P Natarajan

Bio: P Natarajan is an academic researcher from Indian Space Research Organisation. The author has contributed to research in topics: Acceleration & Soft landing. The author has an hindex of 2, co-authored 3 publications receiving 8 citations.

Geometrical guidance algorithm for soft landing on lunar surface

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.

Analytical optimal guidance algorithm for lunar soft landing with terminal control constraints

Abstract: In this paper it is proposed to augment an existing optimal analytical guidance algorithm for the purpose of achieving terminal angle constraint during the terminal powered descent phase of a lunar soft landing mission. Basic algorithm formulation caters to minimizing the acceleration due to onboard engines to minimize the fuel spend and reach the desired position with desired velocity. However, in order to cope up with terminal angle constraint, an augmentation is proposed in the objective function wherein the aim is not only to minimize the energy but also to minimize the terminal error in acceleration achieved and the desired acceleration specified by the designer. This inadvertently leads to the desired terminal angle. Simulations done for the fine braking phase of lunar soft landing mission prove that terminal attitude constraints are met with the modification in objective function.

Integrative Control Approach for Agile Spacecraft Maneuvers

Abstract: Earth observation satellites require rapid attitude maneuvering and high pointing accuracy for imaging payloads. This paper presents the integrative control approach for maneuvering of Indian agile spacecrafts. The maneuver considered is a spot to spot, where the spacecraft has an initial non-zero angular rate and complete the maneuver with final imaging rate. Maneuver Iterative algorithm is used for computing the maneuver time between various imaging targets. The control algorithm is a state feedback form and can be incorporated for initial and final angular rates. The maneuver & control algorithms are integrated together and have been demonstrated for typical rest to rest and rate to rate maneuvers. The Reaction Wheels are used as control actuator and feasibility of the algorithm for on-board implementation is demonstrated by digital simulations.

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

Abstract: 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.

PSO-Based Soft Lunar Landing with Hazard Avoidance: Analysis and Experimentation

Abstract: The problem of real-time optimal guidance is extremely important for successful autonomous missions. In this paper, the last phases of autonomous lunar landing trajectories are addressed. The proposed guidance is based on the Particle Swarm Optimization, and the differential flatness approach, which is a subclass of the inverse dynamics technique. The trajectory is approximated by polynomials and the control policy is obtained in an analytical closed form solution, where boundary and dynamical constraints are a priori satisfied. Although this procedure leads to sub-optimal solutions, it results in beng fast and thus potentially suitable to be used for real-time purposes. Moreover, the presence of craters on the lunar terrain is considered; therefore, hazard detection and avoidance are also carried out. The proposed guidance is tested by Monte Carlo simulations to evaluate its performances and a robust procedure, made up of safe additional maneuvers, is introduced to counteract optimization failures and achieve soft landing. Finally, the whole procedure is tested through an experimental facility, consisting of a robotic manipulator, equipped with a camera, and a simulated lunar terrain. The results show the efficiency and reliability of the proposed guidance and its possible use for real-time sub-optimal trajectory generation within laboratory applications.

Analytical optimal guidance algorithm for lunar soft landing with terminal control constraints

Abstract: In this paper it is proposed to augment an existing optimal analytical guidance algorithm for the purpose of achieving terminal angle constraint during the terminal powered descent phase of a lunar soft landing mission. Basic algorithm formulation caters to minimizing the acceleration due to onboard engines to minimize the fuel spend and reach the desired position with desired velocity. However, in order to cope up with terminal angle constraint, an augmentation is proposed in the objective function wherein the aim is not only to minimize the energy but also to minimize the terminal error in acceleration achieved and the desired acceleration specified by the designer. This inadvertently leads to the desired terminal angle. Simulations done for the fine braking phase of lunar soft landing mission prove that terminal attitude constraints are met with the modification in objective function.

An Optimal Explicit Guidance Algorithm for Terminal Descent Phase of Lunar Soft Landing

Abstract: An explicit guidance algorithm for multi-constrained terminal descent phase of lunar soft landing is presented in this paper. A minimum jerk guidance is designed and extended for this purpose to achieve the terminal control and state constraints. The closed form jerk expression, obtained using the minimum jerk guidance is analyzed to obtain an explicit expression for acceleration command, which is the physical control variable for the guidance loop. The guidance formulation ensures the minimum rate of change of acceleration and vertical touchdown of the spacecraft towards a designated landing site with high terminal accuracy. The design features of the proposed guidance law are demonstrated using simulation results.