scholarly journals Introduction to Nilpotent Approximation Filtering

1988 ◽  
pp. 115-120
Author(s):  
Michiel Hazewinkel
Keyword(s):  
Nilpotent Approximation

Control of a Mobile Robot with a Trailer Based on Nilpotent Approximation

2021 ◽  
Vol 82 (1) ◽  
pp. 73-92
Author(s):  
A. A. Ardentov ◽  
A. P. Mashtakov
Keyword(s):  
Mobile Robot ◽  
Nilpotent Approximation

Characteristics analysis and stabilization of a planar 2R underactuated manipulator

Robotica ◽  
2014 ◽  
Vol 34 (3) ◽  
pp. 584-600 ◽  
Author(s):  
Guang-Ping He ◽  
Zhi-Lü Wang ◽  
Jie Zhang ◽  
Zhi-Yong Geng
Keyword(s):  
Mechanical System ◽  
Closed Loop ◽  
Closed Loop Control ◽  
Algebraic Equations ◽  
Approximation Model ◽  
Nilpotent Approximation ◽  
Loop Control ◽  
Closed Loop Control System ◽  
Nonlinear Algebraic Equations ◽  
Loop Control System

SUMMARYThe weightless planar 2R underactuated manipulators with passive last joint are considered in this paper for investigating a feasible method to stabilize the system, which is a second-order nonholonomic-constraint mechanical system with drifts. The characteristics including the controllability of the linear approximation model, the minimum phase property, the Small Time Local Controllability (STLC), the differential flatness, and the exactly nilpotentizable properties, are analyzed. Unfortunately, these negative characteristics indicate that the simplest underactuated mechanical system is difficult to design a stable closed-loop control system. In this paper, nilpotent approximation and iterative steering methods are utilized to solve the problem. A globally effective nilpotent approximation model is developed and the parameterized polynomial input is adopted to stabilize the system to its non-singularity equilibrium configuration. In accordance with this scheme, it is shown that designing a stable closed-loop control system for the underactuated mechanical system can be ascribed to solving a set of nonlinear algebraic equations. If the nonlinear algebraic equations are solvable, then the controller is asymptotically stable. Some numerical simulations demonstrate the effectiveness of the presented approach.

scholarly journals Nilpotent approximation of a trident snake robot controlling distribution

Kybernetika ◽  
2018 ◽  
pp. 1118-1130 ◽  
Author(s):  
Jaroslav Hrdina ◽  
Radomil Matoušek ◽  
Aleš Návrat ◽  
Petr Vašík
Keyword(s):  
Nilpotent Approximation ◽  
Snake Robot

scholarly journals REALIZATION OF REVERSE MOTION OF THE MODEL OF A SEMITRAILER ROAD TRAIN

2018 ◽  
Vol 3 ◽  
pp. 59-66
Author(s):  
Dmitry Tatievskyi
Keyword(s):  
Feedback Linearization ◽  
Control Object ◽  
Point Of View ◽  
Model Management ◽  
Practical Implementation ◽  
Rectilinear Motion ◽  
Theoretical Point ◽  
Nilpotent Approximation ◽  
Reverse Motion ◽  
Stabilizing Control

The complexity of controlling the road train is due to pronounced nonlinearities, as well as the instability of the control object under reverse motion, often leading to a phenomenon known as jackknifing. Because of this, the task of controlling their motion is relevant, both from the theoretical point of view and from the point of view of the practical implementation of software motion with given constraints. The task of controlling the motion of a road train with a semitrailer under the assumption of non-holonomic constraints (the absence of lateral slippage of support wheels) has a great theoretical and applied significance. Research in this field is stimulated by numerous applied problems. For road trains, the location of the towing device behind the rear axle (off-axle hitching model) is quite typical. This model is used in this study. For this model, management and planning methods are proposed, using a diverse mathematical apparatus. Among the most frequently used methods, let’s select the methods of feedback linearization and chain systems, and methods are used, which are exclusively due to the geometric features of the model kinematics formulated in cascade form. Synthesis of control laws can be performed after the linearization of the model by state feedback, using the Lie algebra apparatus, fuzzy logic, using linear-quadratic controllers, nilpotent approximation, and so on. Studies have been carried out on the state of solving the problem associated with the reverse motion of a road train consisting of a hauler and a semitrailer with a coupling sideshift. The synthesized stabilizing control allowed to study the features of such model, determined by its linear dimensions and dynamic parameters. In this study, one of the possibilities of stabilizing the reversal motion of the dynamic model of a two-link road train on a rectilinear and circular track is considered. Synthesis of the stabilizing control is obtained for the case of rectilinear motion, hauler, stable circular stationary regimes are realized. The obtained theoretical relationships that determine the properties of the crew's ability to rotate when moving in reverse, allow the latter to be used when the algorithm is implemented.

Sign in / Sign up

Export Citation Format

Share Document