scholarly journals Real-Time Sequential Convex Programming for Optimal Control Applications

2012 ◽  
pp. 91-102 ◽  
Author(s):  
Tran Dinh Quoc ◽  
Carlo Savorgnan ◽  
Moritz Diehl
Keyword(s):  
Optimal Control ◽  
Real Time ◽  
Convex Programming ◽  
Control Applications ◽  
Sequential Convex Programming

scholarly journals Real-Time Autonomous Obstacle Avoidance For Unmanned Aerial Vehicles

2021 ◽  
Author(s):  
Min Prasad Adhikari
Keyword(s):  
Unmanned Aerial Vehicles ◽  
Real Time ◽  
Convex Programming ◽  
Obstacle Avoidance ◽  
Kinematic Model ◽  
Trajectory Generation ◽  
Computation Time ◽  
Programming Approach ◽  
Sequential Convex Programming ◽  
Aerial Vehicles

<div>In this dissertation, methods for real-time trajectory generation and autonomous obstacle avoidance for fixed-wing and quad-rotor unmanned aerial vehicles (UAV) are studied. A key challenge for such trajectory generation is the high computation time required to plan a new path to safely maneuver around obstacles instantaneously. Therefore, methods for rapid generation of obstacle avoidance trajectory are explored. The high computation time is a result of the computationally intensive algorithms used to generate trajectories for real-time object avoidance. Recent studies have shown that custom solvers have been developed that are able to solve the problem with a lower computation time however these designs are limited to small sized problems or are proprietary. Additionally, for a swarm problem, which is an area of high interest, as the number of agents increases the problem size increases and in turn creates further computational challenges. A solution to these challenges will allow for UAVs to be used in autonomous missions robust to environmental uncertainties.</div><div><br></div><div>In this study, a trajectory generation problem posed as an optimal control problem is solved using a sequential convex programming approach; a nonlinear programming algorithm, for which custom solver is used. First, a method for feasible trajectory generation for fast-paced obstacle-rich environments is presented for the case of fixed-wing UAVs. Next, a problem of trajectory generation for fixed-wing and quad-rotor UAVs is defined such that starting from an initial state a UAV moves forward along the direction of flight while avoiding obstacles and remaining close to a reference path. The problem is solved within the framework of finite-horizon model predictive control. Finally, the problem of trajectory generation is extended to a swarm of quad-rotors where each UAV in a swarm has a reference path to fly along. Utilizing a centralized approach, a swarm scenario with moving targets is studied in two different cases in an attempt to lower the solution time; the first, solve the entire swarm problem at once, and the second, solve iteratively for a UAV in the swarm while considering trajectories of other UAVs as fixed.</div><div><br></div><div>Results show that a feasible trajectory for a fixed-wing UAV can be obtained within tens of milliseconds. Moreover, the obtained feasible trajectories can be used as initial guesses to the optimal solvers to speed up the solution of optimal trajectories. The methods explored demonstrated the ability for rapid feasible trajectory generation allowing for safe obstacle avoidance, which may be used in the case an optimal trajectory solution is not available. A comparative study between a dynamic and a kinematic model shows that the dynamic model provides better trajectories including aggressive trajectories around obstacles compared to the kinematic counterpart for fixed-wing UAVs, despite having approximately the same computational demands. Whereas, for the case of quad-rotor UAVs, the kinematic model takes almost half the solution time than with a reduced dynamic model, despite having approximately the similar range of values for the cost function. When extended to a swarm, solving the problem for each UAV is four to seven times computationally cheaper than solving the swarm as a whole. With the improved computation time for trajectory generation for a swarm of quad-rotors using centralized approach, the problem is now reasonably scalable, which opens up the possibility to increase the number of agents in a swarm using high-end computing machines for real-time applications. Overall, a custom solver jointly with a sequential convex programming approach solves an optimization problem in a low computation time.</div>

scholarly journals Real-Time Autonomous Obstacle Avoidance For Unmanned Aerial Vehicles

2021 ◽  
Author(s):  
Min Prasad Adhikari
Keyword(s):  
Unmanned Aerial Vehicles ◽  
Real Time ◽  
Convex Programming ◽  
Obstacle Avoidance ◽  
Kinematic Model ◽  
Trajectory Generation ◽  
Computation Time ◽  
Programming Approach ◽  
Sequential Convex Programming ◽  
Aerial Vehicles

<div>In this dissertation, methods for real-time trajectory generation and autonomous obstacle avoidance for fixed-wing and quad-rotor unmanned aerial vehicles (UAV) are studied. A key challenge for such trajectory generation is the high computation time required to plan a new path to safely maneuver around obstacles instantaneously. Therefore, methods for rapid generation of obstacle avoidance trajectory are explored. The high computation time is a result of the computationally intensive algorithms used to generate trajectories for real-time object avoidance. Recent studies have shown that custom solvers have been developed that are able to solve the problem with a lower computation time however these designs are limited to small sized problems or are proprietary. Additionally, for a swarm problem, which is an area of high interest, as the number of agents increases the problem size increases and in turn creates further computational challenges. A solution to these challenges will allow for UAVs to be used in autonomous missions robust to environmental uncertainties.</div><div><br></div><div>In this study, a trajectory generation problem posed as an optimal control problem is solved using a sequential convex programming approach; a nonlinear programming algorithm, for which custom solver is used. First, a method for feasible trajectory generation for fast-paced obstacle-rich environments is presented for the case of fixed-wing UAVs. Next, a problem of trajectory generation for fixed-wing and quad-rotor UAVs is defined such that starting from an initial state a UAV moves forward along the direction of flight while avoiding obstacles and remaining close to a reference path. The problem is solved within the framework of finite-horizon model predictive control. Finally, the problem of trajectory generation is extended to a swarm of quad-rotors where each UAV in a swarm has a reference path to fly along. Utilizing a centralized approach, a swarm scenario with moving targets is studied in two different cases in an attempt to lower the solution time; the first, solve the entire swarm problem at once, and the second, solve iteratively for a UAV in the swarm while considering trajectories of other UAVs as fixed.</div><div><br></div><div>Results show that a feasible trajectory for a fixed-wing UAV can be obtained within tens of milliseconds. Moreover, the obtained feasible trajectories can be used as initial guesses to the optimal solvers to speed up the solution of optimal trajectories. The methods explored demonstrated the ability for rapid feasible trajectory generation allowing for safe obstacle avoidance, which may be used in the case an optimal trajectory solution is not available. A comparative study between a dynamic and a kinematic model shows that the dynamic model provides better trajectories including aggressive trajectories around obstacles compared to the kinematic counterpart for fixed-wing UAVs, despite having approximately the same computational demands. Whereas, for the case of quad-rotor UAVs, the kinematic model takes almost half the solution time than with a reduced dynamic model, despite having approximately the similar range of values for the cost function. When extended to a swarm, solving the problem for each UAV is four to seven times computationally cheaper than solving the swarm as a whole. With the improved computation time for trajectory generation for a swarm of quad-rotors using centralized approach, the problem is now reasonably scalable, which opens up the possibility to increase the number of agents in a swarm using high-end computing machines for real-time applications. Overall, a custom solver jointly with a sequential convex programming approach solves an optimization problem in a low computation time.</div>

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>

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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