Fourth-Order Trajectory Planning for Time-Optimal Motion Control
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Solution Overview
Problem
Current methods for fourth-order trajectory planning in motion control systems are not time-optimal for all movement tasks, especially when the distance to be covered is small, leading to suboptimal solutions and incomplete results.
Innovation Solution
A method for determining time-optimal fourth-order trajectories by calculating snap profiles (TYPE1, TYPE2, and TYPE3 profiles) based on predefined velocity, acceleration, jerk, and snap constraint values, ensuring maximum derivative values are reached and maintained to minimize movement time.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Loss of time
If fourth order trajectory planning is used to reduce settling time, then positioning precision and speed are improved, but the method is not time-optimal for all movement tasks especially when distance is small
Solution Approach 1:
The patent applies parameter changes by dynamically adjusting trajectory parameters (snap, jerk, acceleration, velocity) based on the distance to be covered. The method calculates different snap profiles (TYPE1, TYPE2, TYPE3) with varying parameter combinations to achieve time-optimality for different movement scenarios, particularly for small distances where maximum velocity cannot be reached.
2Speed
If maximum derivative values are used to minimize movement time, then speed is improved, but constraint violations may occur
Solution Approach 1:
The patent implements feedback by continuously monitoring the actual position, velocity, acceleration, jerk, and snap during movement, and comparing them against the planned trajectory and constraints. The method adjusts the snap profile in real-time to ensure constraints are satisfied while maintaining time-optimality, preventing violations of maximum velocity, acceleration, jerk, or snap limits.
Data Source
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AI summary
A method for obtaining a fourth order trajectory (150, 250, 350) for moving an object (O) from a first point (A) to a second point (B) covering a distance (d) using predefined velocity, acceleration, jerk and snap constraint values (vmax, amax. jmax, smax), wherein the fourth order trajectory (150, 250, 350) is obtained on the basis of an operating snap profile (190, 290, 390) representing the fourth derivative of the trajectory (150, 250, 350) of the position of the object (O) and comprising a plurality of time intervals with corresponding snap values, and wherein a first snap profile (190) is determined on the basis of the distance (d) and of the velocity, acceleration, jerk and snap constraint values (vmax, amax, jmax, smax) and is defined as the operating snap profile (190) if the velocity constraint value (vmax) is attained in a first velocity profile (160) representing the first derivative of a first trajectory (150) corresponding to the first snap profile (190), is provided, wherein, according to the invention, a second snap profile (290) different from the first snap profile (190) is determined on the basis of the distance (d) and of the acceleration, jerk and snap constraint values (amax, jmax, smax) and is defined as the operating snap profile (290) if the velocity constraint value (vmax) is not attained in the first velocity profile (160) and if a maximum velocity in a second velocity profile (260) representing the first derivative of a second trajectory (250) corresponding to the second snap profile (290) does not exceed the velocity constraint value (vmax), and a third snap profile (390) different from the first snap profile (190) and from the second snap profile (290) is determined on the basis of the distance (d), of the maximum velocity in the second velocity profile (260) and of the velocity, acceleration, jerk and snap constraint values (vmax, amax, jmax, smax) and is defined as the operating snap profile (390) if the maximum velocity in the second velocity profile (260) does exceed the velocity constraint value (vmax). The invention also relates to a corresponding device.