Aerospace Science and Technology 45 (2015) 359–366
Contents lists available at ScienceDirect
Aerospace Science and Technology
www.elsevier.com/locate/aescte
Optimal nonlinear feedback guidance algorithm for Mars powered
descent
Yiyu Zheng, Hutao Cui
∗
Deep Space Exploration Research Center, Harbin Institute of Technology, Harbin, 150001, People’s Republic of China
a r t i c l e i n f o a b s t r a c t
Article history:
Received
11 July 2014
Received
in revised form 23 May 2015
Accepted
6 June 2015
Available
online 10 June 2015
Keywords:
Mars
landing
Powered
descent guidance
Optimal
feedback control
Fuel
consumption
In this paper, an optimal nonlinear feedback guidance algorithm with complex state and control
constraints is developed for Mars powered decent. The analysis of the optimal control problem for Mars
powered descent is undertaken firstly. Then based on the real-time sampling optimal feedback control
theory, the Mars powered descent guidance (PDG) algorithm is designed and analysed. A practical method
is also proposed to solve the problem of the initialization of the PDG algorithm. Numerical simulations
are performed to evaluate the effectiveness of the proposed PDG algorithm. The effects of the sampling
period and the prediction errors on landing errors are studied in the numerical simulations. The fuel
consumption performances of the proposed PDG algorithm and the Apollo guidance algorithm are also
studied and compared. The simulation results show that the less fuel consumption is obtained with the
proposed PDG algorithm. Monte Carlo simulation verifies the high landing precision of the proposed PDG
algorithm.
© 2015 Elsevier Masson SAS. All rights reserved.
1. Introduction
The process of delivering a Mars lander from the planetary or-
bit
to a stationary position on the Mars surface, which presents a
unique
set of challenges, may generally be split into three phases:
entry, descent, and landing (EDL) for MSL-class landers [1,2]. The
future Mars missions, such as the sample return, may target sci-
entifically
interesting features that lie in areas far more hazardous.
To avoid hazards and land safely and precisely, during the powered
decent phase, future landers must have the ability to detect haz-
ards
in the landing zone and manoeuvre to a selected safe landing
site, which requires autonomous, onboard trajectory planning and
execution, with hazard detection sensors in the control loop [3].
A
substantial number of papers that examine the trajectory
optimization and guidance algorithm design for Mars powered de-
scend
have been published. Wong presents a Mars powered decent
guidance (PDG) algorithm similar to that used for the Apollo lunar
module, using polynomials of time to describe the desired position,
velocity, and acceleration profiles [3]. This guidance algorithm is
autonomous in nature and satisfies the request of real-time guid-
ance.
This guidance algorithm is not an optimal guidance law in
that it does not minimize fuel or any other cost functional. Also,
the state and control constraints are neglected by Wong in his pa-
*
Corresponding author.
E-mail
addresses: banlamyu@gmail.com (Y. Zheng), cuiht@hit.edu.cn (H. Cui).
per. Topcu derives a solution with maximum–minimum–maximum
structure for the minimum-fuel powered descent guidance [4].
However, the state constraints are not considered in [4]. Taking
state and control constraints into account, Acikmese [5] presents
a convex optimization approach for the fuel-optimal Mars pow-
ered
descent. Blackmore [6] further develops this method for the
case where no feasible pinpoint landing trajectories exist. Guo
investigates an optimization approach to generate waypoints in
the context of employing the zero-effort-miss/zero-effort-velocity
feedback guidance algorithm for the Mars landing problem [7],
in which two cases with power-limited and thrust-limited engine
are considered respectively. The approaches [4–6] require precise
mathematical model of the lander dynamics and are not robust
against uncertainties, e.g., the aerodynamic drag and wind, due to
the open-loop strategy. This may lead to great errors at the fi-
nal
time. It is shown in [4–6] that the optimal solutions can be
efficiently computed numerically using the interior point meth-
ods
or indirect methods. But the uses of interior point methods
and indirect methods in a real-time terminal descent scenario are
still an open research issue [8]. Although a closed-loop feedback is
adopted to improve the robustness in [7], the complex constraints,
e.g., thrust pointing constraints introduced by [5], cannot be han-
dled
sufficiently. Using the desensitized optimal control methodol-
ogy,
Shen [9] develops a Mars powered decent guidance law, which
aims at reducing the sensitivity of the minimum-fuel powered de-
scent
trajectory in the presence of uncertainties and perturbations.
http://dx.doi.org/10.1016/j.ast.2015.06.008
1270-9638/
© 2015 Elsevier Masson SAS. All rights reserved.