Trajectory Generation Using Passing Points for Smooth Curve Connection
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Solution Overview
Problem
Existing trajectory generation methods for NC machine tools and industrial robots struggle to smoothly connect interpolating curves at passing points, making it difficult for users to estimate the trajectory in partial sections, especially when different types of functions are involved.
Innovation Solution
A trajectory generation device that includes a storage unit for storing passing points and a processor configured to receive designated path information for a partial section. The processor generates a trajectory using this information, incorporating both anterior and posterior passing points to ensure smooth connection of interpolating curves.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Manufacturing precision
If quadratic curves are used to connect three points for trajectory generation, then the trajectory can be calculated using differential coefficients, but the connection between interpolating curves at passing points becomes difficult to estimate and may not be smooth
Solution Approach 1:
The patent changes the mathematical parameters from simple quadratic curves to cubic curves, and further to cubic curves with constrained coefficients. This parameter change allows the trajectory to pass through multiple points while ensuring smooth connections at passing points, resolving the contradiction between connection smoothness and estimation ease.
Solution Approach 2:
The patent pre-calculates and stores differential coefficients (first and second derivatives) at each passing point before generating the final trajectory. This preliminary action allows the interpolating curves to be smoothly connected by using these pre-computed coefficients, eliminating the need for complex real-time calculations and making the trajectory estimation easier.
2Reliability
If multiple adjoining points are used for interpolating curve calculation, then the trajectory connection between sections can be improved, but the calculation complexity increases
Solution Approach 1:
The patent uses cubic curves instead of quadratic curves, and imposes constraints on the cubic curve coefficients to reduce the number of independent parameters. This allows the use of multiple adjoining points (Pm-1, Pm, Pm+1, Pm+2) for higher reliability in connection while keeping the calculation complexity manageable through parameter reduction.
Solution Approach 2:
The patent pre-calculates the differential coefficients at each passing point and stores them for later use. This preliminary calculation separates the complex mathematical operations from the real-time trajectory generation, reducing the calculation complexity during actual operation while maintaining high reliability through the use of multiple adjoining points.
3Productivity
If interpolating curves are smoothly connected at passing points, then the tool can pass through without slowing down, but the trajectory in partial sections becomes difficult for users to estimate
Solution Approach 1:
The patent uses cubic curves with constrained coefficients instead of simple quadratic curves. This parameter change allows the trajectory to be smoothly connected (enabling continuous motion without slowing down) while the constrained coefficients make the trajectory shape more predictable and easier for users to estimate in partial sections.
Data Source
AI summary
A trajectory generation device configured to generate a trajectory along which a control target passes, the device including a storage unit configured to store a plurality of points, and a processor. the processor is configured to perform receiving process of receiving designated path information about a path designated by a user in a partial section between two points in the plurality of points, and trajectory generation process of generating a trajectory in the partial section by using the designated path information, a first path passing through the two points in the plurality of points and at least one anterior passing point through which the control target passes before passing through the two points, and a second path passing through the two points in the plurality of points and at least one posterior passing point through which the control target passes after passing through the two points.