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

Investigation on the influence of parameter uncertainties in the position tracking of robot manipulators

This paper presents a novel trajectory tracking method for robot arms with uncertainties in parameters. The new controller applies the robust output feedback linearization method and is designed so that it is robust to the variation of parameters. Robustness of the algorithm is evaluated when the parameters of the system are floating over 10 percent up and down. An Unscented Kalman Filter (UKF) is applied for state and parameter estimation purposes. As the considered system has 8 unknown parameters while only 5 of them are independent parameters, UKF is applied only to the augmented system with independent parameters. Three types of simulations are applied depending on sensor groups – first with both position and joint sensors, second with only position sensors and third with only joint sensors. The observation of parameters in these groups is discussed. Simulation results show that when both position sensors and joint sensors are used, all the parameters and states are observable and good tracking performances are obtained. When only position sensors are used, the accuracy of the estimated parameters is reduced, and low tracking performances are revealed. Finally, when only joint sensors are applied, the lengths of robot arms are unobservable, but other parameters related to the dynamic system are observable, and poor tracking performances are given