Optimal trigonometric robot joint trajectories

Robotica ◽  
1991 ◽  
Vol 9 (4) ◽  
pp. 379-386 ◽  
Author(s):  
Dan Simon ◽  
Can Isik
Keyword(s):  
Objective Function ◽  
Minimum Energy ◽  
Closed Form Solution ◽  
Form Solution ◽  
Path Optimization ◽  
Interpolation Algorithm ◽  
Minimum Jerk ◽  
Trigonometric Splines ◽  
Original Application ◽  
Trajectory Interpolation

SUMMARYInterpolation of a robot joint trajectory is realized using trigonometric splines. This original application has several advantages over existing methods (e.g. those using algebraic splines). For example, the computational expense is lower, more constraints can be imposed on the trajectory, obstacle avoidance can be implemented in real time, and smoother trajectories are obtained. Some of the spline parameters can be chosen to minimize an objective function (e.g. minimum jerk or minimum energy). If jerk is minimized, the optimization has a closed form solution. This paper introduces a trajectory interpolation algorithm, discusses a method for path optimization, and includes examples.

scholarly journals Energy Consumption Improvement of OOK Transmitter Based on Minimum Energy Coding

2021 ◽  
Author(s):  
yue peng ◽  
Guillaume Andrieux ◽  
Jean-francois diouris
Keyword(s):  
Energy Consumption ◽  
Minimum Energy ◽  
Closed Form Solution ◽  
Life Time ◽  
Form Solution ◽  
Battery Life ◽  
Transmission Range ◽  
Energy Consumption Model ◽  
Time Requirements ◽  
Consumption Model

Abstract Energy consumption of Wireless Sensor Networks (WSNs) including OOK transmitter is important for short range transmission and long battery life time requirements. In this paper, the Minimum Energy (ME) coding strategy is adopted to improve the energy efficiency of an OOK transmitter. We first give the energy consumption model based on a real OOK transmitter, which can completely switch off the transmitter during the transmission of low bit '0' and has an energy effciency of 52 pJ/bit. Based on this energy consumption model, ME-Coding provides an energy effciency of 30 pJ/bit for coding size k = 3. Moreover, larger coding size others more significant improvement, at the sacrifice of spectral effciency and transmission range. In this paper, we have also determined a closed-form solution for the optimal coding size for a given transmission range constraint.

scholarly journals A Closed-Form Solution to Linear Feature-Based Registration of LiDAR Point Clouds

2021 ◽  
Vol 13 (18) ◽  
pp. 3571
Author(s):  
Yongbo Wang ◽  
Nanshan Zheng ◽  
Zhengfu Bian ◽  
Hua Zhang
Keyword(s):  
Objective Function ◽  
Closed Form ◽  
Closed Form Solution ◽  
Point Clouds ◽  
Form Solution ◽  
Linear Features ◽  
Registration Method ◽  
Linear Feature ◽  
Feature Based ◽  
Transformation Parameters

Due to the high complexity of geo-spatial entities and the limited field of view of LiDAR equipment, pairwise registration is a necessary step for integrating point clouds from neighbouring LiDAR stations. Considering that accurate extraction of point features is often difficult without the use of man-made reflectors, and the initial approximate values for the unknown transformation parameters must be estimated in advance to ensure the correct operation of those iterative methods, a closed-form solution to linear feature-based registration of point clouds is proposed in this study. Plücker coordinates are used to represent the linear features in three-dimensional space, whereas dual quaternions are employed to represent the spatial transformation. Based on the theory of least squares, an error norm (objective function) is first constructed by assuming that each pair of corresponding linear features is equivalent after registration. Then, by applying the extreme value analysis to the objective function, detailed derivations of the closed-form solution to the proposed linear feature-based registration method are given step by step. Finally, experimental tests are conducted on a real dataset. The derived experimental result demonstrates the feasibility of the proposed solution: By using eigenvalue decomposition to replace the linearization of the objective function, the proposed solution does not require any initial estimates of the unknown transformation parameters, which assures the stability of the registration method.

