A geometric approach to the transpositional relations in dynamics of nonholonomic mechanical systems

Exploring the geometry of mechanical systems subject to nonholonomic constraints and using various bundle and variational structures intrinsically present in the nonholonomic setting, we study the structure of the equations of motion in a way that aids the analysis and helps to isolate the important geometric objects that govern the motion of such systems. Furthermore, we show that considering different sets of transpositional relations corresponding to different transitivity choices provides different variational structures associated with nonholonomic dynamics, but the derived equations (being referred to as the generalized Hamel–Voronets equations) are equivalent to the Lagrange–d’Alembert equations. To illustrate results of this work and as some applications of the generalized Hamel–Voronets formalisms discussed in this paper, we conclude with considering the balanced Tennessee racer, as well as its modification being referred to as the generalized nonholonomic cart, and an [Formula: see text]-snake with three wheeled planar platforms whose snake-like motion is induced by shape variations of the system.

An Analytical Measuring Rectification Algorithm of Monocular Systems in Dynamic Environment

Range estimation is crucial for maintaining a safe distance, in particular for vision navigation and localization. Monocular autonomous vehicles are appropriate for outdoor environment due to their mobility and operability. However, accurate range estimation using vision system is challenging because of the nonholonomic dynamics and susceptibility of vehicles. In this paper, a measuring rectification algorithm for range estimation under shaking conditions is designed. The proposed method focuses on how to estimate range using monocular vision when a shake occurs and the algorithm only requires the pose variations of the camera to be acquired. Simultaneously, it solves the problem of how to assimilate results from different kinds of sensors. To eliminate measuring errors by shakes, we establish a pose-range variation model. Afterwards, the algebraic relation between distance increment and a camera’s poses variation is formulated. The pose variations are presented in the form of roll, pitch, and yaw angle changes to evaluate the pixel coordinate incensement. To demonstrate the superiority of our proposed algorithm, the approach is validated in a laboratory environment using Pioneer 3-DX robots. The experimental results demonstrate that the proposed approach improves in the range accuracy significantly.