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

Aerospace ◽  
2021 ◽  
Vol 8 (7) ◽  
pp. 195
Author(s):  
Andrea D’Ambrosio ◽  
Andrea Carbone ◽  
Dario Spiller ◽  
Fabio Curti
Keyword(s):  
Real Time ◽  
Inverse Dynamics ◽  
A Priori ◽  
Closed Form Solution ◽  
Control Policy ◽  
Form Solution ◽  
Soft Landing ◽  
Lunar Landing ◽  
Optimal Guidance ◽  
Time Optimal

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.

Real Time Trajectory Modification Using a Closed Form Solution

1992 ◽  
Author(s):  
Michael R. Hummels ◽  
Raymond J. Cipra
Keyword(s):  
Closed Form ◽  
Real Time ◽  
Closed Form Solution ◽  
Form Solution ◽  
Time Interval ◽  
Efficient Manner ◽  
Planning Strategy ◽  
Higher Derivatives ◽  
On Line ◽  
Line Trajectory

Abstract An on-line trajectory modification and path planning strategy is developed which will allow a robot to respond in an efficient manner to real time sensory input. The approach developed here eliminates the need for solving many equations by developing a closed form algorithm. It uses two fourth order curves for the transition phases with a constant velocity section in between. Although this is done by providing additional constraints to the curve, it makes the problem of determining the trajectory much easier to solve, while providing continuous higher derivatives. It also provides a safe and efficient way of modifying trajectories based on the robots joint rate limits, joint acceleration limits, jerk limits, and desired time interval between trajectory modifications for a 4-1-4 trajectory. This method involves the solution of one second order equation and is directed toward real time applications.

Real-Time Optimal Guidance for Orbital Maneuvering

AIAA Journal ◽  
1973 ◽  
Vol 11 (9) ◽  
pp. 1266-1272 ◽  
Author(s):  
AUDREY O. COHEN ◽  
KENNETH R. BROWN
Keyword(s):  
Real Time ◽  
Optimal Guidance ◽  
Time Optimal

scholarly journals The generalized viscoelastic spring

2020 ◽  
Vol 476 (2236) ◽  
pp. 20190881
Author(s):  
Kostas P. Soldatos
Keyword(s):  
Viscous Flow ◽  
A Priori ◽  
Closed Form Solution ◽  
Form Solution ◽  
Viscoelastic Deformation ◽  
One Dimensional ◽  
Flow Formation ◽  
Inelastic Material ◽  
Flow Potential ◽  
Well Posed

A spring/rod model is presented that describes one-dimensional behaviour of solids susceptible to large or small viscoelastic deformation. Derivation of its constitutive equation is underpinned by the fact that the internal energy, which the elastic part of deformation stores in the spring, changes in time with the observed strain as well as with some, unknown part of the strain-rate. The latter emerges through the action of a viscous flow potential and is the source of inelastic deformation. Thus, unlike its conventional viscoelasticity counterparts, the model does not postulate a priori a rule that relates strain with viscous flow formation. Instead, it considers that such a rule, as well as other important features of combined elastic and inelastic material response, should become known a posteriori through the solution of a relevant, well-posed boundary value problem. This paper begins with considerations compatible with large viscoelastic deformations and gradually progresses through simpler modelling situations. The latter also include the case of small viscoelastic strain that underpins formulation of classical, spring-dashpot viscoelastic models. In an example application, a relevant closed-form solution is obtained for a spring undergoing small viscoelastic deformation under the influence of a viscous flow potential which is quadratic in the stress.

scholarly journals Closed-form solution of discrete-time optimal control and its convergence

2018 ◽  
Vol 12 (3) ◽  
pp. 413-418 ◽  
Author(s):  
Hehong Zhang ◽  
Yunde Xie ◽  
Gaoxi Xiao ◽  
Chao Zhai
Keyword(s):  
Optimal Control ◽  
Closed Form ◽  
Discrete Time ◽  
Closed Form Solution ◽  
Form Solution ◽  
Time Optimal Control ◽  
Time Optimal

Data-Driven Predictive Control for Autonomous Systems

2018 ◽  
Vol 1 (1) ◽  
pp. 259-286 ◽  
Author(s):  
Ugo Rosolia ◽  
Xiaojing Zhang ◽  
Francesco Borrelli
Keyword(s):  
Real Time ◽  
Predictive Control ◽  
Performance Index ◽  
Autonomous Systems ◽  
Control Policy ◽  
Data Driven ◽  
Large Set ◽  
Time Step ◽  
Time Optimal ◽  
Operating Constraints

In autonomous systems, the ability to make forecasts and cope with uncertain predictions is synonymous with intelligence. Model predictive control (MPC) is an established control methodology that systematically uses forecasts to compute real-time optimal control decisions. In MPC, at each time step an optimization problem is solved over a moving horizon. The objective is to find a control policy that minimizes a predicted performance index while satisfying operating constraints. Uncertainty in MPC is handled by optimizing over multiple uncertain forecasts. In this case, performance index and operating constraints take the form of functions defined over a probability space, and the resulting technique is called stochastic MPC. Our research over the past 10 years has focused on predictive control design methods that systematically handle uncertain forecasts in autonomous and semiautonomous systems. In the first part of this article, we present an overview of the approach we use, its main advantages, and its challenges. In the second part, we present our most recent results on data-driven predictive control. We show how to use data to efficiently formulate stochastic MPC problems and autonomously improve performance in repetitive tasks. The proposed framework is able to handle a large set of predicted scenarios in real time and learn from historical data.

Equivalent Elastic Constants of Truss Core Sandwich Plates

2011 ◽  
Vol 133 (4) ◽  
Author(s):  
Hong-Xia Wang ◽  
Samuel W. Chung
Keyword(s):  
Elastic Constants ◽  
A Priori ◽  
Three Dimensional ◽  
Closed Form Solution ◽  
Elastic Stiffness ◽  
Form Solution ◽  
Laminated Plates ◽  
Element Analysis ◽  
Truss Core ◽  
Anisotropic Elastic

A plate structure of a triangular truss core sandwiched by two panels is treated as an equivalent homogeneous laminated plate by obtaining equivalent anisotropic elastic constants. The equivalent elastic constants are obtained by considering generalized Hook’s law of a three dimensional elastic body with no a priori assumption and the equilibrium of a segment deformed by bending moments. To verify the accuracy of the equivalent elastic constants, a linear static analysis of sandwiched aluminum plates subjected to lateral pressure is carried out. The results of the finite element analysis applied to the equivalent laminated plates are compared with those of a NASTRAN analysis of the original structural layouts. The results are also compared with a closed-form solution, which simplifies the sandwiched plate as a homogeneous orthotropic thick plate continuum (Lok and Cheng, 2000, “Elastic Stiffness Properties and Behavior of Truss-Core Sandwich Panel,” J. Struct. Eng., 126(5), pp. 552–559). As the maximum deflections of three analyses agreed closely, one has assurance that the method of the homogeneous plate with equivalent elastic constants is valid and useful.

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