Program Construction Method for Sequential Statistics Class Algorithm Based on Bidirectional Scanning Induction

The program construction process is based on rigorous mathematical reasoning,which leads to a fully correct algorithmic program via step-by-step refinement of the program specifications.The existing program construction methods'refinement process is partly based on individual subjective speculation and analysis,which lacks a precise guidance method.Meanwhile,efficiency factors have usually been ignored in the construction process,and most of the constructed abstract programs cannot be run directly by machines.In order to solve these problems,a novel program construction method for the sequence statistical class algorithms based on bidirectional scan induction is proposed in this paper.The method takes into account the efficiency factor and thus improves the Morgan's refinement calculus.Furthermore,this paper validates the method's feasibility using an efficiency-sensitive sequential statistics class algorithm as a program construction example.The method proposed in this paper realizes the correctness construction process from program specifications to efficient executable programs.

A Real-time Look-ahead Trajectory Planning Methodology for Multi Small Line Segments Path

When a robot is required to machine a complex curved workpiece with high precision and speed,the tool path is typically dispersed into a series of points and transmitted to the robot.The conventional trajectory planning method requires frequent starts and stops at each dispersed point to complete the task.This method not only reduces precision but also causes damage to the motors and robot.A real-time look-ahead algorithm is proposed in this paper to improve precision and minimize damage.The proposed algorithm includes a path-smoothing algorithm,a trajectory planning method,and a bidirectional scanning module.The path-smoothing method inserts a quintic Bezier curve between small adjacent line segments to achieve G^(2)continuity at the junctions.The trajectory planning method utilizes a quartic polynomial and a double-quartic polynomial that can achieve a constant velocity at the velocity limitation.The bidirectional scanning module calculates the velocity at each trajectory planning segment point,simplifying calculation complexity and can be run in real time.The feasibility of the proposed algorithm is verified through simulations and experiments,which can be run in real time.In addition,high machining precision can be achieved by adjusting the relevant parameters.

Improved time-optimal B-spline feedrate scheduling for NURBS tool paths in CNC machining

Feedrate scheduling in computer numerical control(CNC)machining is of great importance to fully develop the capabilities of machine tools while maintaining the motion stability of each actuator.Smooth and time-optimal feedrate scheduling plays a critical role in improving the machining efficiency and precision of complex surfaces considering the irregular curvature characteristics of tool paths and the limited drive capacities of machine tools.This study develops a general feedrate scheduling method for non-uniform rational B-splines(NURBS)tool paths in CNC machining aiming at minimizing the total machining time without sacrificing the smoothness of feed motion.The feedrate profile is represented by a B-spline curve to flexibly adapt to the frequent acceleration and deceleration requirements of machining along complex tool paths.The time-optimal B-spline feedrate is produced by continuously increasing the control points sequentially from zero positions in the bidirectional scanning and sampling processes.The required number of knots for the time-optimal B-spline feedrate can be determined using a progressive knot insertion method.To improve the computational efficiency,the B-spline feedrate profile is divided into a series of independent segments and the computation in each segment can be performed concurrently.The proposed feedrate scheduling method is capable of dealing with not only the geometry constraints but also high-order drive constraints for any complex tool path with little computational overhead.Simulations and machining experiments are conducted to verify the effectiveness and superiorities of the proposed method.