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

Plane Wave Resonance in the Tire Air Cavity as a Vehicle Interior Noise Source

1995 ◽  
Vol 23 (1) ◽  
pp. 2-10 ◽  
Author(s):  
J. K. Thompson
Keyword(s):  
Closed Form Solution ◽  
Form Solution ◽  
Interior Noise ◽  
Cavity Resonance ◽  
Test Results ◽  
Vehicle Interior ◽  
Air Cavity ◽  
Vehicle Interior Noise ◽  
Wave Resonance ◽  
Resonance Frequencies

Abstract Vehicle interior noise is the result of numerous sources of excitation. One source involving tire pavement interaction is the tire air cavity resonance and the forcing it provides to the vehicle spindle: This paper applies fundamental principles combined with experimental verification to describe the tire cavity resonance. A closed form solution is developed to predict the resonance frequencies from geometric data. Tire test results are used to examine the accuracy of predictions of undeflected and deflected tire resonances. Errors in predicted and actual frequencies are shown to be less than 2%. The nature of the forcing this resonance as it applies to the vehicle spindle is also examined.

Capacity Analysis for Correlated Multi-Hop MIMO Channels under Colored Noise

2015 ◽  
Vol 1 ◽  
pp. 41
Author(s):  
Nguyen N. Tran ◽  
Ha X. Nguyen
Keyword(s):  
Computational Complexity ◽  
Mutual Information ◽  
Closed Form Solution ◽  
Optimal Solution ◽  
Form Solution ◽  
Maximization Problem ◽  
Capacity Analysis ◽  
Mimo Channels ◽  
Average Mutual Information ◽  
Channel Output

A capacity analysis for generally correlated wireless multi-hop multi-input multi-output (MIMO) channels is presented in this paper. The channel at each hop is spatially correlated, the source symbols are mutually correlated, and the additive Gaussian noises are colored. First, by invoking Karush-Kuhn-Tucker condition for the optimality of convex programming, we derive the optimal source symbol covariance for the maximum mutual information between the channel input and the channel output when having the full knowledge of channel at the transmitter. Secondly, we formulate the average mutual information maximization problem when having only the channel statistics at the transmitter. Since this problem is almost impossible to be solved analytically, the numerical interior-point-method is employed to obtain the optimal solution. Furthermore, to reduce the computational complexity, an asymptotic closed-form solution is derived by maximizing an upper bound of the objective function. Simulation results show that the average mutual information obtained by the asymptotic design is very closed to that obtained by the optimal design, while saving a huge computational complexity.

scholarly journals Geometric Average Asian Option Pricing with Paying Dividend Yield under Non-Extensive Statistical Mechanics for Time-Varying Model

Entropy ◽  
2018 ◽  
Vol 20 (11) ◽  
pp. 828 ◽  
Author(s):  
Jixia Wang ◽  
Yameng Zhang
Keyword(s):  
Statistical Mechanics ◽  
Option Pricing ◽  
Asset Price ◽  
Closed Form Solution ◽  
Real Data ◽  
Form Solution ◽  
Asian Option ◽  
Time Varying ◽  
Dividend Yield ◽  
Geometric Average

This paper is dedicated to the study of the geometric average Asian call option pricing under non-extensive statistical mechanics for a time-varying coefficient diffusion model. We employed the non-extensive Tsallis entropy distribution, which can describe the leptokurtosis and fat-tail characteristics of returns, to model the motion of the underlying asset price. Considering that economic variables change over time, we allowed the drift and diffusion terms in our model to be time-varying functions. We used the I t o ^ formula, Feynman–Kac formula, and P a d e ´ ansatz to obtain a closed-form solution of geometric average Asian option pricing with a paying dividend yield for a time-varying model. Moreover, the simulation study shows that the results obtained by our method fit the simulation data better than that of Zhao et al. From the analysis of real data, we identify the best value for q which can fit the real stock data, and the result shows that investors underestimate the risk using the Black–Scholes model compared to our model.

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