Sequential Convex Programming Methods for Real-time Trajectory Optimization in Autonomous Vehicle Racing

<div>We present a real-time-capable Model Predictive Controller (MPC) based on a single-track vehicle model and Pacejka’s magic tire formula for autonomous racing applications. After formulating the general non-convex trajectory optimization problem, the model is linearized around estimated operating points and the constraints are convexified using the Sequen- tial Convex Programming (SCP) method. We use two different methods to convexify the non-convex track constraints, namely Sequential Linearization (SL) and Sequential Convex Restriction (SCR). SL, a method of relaxing the constraints, was introduced in our previous paper. SCR, a method of restricting the con- straints, is introduced in this paper. We show the application of SCR to autonomous racing and prove that it does not interfere with recursive feasibility. We compare the predicted trajectory quality for the nonlinear single-track model to the linear double integrator model from our previous paper. The MPC performance is evaluated on a scaled version of the Hockenheimring racing track. We show that an MPC with SCR yields faster lap times than an MPC with SL – for race starts as well as flying laps – while still being real-time capable. A video showing the results is available at https://youtu.be/21iETsolCNQ.<br></div>

Sequential Convex Programming Methods for Real-time Trajectory Optimization in Autonomous Vehicle Racing

<div>We present a real-time-capable Model Predictive Controller (MPC) based on a single-track vehicle model and Pacejka’s magic tire formula for autonomous racing applications. After formulating the general non-convex trajectory optimization problem, the model is linearized around estimated operating points and the constraints are convexified using the Sequen- tial Convex Programming (SCP) method. We use two different methods to convexify the non-convex track constraints, namely Sequential Linearization (SL) and Sequential Convex Restriction (SCR). SL, a method of relaxing the constraints, was introduced in our previous paper. SCR, a method of restricting the con- straints, is introduced in this paper. We show the application of SCR to autonomous racing and prove that it does not interfere with recursive feasibility. We compare the predicted trajectory quality for the nonlinear single-track model to the linear double integrator model from our previous paper. The MPC performance is evaluated on a scaled version of the Hockenheimring racing track. We show that an MPC with SCR yields faster lap times than an MPC with SL – for race starts as well as flying laps – while still being real-time capable. A video showing the results is available at https://youtu.be/21iETsolCNQ.<br></div>

Motion Control of Electric Propulsion Spacecraft Transfers between the Libration Points L1 and L2 of the Earth–Moon System

This article presents a study of nonlinear motion of an electric propulsion spacecraft. Spacecraft transfers between the libration points L1 and L2 of the Earth-Moon system are analyzed. The influence of the shaded areas and gravitational effects of the Earth, the Moon and the Sun is taken into account. The mathematical model of the transfers is described within the barycentric coordinate frame. The exact optimal solution of the problem is obtained using Pontryagin’s maximum principle formalism and the numerical solution of the boundary value problem. The method of optimizing the parameters and controls of interplanetary trajectories of the spacecraft based on the optimization of dynamic system components and on Fedorenko’s method of sequential linearization is applied in this study. This method allows limitations on composite functions with Fréchet derivatives. As the results of the simulation, the control laws and corresponding trajectories are obtained.

Optimal resource allocation of the servicing companies in the field of housing and public utilities on the basis of the theory of multiphase queueing systems

The mathematical model describing technological process of functioning of the servicing companies in the sphere of housing sector and communal services is offered. The model allows you to manage the resources of serving companies in the housing sector in order to improve the quality of service. The problem statement and the solution of a problem of rational distribution of resources of the service company on the example of functioning of the center of maintenance of the measuring equipment used in the sphere of housing and communal services is given. The service center is modeled as a multiphase queueing system, which includes single-phase Queuing systems with limited and unlimited queue length. Used in the paper a method of sequential linearization allows to solve tasks of control production capacity of multiphase queueing systems for the simplest incoming flows with exponential service of requirements and free streams of requirements that are describing by means of simulation modeling methods. The software was developed. The results of applying the method of consistent linearization and corresponding software to the problem of optimal redistribution of production capacity of the center for maintenance of measuring equipment used in the sphere of housing and communal services are presented.