Constraint-Classified Speed Planning for Complex Curved Paths
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Solution Overview
Problem
Existing speed planning methods for machining complex curved surfaces fail to achieve time optimality and often result in excessive scaling due to poor constraint solution stability, especially when path curvature and constraints change significantly.
Innovation Solution
A time optimal speed planning method based on constraint classification, which involves reading path information, curve fitting, sampling, considering static and dynamic constraints, constructing a time optimal speed model, performing convex transformation, and solving the model using a quadratic sequence planning method to obtain a final speed curve.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Loss of time
If the optimal planning method is used for complex paths, then the machining time is reduced, but excessive scaling occurs and constraint solution stability deteriorates
Solution Approach 1:
The patent segments the speed planning problem by classifying constraints into static constraints (path curvature, feed rate limits) and dynamic constraints (acceleration, jerk limits). This segmentation allows the use of different planning strategies for different constraint types, achieving time optimality while maintaining solution stability through structured constraint handling.
Solution Approach 2:
The patent applies dynamics by transitioning from static speed planning to dynamic speed planning. The dynamic constraint satisfaction method continuously adjusts speed profiles based on real-time constraint violations, using acceleration and jerk limits to smoothly adapt speed changes. This dynamic approach prevents excessive scaling while maintaining time optimality through continuous constraint monitoring and adjustment.
2Reliability
If the S-shaped planning method is used for complex paths, then the constraint solution stability is improved, but time optimality cannot be achieved
Solution Approach 1:
The patent merges the advantages of S-shaped planning (constraint stability) with optimal planning (time efficiency) by combining static constraint satisfaction with dynamic constraint satisfaction. The static phase establishes a stable baseline speed profile, while the dynamic phase optimizes timing through accelerated constraint handling, achieving both stability and time optimality simultaneously.
Solution Approach 2:
The patent changes parameters by introducing dynamic adjustment of speed, acceleration, and jerk parameters based on constraint violation detection. Instead of fixed S-shaped profiles, the system dynamically modifies these parameters in response to constraint conditions, enabling time optimality while maintaining stability through adaptive parameter control.
3Productivity
If the speed is increased to improve productivity, then the machining efficiency is improved, but constraint violations occur and solution stability deteriorates
Solution Approach 1:
The patent implements feedback through continuous monitoring of constraint satisfaction during speed planning. When constraint violations are detected (acceleration or jerk limits exceeded), the system provides feedback to adjust the speed profile dynamically. This feedback mechanism enables high productivity speeds while maintaining solution stability by automatically correcting constraint violations in real-time.
Solution Approach 2:
The patent uses dynamics to enable high-speed machining with stable constraints by continuously adapting the speed profile. The dynamic constraint satisfaction method allows aggressive speed increases for productivity while dynamically adjusting acceleration and jerk to prevent constraint violations, achieving both high productivity and solution stability through real-time dynamic control.
Data Source
AI summary
A time optimal speed planning method and system based on constraint classification. The method comprises: reading path information and carrying out curve fitting to obtain a path curve; sampling the path curve, and considering static constraint to obtain a static upper bound value of a speed curve; considering dynamic constraint, and combining the static upper bound value of the speed curve to construct a time optimal speed model; carrying out convex transformation on the time optimal speed model to obtain a convex model; and solving the convex model based on a quadratic sequence planning method to obtain a final speed curve. The system comprises: a path curve module, a static constraint module, a dynamic constraint module, a model transformation module and a solving module.