SUMMARYThis paper presents an optimal trajectory planning method for industrial robots. The paper specially focuses on the applications of path tracking. The problem is to plan the trajectory with a specified geometric path, while allowing the position and orientation of the path to be arbitrarily selected within the specific ranges. The special contributions of the paper include (1) an optimal path tracking formulation focusing on the least time and energy consumption without violating the kinematic constraints, (2) a special mechanism to discretize a prescribed path integration for segment interpolation to fulfill the optimization requirements of a task with its constraints, (3) a novel genetic algorithm (GA) optimization approach that transforms a target path to be tracked as a curve with optimal translation and orientation with respect to the world Cartesian coordinate frame, (4) an integration of the interval analysis, piecewise planning and GA algorithm to overcome the challenges for solving the special trajectory planning and path tracking optimization problem. Simulation study shows that it is an insufficient condition to define a trajectory just based on the consideration that each point on the trajectory should be reachable. Simulation results also demonstrate that the optimal trajectory for a path tracking problem can be obtained effectively and efficiently using the proposed method. The proposed method has the properties of broad adaptability, high feasibility and capability to achieve global optimization.
Novel HPLC methods were developed for the analytical and semipreparative resolution of new antianginal drug ranolazine enantiomers. Good baseline enantioseparation was achieved using cellulose tris (3,5-dimethylphenylcarbamate) (CDMPC) chiral stationary phases (CSPs) under both normal-phase and polar organic modes. The validation of the analytical methods including linearity, LODs, recovery, and precision, and the semipreparative resolution of ranolazine racemate were carried out using methanol as mobile phase without any basic and acidic additives under polar organic mode, using CDMPC CSPs. At analytical scale, the elution times of both enantiomers were less than 7.5 min at 20 degrees C and 1.0 mL/min, with the separation factor (a) 1.88 and the resolution factor (R(s)) 2.95. At semipreparative scale, about 14.3 mg/h enantiomers could be isolated and elution times of both enantiomers were less than 13 min at 2.0 mL/min. To increase the throughput, the technique of overlapping injections was used. The first eluted enantiomer was isolated with a purity of 99.6% enantiomer excess (e.e.) and > 99.0% yield. The second enantiomer was isolated with a purity of 98.8% e.e. and > 99.0% yield. In addition, optical rotation and circular dichroism spectroscopy of both ranolazine enantiomers isolated were also investigated.
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