Minimum Time Trajectory Optimization Research Articles

Minimum Time Trajectory Optimization of CNC Machining with Tracking Error Constraints

An off-line optimization approach of high precision minimum time feedrate for CNC machining is proposed. Besides the ordinary considered velocity, acceleration, and jerk constraints, dynamic performance constraint of each servo drive is also considered in this optimization problem to improve the tracking precision along the optimized feedrate trajectory. Tracking error is applied to indicate the servo dynamic performance of each axis. By using variable substitution, the tracking error constrained minimum time trajectory planning problem is formulated as a nonlinear path constrained optimal control problem. Bang-bang constraints structure of the optimal trajectory is proved in this paper; then a novel constraint handling method is proposed to realize a convex optimization based solution of the nonlinear constrained optimal control problem. A simple ellipse feedrate planning test is presented to demonstrate the effectiveness of the approach. Then the practicability and robustness of the trajectory generated by the proposed approach are demonstrated by a butterfly contour machining example.

Optimization of Complex Robot Applications under Real Physical Limitations

This paper deals with minimum time trajectory optimization along a specified path subject to thermal constraints. We point out here that robots are often integrated into complex robotic cells, and the interactions between the robot and its environment are often difficult or even impossible to model. The structure of the optimization problem allows us to decompose the optimization into two levels, the first being based on models and results of the theory of the calculus of variations, the second being based on measurements and derivative free algorithms. This decomposition allows us to optimize the velocity profiles efficiently without any advance knowledge of the interactions between the robot and its environment. We propose here two numerical algorithms for these two levels of the decomposition which show good convergence properties. The resulting optimal velocity profiles are 5—10% faster than classical profiles, and have been executed successfully on a real Stäubli Rx90 manipulator robot.

Minimum Time Trajectory Optimization and Learning

This paper presents a numerical algorithm for finding the bang-bang control input associated with the time optimal solution of a class of nonlinear dynamic systems. The proposed algorithm directly searches for the optimal switching instants based on a projected gradient optimization method. It is shown that this algorithm can be made into a learning algorithm by using on-line measurements of the state trajectory. The learning is shown to have the potential for significant robustness to mismatch between the model and the system. It learns a nearly optimal input through repeated trials in which it utilizes the measured terminal state error of the actual system and gradients based on the theoretical state equation of the system but evaluated along the actual state trajectory. The success of the method is demonstrated on an underactuated double pendulum system called the acrobot.

Aircraft Trajectory Optimization in the Horizontal Plane

Abstract The problem of minimum time trajectory optimization for aircraft in the presence of winds is considered. The solutions are obtained by employing a parametrization technique based on the famous theorem of Caratheodory in order to reduce the problem into a finite dimensional optimization problem, without using the minimum principle or similar analysis methods. Numerical solutions are presented for cases with and without the presence of winds in order to demonstrate the effect of winds on the trajectory planning.

Aircraft Trajectory Optimization in the Horizontal Plane

The problem of minimum time trajectory optimization for aircraft in the presence of winds is considered. The solutions are obtained by employing a parametrization technique based on the famous theorem of Caratheodory in order to reduce the problem into a finite dimensional optimization problem, without using the minimum principle or similar analysis methods. Numerical solutions are presented for cases with and without the presence of winds in order to demonstrate the effect of winds on the trajectory planning.