Servo Driver Interpolation for Low-Jerk Command Tracking
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Solution Overview
Problem
Existing interpolation techniques for command values in servo drivers face challenges in minimizing follow-up delay and jerk (increasing acceleration) when command values are sequentially input, particularly requiring fewer command values for smoother operation.
Innovation Solution
A servo driver employs a fifth-order interpolation function generation method that uses four command values to create interpolation functions where function values and derivatives match at interval boundaries, reducing jerk and follow-up delay by ensuring continuity of first and second derivatives.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Loss of time
If a fifth-order interpolation function is used with four command values, then follow-up delay is reduced, but jerk (increasing acceleration) may increase if derivatives are not continuous
Solution Approach 1:
The patent applies parameter changes by using a fifth-order polynomial interpolation function instead of lower-order functions. This higher-order function provides more degrees of freedom to satisfy multiple continuity conditions (position, velocity, and acceleration continuity) while reducing follow-up delay. The interpolation function y = a0 + a1*t + a2*t^2 + a3*t^3 + a4*t^4 + a5*t^5 allows six parameters to be optimized to meet the boundary conditions and minimize both delay and jerk.
Solution Approach 2:
The patent implements preliminary action by pre-calculating the interpolation function coefficients based on four command values before actual motion execution. The system computes the fifth-order polynomial coefficients in advance to ensure smooth transitions and minimize jerk from the start of each interpolation interval, rather than adjusting parameters during motion.
2Loss of time
If fewer command values are used for interpolation, then follow-up delay is reduced, but smoothing capability deteriorates
Solution Approach 1:
The patent uses parameter changes by elevating the interpolation function to fifth-order, which provides six coefficients (a0 through a5) that can be determined from four command values with appropriate boundary conditions. This parameter expansion enables the system to achieve both rapid response with fewer command values and smooth interpolation by satisfying continuity conditions for position, velocity, and acceleration at interval boundaries.
Solution Approach 2:
The patent applies dimensionality change by transitioning from lower-order (first or second order) interpolation to fifth-order interpolation. This increases the dimensional complexity of the mathematical model, providing additional degrees of freedom that allow the system to simultaneously reduce follow-up delay and maintain smoothness by enforcing continuity of the function and its first and second derivatives.
3Object-generated harmful factors
If second derivatives are made continuous across intervals, then jerk is reduced, but computational complexity increases
Solution Approach 1:
The patent uses parameter changes by formulating the fifth-order polynomial with six coefficients that can be systematically determined from boundary conditions. The continuity of second derivatives is achieved by setting up equations that equate the second derivatives at interval boundaries, providing a structured method to reduce jerk while managing computational complexity through consistent mathematical formulation.
Solution Approach 2:
The patent implements preliminary action by pre-computing all interpolation coefficients including those ensuring second derivative continuity before motion execution. This advance calculation of all six parameters (a0 through a5) for each interpolation interval eliminates the need for complex real-time adjustments during motion, reducing online computational burden while maintaining smooth acceleration transitions.
Data Source
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AI summary
Provided is an interpolation technique in which command values chronologically input can be interpolated without increasing a jerk and with less follow-up delay with respect to a command. A control unit (10) of a servo driver (20) has a function of sequentially generating, on the basis of four command values from x(k-2) to x(k+1), a kth interpolation function for calculating command values in a kth (≥3) time interval and a function of generating, as the kth interpolation function, a fifth-order equation with respect to time in which function values at a start time and an end time of the kth time interval match x(k) and x(k+1), respectively, and in which a second derivative value at a start time of the kth time interval matches a second derivative value at an end time of a (k-1)th time interval corresponding to a (k-1)th interpolation function.