General Optimal Trajectory Planning:Enabling Autonomous Vehicles with the Principle of Least Action

This study presents a general optimal trajectory planning(GOTP)framework for autonomous vehicles(AVs)that can effectively avoid obstacles and guide AVs to complete driving tasks safely and efficiently.Firstly,we employ the fifth-order Bezier curve to generate and smooth the reference path along the road centerline.Cartesian coordinates are then transformed to achieve the curvature continuity of the generated curve.Considering the road constraints and vehicle dynamics,limited polynomial candidate trajectories are generated and smoothed in a curvilinear coordinate system.Furthermore,in selecting the optimal trajectory,we develop a unified and auto-tune objective function based on the principle of least action by employing AVs to simulate drivers’behavior and summarizing their manipulation characteristics of“seeking benefits and avoiding losses.”Finally,by integrating the idea of receding-horizon optimization,the proposed framework is achieved by considering dynamic multi-performance objectives and selecting trajectories that satisfy feasibility,optimality,and adaptability.Extensive simulations and experiments are performed,and the results demonstrate the framework’s feasibility and effectiveness,which avoids both dynamic and static obstacles and applies to various scenarios with multi-source interactive traffic participants.Moreover,we prove that the proposed method can guarantee real-time planning and safety requirements compared to drivers’manipulation.

THE PRINCIPLES OF LEAST ACTION OF VARIABLE MASS NONHOLONOMIC NONCONSERVATIVE SYSTEM IN NONINERTIAL REFERENCE FRAMES

This paper presents the generalized principles of least action of variable mass nonholonomic nonconservative system in noninertial reference frame, proves the equivalence between Holder form and Suslov form, and then obtains differential equations of motion of variable mass nonholonomic nonconservative system in noninertial reference frame.

Towards the Unified Principles for Level 5 Autonomous Vehicles

The rapid advance of autonomous vehicles(AVs)has motivated new perspectives and potential challenges for existing modes of transportation.Currently,driving assistance systems of Level 3 and below have been widely produced,and several applications of Level 4 systems to specific situations have also been gradually developed.By improving the automation level and vehicle intelligence,these systems can be further advanced towards fully autonomous driving.However,general development concepts for Level 5 AVs remain unclear,and the existing methods employed in the development processes of Levels 0-4 have been mainly based on task-driven function development related to specific scenarios.Therefore,it is difficult to identify the problems encountered by high-level AVs.The essential logical and physical mechanisms of vehicles have hindered further progression towards Level 5 systems.By exploring the physical mechanisms behind high-level autonomous driving systems and analyzing the essence of driving,we put forward a coordinated and balanced framework based on the brain-cerebellum-organ concept through reasoning and deduction.Based on a mixed mode relying on the crow inference and parrot imitation approach,we explore the research paradigm of autonomous learning and prior knowledge to realize the characteristics of self-learning,self-adaptation,and self-transcendence for AVs.From a systematic,unified,and balanced point of view and based on least action principles and unified safety field concepts,we aim to provide a novel research concept and develop an effective approach for the research and development of high-level AVs,specifically at Level 5.

A new method for calculating the activity of stable compound from binary phase diagram

A new method to calculate the activity of a stable compound in a binary phase diagram was presented and discussed. According to the formula for calculating activity from the binary phase diagram, the equilibrium constant can be calculated through the mass action principle after the activities of two pure components were computed respectively. Based on that, the activity of a stable compound can be easily obtained at last. The activity of the stable compound InSb is calculated in the In-Sb binary system by using this method. The result is well consistent with another calculation value.

Evolutionary Algorithms in Astrodynamics

This paper presents the method of solving the equations of motions by evolutionary algorithms. Starting from random trajectory, the solution is obtained by accepting the mutation if it leads to a better approximations of Newton’s second law. The general method is illustrated by finding trajectory to the Moon.

THE EXISTENCE OF PERIODIC SOLUTIONS TO SECOND ORDER SELF-ADJOINT DIFFERENCE EQUATIONS

In this paper, we consider the existence of periodic solutions to a class of second order self-adjoint difference equations. By the least action principle and saddle point theorem in the critical point theory, some new results are obtained. As an application, we also give two examples to demonstrate our main results.