the open loop reference trajectory using the closed loop linear quadratic regulator contribute greatly in trajectory dispersions. The goal is to desensitize this multi-phase optimal trajectory with reduced error in presence of initial state error, thrust error, Moon's gravity uncertainty. To achieve this, the fuel minimization cost function is augmented with closed loop covariance to generate the open loop reference trajectory. Following this reference trajectory using closed loop linear quadratic regulator, shows significant reduction in landing error. The amount of extra fuel consumed by desensitizing optimal trajectory is less significant when compared to improvement in landing accuracy to meet mission constraints assuring the desensitized optimal control a viable technique for lunar landing trajectory design. (C) 2017, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved

Constrained optimal multi-phase lunar landing trajectory with minimum fuel consumption

A Legendre pseudo spectral philosophy based multi-phase constrained fuel-optimal trajectory design approach is presented in this paper. The objective here is to find an optimal approach to successfully guide a lunar lander from perilune (18 km altitude) of a transfer orbit to a height of 100 m over a specific landing site. After attaining 100 m altitude, there is a mission critical re-targeting phase, which has very different objective (but is not critical for fuel optimization) and hence is not considered in this paper. The proposed approach takes into account various mission constraints in different phases from perilune to the landing site. These constraints include phase-1 ('braking with rough navigation') from 18 km altitude to 7 km altitude where navigation accuracy is poor, phase-2 ('attitude hold') to hold the lander attitude for 35 sec for vision camera processing for obtaining navigation error, and phase-3 ('braking with precise navigation') from end of phase-2 to 100 m altitude over the landing site, where navigation accuracy is good (due to vision camera navigation inputs). At the end of phase-1, there are constraints on position and attitude. In Phase-2, the attitude must be held throughout. At the end of phase-3, the constraints include accuracy in position, velocity as well as attitude orientation. The proposed optimal trajectory technique satisfies the mission constraints in each phase and provides an overall fuel-minimizing guidance command history. (C) 2017 COSPAR. Published by Elsevier Ltd. All rights reserved

Optimal Trajectory Planning for Multiphase Lunar Landing

Lunar landing problem is formulated as an optimal control problem and has been solved by Legendre Pseudospectral method. The landing problem is split into various stages to take into account various mission constraints. Based on These constraints, the problem is split into three stages Hough Braking, Attitude Hold and Retargeting Legendre Pseudospectral method is used for solving this multiphase lunar landing problem. The idea of this method is to discretize the trajectory optimization as a nonlinear programming problem. Legendre Pseudospectral method was applied to approximate the state and the state differential equations as algebraic constraints. Optimal solutions of the above problem are those control variables which dynamically satisfy all mission constraints. The cost function considered is minimum fuel satisfying all mission constraints envisaged. The method guarantees a null (Mann fuel solution which satisfies terminal mission constraints in each stage as part of the formulation. The mission constraints considered in studying this problem are desired altitude, attitude and velocity while reaching the desired landing site from a specified perilune height. At touchdown, the lander orientation should be vertical favoring landing leg of the Lander to touch the Moons surface as desired. The commanded acceleration should be within the limit of the main engine thruster capability (saturation limit) which enforces maximum and minimum thrust constraints. (C) 2016, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved