scholarly journals Improved sequential convex programming using modified Chebyshev–Picard iteration for ascent trajectory optimization

2021 ◽  
pp. 107234
Author(s):  
Yangyang Ma ◽  
Binfeng Pan ◽  
Chuanchuan Hao ◽  
Shuo Tang
Keyword(s):  
Convex Programming ◽  
Trajectory Optimization ◽  
Picard Iteration ◽  
Sequential Convex Programming

Trajectory Optimization Using Sequential Convex Programming with Collision Avoidance

2018 ◽  
Vol 29 (3) ◽  
pp. 318-327 ◽  
Author(s):  
Guilherme Matiussi Ramalho ◽  
Sidney Roberto Carvalho ◽  
Erlon Cristian Finardi ◽  
Ubirajara Franco Moreno
Keyword(s):  
Convex Programming ◽  
Collision Avoidance ◽  
Trajectory Optimization ◽  
Sequential Convex Programming

Rapid ascent trajectory optimization for guided rockets via sequential convex programming

2019 ◽  
Vol 233 (13) ◽  
pp. 4800-4809 ◽  
Author(s):  
Kai Zhang ◽  
Shuxing Yang ◽  
Fenfen Xiong
Keyword(s):  
Optimal Control ◽  
Convex Programming ◽  
Trajectory Optimization ◽  
Optimization Problems ◽  
Aerodynamic Drag ◽  
Programming Algorithm ◽  
Planning Problem ◽  
Dynamical Equations ◽  
Control Variables ◽  
Sequential Convex Programming

A sequential convex programming algorithm is proposed to solve the complex ascent trajectory optimization problems for guided rockets in this paper. Due to the nonlinear dynamics and constraints, especially, the nonlinear thrust terms and aerodynamic drag, ascent trajectory optimization problems for guided rockets are always difficult to be solved rapidly. In this paper, first, the complex thrust terms in the dynamic equation are approximately transformed into linear (convex) functions of the angle of attack. Secondly, the nonlinear drag coefficient is transformed into a linear (convex) function of design variables by introducing two new control variables. The relaxation technique is used to relax the constraints between the control variables to avoid non- convexity, and the accuracy of the relaxation is proved using the optimal control theory. Then, nonconvex objective functions and dynamical equations are convexified by first-order Taylor expansions. At last, a sequential convex programming iterative algorithm is proposed to solve the ascent trajectory planning problem accurately and rapidly. The ascent trajectory optimization problem for the terminal velocity maximum is simulated comparing with the general pseudospectral optimal control software method, which demonstrates the effectiveness and rapidity of the proposed method.

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

2021 ◽  
Author(s):  
Bassam Alrifaee ◽  
Patrick Scheffe ◽  
Maximilian Kloock ◽  
Theodor Mario Henneken
Keyword(s):  
Real Time ◽  
Convex Programming ◽  
Trajectory Optimization ◽  
Autonomous Vehicle ◽  
Single Track ◽  
Sequential Convex Programming ◽  
Predictive Controller ◽  
Integrator Model ◽  
Sequential Linearization ◽  
Operating Points

<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>

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