scholarly journals Diverse and Admissible Trajectory Forecasting Through Multimodal Context Understanding

2020 ◽  
pp. 282-298
Author(s):  
Seong Hyeon Park ◽  
Gyubok Lee ◽  
Jimin Seo ◽  
Manoj Bhat ◽  
Minseok Kang ◽  
...  
Keyword(s):  
Admissible Trajectory

scholarly journals Precise propagation of singularities for a hyperbolic system with characteristics of variable multiplicity

1986 ◽  
Vol 101 ◽  
pp. 111-130 ◽  
Author(s):  
Chisato Iwasaki ◽  
Yoshinori Morimoto
Keyword(s):  
Cauchy Problem ◽  
Wave Front ◽  
Hyperbolic System ◽  
Wave Front Set ◽  
Variable Multiplicity ◽  
The Cauchy Problem ◽  
Propagation Of Singularities ◽  
Admissible Trajectory

In this paper we consider the Cauchy problem for a hyperbolic system with characteristics of variable multiplicity and construct a certain solution whose wave front set propagates precisely along the so-called “broken null bicharacteristic flow”, in other words, along the admissible trajectory if we use the terminology of [6].

Optimal Trajectories With Respect to a Sthenic Criterion for Three Quadruped Walking Gaits

2001 ◽  
Author(s):  
A. Muraro ◽  
C. Chevallereau ◽  
Y. Aoustin
Keyword(s):  
Optimization Technique ◽  
Slow Motion ◽  
Maximal Speed ◽  
Optimization Parameters ◽  
Ground Reactions ◽  
Efficient Gait ◽  
Definition Of ◽  
Algebraic Optimization ◽  
Reference Trajectories ◽  
Admissible Trajectory

Abstract In this paper, optimal cyclic reference trajectories are designed for three walking gaits of a quadruped robot, the curvet, the amble, the trot, taking into account the actuators characteristics and for a given motion robot velocity. The objectives of this study are multiple: • Automatic design of admissible reference trajectories, • Definition of the maximal speed of the robot for given actuators, • Study of the evolution of the torque cost for various motion velocities, • Comparison of three different gaits with respect to a sthenic criterion. For the gaits studied, during some phases the system is underactuated. The design of the cyclic gaits takes this fact into account. The optimization problem is solved with an algebraic optimization technique. The actuated joint evolution is chosen as a polynomial function of time. The coefficients of the polynomial functions are optimization parameters. The evolution of the passive joint is defined using the dynamic model to have admissible trajectory. During the optimization process, the constraints on the ground reactions, the validity of impact, the torques, the joints velocities of the robot are taken into account. Simulation results are presented for the three gaits. All motions are realistics. Curvet is the less efficient gait with respect to the criterion studied. For slow motion, trot is the more efficient gait. But amble permits the fastest motion with the same actuators.

Individual consumer surplus in the Edgeworth Box

2021 ◽  
Vol 20 (11) ◽  
pp. 2151-2167
Author(s):  
Sergei A. MOSKAL'ONOV
Keyword(s):  
Mathematical Theory ◽  
Consumer Surplus ◽  
Main Property ◽  
Indifference Curve ◽  
Exchange Economy ◽  
Reservation Price ◽  
Microeconomic Theory ◽  
Individual Consumer ◽  
Admissible Trajectory ◽  
Correct Measure

Subject. The consumer surplus conception is an important part of the modern microeconomic theory at the introductory and intermediate levels. Consumer surplus measures the change in the consumer’s real welfare. The article addresses the peculiarities of generation and the main property of the generalized individual consumer surplus, using the Edgeworth Box case. Objectives. The purpose is to find the main property of individual consumer surplus in the Edgeworth Box economy. Methods. The study draws on methods of logical and mathematical analysis. The generalized consumer surplus is correctly constructed, using the mathematical theory of curve integrals of the second type (the theory of line integrals in the Western mathematics). Results. The generalized individual consumer surplus is defined through the respective curve integral along some admissible trajectory in the simple exchange economy (Edgeworth Box). The paper also introduces the notion of the marginal individual consumer surplus, and demonstrates that consumer surplus is a correct individual welfare measure in the Edgeworth Box, and that consumer surplus is zero along any given indifference curve. I consider the numerical example of individual surplus calculation and presentation in the Edgeworth Box. Conclusions. The generalized individual consumer surplus is a correct measure of consumer’s utility change along monotone (weakly monotone) trajectories in the Edgeworth Box. Geometrically, the consumer surplus is presented as an area limited by the reservation price curve from the top and by the reallocation line (curve) from the bottom.

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