Speed Profile Optimization for Optimal Path Tracking

Presented at American Control Conference, Washington, DC, June 17-19, 2013.In this paper, we study the problem of minimum-time, and minimum-energy speed profile optimization along a given path, which is a key step for solving the optimal path tracking problems for a particular class of dynamical systems. We focus on characterizing the optimal switching structure between extremal controls using optimal control theory, and present semi-analytical solutions to both problems. It is shown that the optimal solutions of these two problems are closely related

Minimum-time path planning for robot manipulators using path parameter optimization with external force and frictions

This paper presents a new minimum-time trajectory planning method which consists of a desired path in the Cartesian space to a manipulator under external forces subject to the input voltage of the actuators. Firstly, the path is parametrized with an unknown parameter called a path parameter. This parameter is considered a function of time and an unknown parameter vector for optimization. Secondly, the optimization problem is converted into a regular parameter optimization problem, subject to the equations of motion and limitations in angular velocity, angular acceleration, angular jerk, input torques of actuators’, input voltage and final time, respectively. In the presented algorithm, the final time of the task is divided into known partitions, and the final time is an additional unknown variable in the optimization problem. The algorithm attempts to minimize the final time by optimizing the path parameter, thus it is parametrized as a polynomial of time with some unknown parameters. The algorithm can have a smooth input voltage in an allowable range; then all motion parameters and the jerk will remain smooth. Finally, the simulation study shows that the presented approach is efficient in the trajectory planning for a manipulator that wants to follow a Cartesian path. In simulations, the constraints are respected, and all motion variables and path parameters remain smooth

Speed Profile Optimization for Optimal Path Tracking

In this paper, we study the problem of minimumtime, and minimum-energy speed profile optimization along a given path, which is a key step for solving the optimal path tracking problems for a particular class of dynamical systems. We focus on characterizing the optimal switching structure between extremal controls using optimal control theory, and present semi-analytical solutions to both problems. It is shown that the optimal solutions of these two problems are closely related