Registration of a hybrid robot using the Degradation-Kronecker method and a purely nonlinear method

Robotica ◽  
2015 ◽  
Vol 34 (12) ◽  
pp. 2729-2740 ◽  
Author(s):  
S. J. Yan ◽  
S. K. Ong ◽  
A. Y. C. Nee
Keyword(s):  
Closed Form ◽  
Real Time ◽  
Good Accuracy ◽  
Tracking System ◽  
Closed Form Solution ◽  
Form Solution ◽  
Fast Computation ◽  
Nonlinear Method ◽  
Simulation And Experiment ◽  
Limited Accuracy

SUMMARYAlthough the registration of a robot is crucial in order to identify its pose with respect to a tracking system, there is no reported solution to address this issue for a hybrid robot. Different from classical registration, the registration of a hybrid robot requires the need to solve an equation with three unknowns where two of these unknowns are coupled together. This property makes it difficult to obtain a closed-form solution. This paper is a first attempt to solve the registration of a hybrid robot. The Degradation-Kronecker (D-K) method is proposed as an optimal closed-form solution for the registration of a hybrid robot in this paper. Since closed-form methods generally suffer from limited accuracy, a purely nonlinear (PN) method is proposed to complement the D-K method. With simulation and experiment results, it has been found that both methods are robust. The PN method is more accurate but slower as compared to the D-K method. The fast computation property of the D-K method makes it appropriate to be applied in real-time circumstances, while the PN method is suitable to be applied where good accuracy is preferred.

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.

An Adaptive Nonlinear Trajectory Tracking Design for Mobile Robots and it’s Practical Implementation

2013 ◽  
Vol 284-287 ◽  
pp. 1744-1748
Author(s):  
Yung Hsiang Chen ◽  
Tzuu Hseng S. Li ◽  
Yung Yue Chen
Keyword(s):  
Mobile Robot ◽  
Closed Form ◽  
Trajectory Tracking ◽  
Tracking System ◽  
Closed Form Solution ◽  
Form Solution ◽  
Practical Implementation ◽  
Time Varying ◽  
Nonlinear Controller ◽  
Reference Trajectories

An adaptive nonlinear trajectory tracking design for mobile robot and its practical implementation are presented in this paper. The design objective is to specify one nonlinear controller with a parameter adaptive law that satisfies the adaptive H2 optimal performance. In general, it is hard to obtain the closed-form solution from this nonlinear trajectory-tracking problem. Fortunately, based on the property of the trajectory tracking system of the nonholonomic mobile robot, the adaptive H2 trajectory tracking problems can be reduced to solving one nonlinear time varying Riccati-like equations. Furthermore, one closed-form solution to this nonlinear time varying Riccati-like equation can be obtained with very simple forms for the preceding control design. Finally, there are two practical testing conditions: circular and S type reference trajectories are used for performance verification.

scholarly journals A Nonlinear Circuit Analysis Technique for Time-Variant Inductor Systems

Sensors ◽  
2019 ◽  
Vol 19 (10) ◽  
pp. 2321 ◽  
Author(s):  
Xinning Wang ◽  
Chong Li ◽  
Dalei Song ◽  
Robert Dean
Keyword(s):  
Closed Form ◽  
Eddy Currents ◽  
High Efficiency ◽  
Nonlinear Differential Equations ◽  
Closed Form Solution ◽  
Form Solution ◽  
Circuit Analysis ◽  
Nonlinear Method ◽  
Sensors And Actuators ◽  
Computation Efficiency

Time-variant inductors exist in many industrial applications, including sensors and actuators. In some applications, this characteristic can be deleterious, for example, resulting in inductive loss through eddy currents in motors designed for high efficiency operation. Therefore, it is important to investigate the electrical dynamics of systems with time-variant inductors. However, circuit analysis with time-variant inductors is nonlinear, resulting in difficulties in obtaining a closed form solution. Typical numerical algorithms used to solve the nonlinear differential equations are time consuming and require powerful processors. This investigation proposes a nonlinear method to analyze a system model consisting of the time-variant inductor with a constraint that the circuit is powered by DC sources and the derivative of the inductor is known. In this method, the Norton equivalent circuit with the time-variant inductor is realized first. Then, an iterative solution using a small signal theorem is employed to obtain an approximate closed form solution. As a case study, a variable inductor, with a time-variant part stimulated by a sinusoidal mechanical excitation, is analyzed using this approach. Compared to conventional nonlinear differential equation solvers, this proposed solution shows both improved computation efficiency and numerical robustness. The results demonstrate that the proposed analysis method can achieve high accuracy.

On a Closed-Form Solution of Prandtl's System of Equations

2013 ◽  
Vol 40 (2) ◽  
pp. 106-114
Author(s):  
J. Venetis ◽  
Aimilios (Preferred name Emilios) Sideridis
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
System Of Equations
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