Filtered B-Spline Trajectory Control for Servo Motion Errors
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Solution Overview
Problem
Existing tracking control methods for dynamic systems, such as CNC machines, fail to effectively minimize servo-induced motion errors and track higher-order derivatives while adhering to kinematic constraints and non-zero initial conditions, especially in the presence of unwanted vibration modes.
Innovation Solution
The use of filtered basis splines (B-splines) to generate a modified trajectory command that minimizes tracking errors by optimizing control points, allowing for constraint enforcement and higher-order derivative tracking, and incorporating limited look-ahead capabilities through recursive submatrix partitioning.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Manufacturing precision
If traditional tracking control methods are used, then the control system is simple, but servo-induced motion errors and tracking errors are not effectively minimized
Solution Approach 1:
The trajectory is segmented into multiple segments using B-spline basis functions with distinct knot vectors for different portions of the trajectory. This allows different control strategies to be applied to different segments, improving overall tracking accuracy while maintaining computational tractability through localized optimization.
Solution Approach 2:
The B-spline trajectory is pre-computed offline by optimizing control points to minimize tracking errors, considering system dynamics and constraints. This preliminary optimization reduces online computational burden while achieving high tracking accuracy, as the optimized trajectory can be executed with simple feedback control.
2Manufacturing precision
If filtered basis splines are used to minimize tracking errors, then tracking accuracy improves, but computational complexity increases
Solution Approach 1:
The trajectory optimization problem is divided into smaller sub-problems by segmenting the trajectory and using local knot vectors. This segmentation reduces the dimensionality of each optimization problem, making it computationally tractable while still achieving global optimization through coordinated control of all segments.
Solution Approach 2:
Instead of optimizing the entire trajectory at once, the method optimizes local segments iteratively. This partial action approach reduces computational burden at each step while converging to a globally optimized trajectory through repeated refinement of local segments.
3Manufacturing precision
If look-ahead capabilities are incorporated, then tracking performance improves, but data requirements and processing load increase
Solution Approach 1:
The look-ahead window is divided into smaller sub-segments for progressive optimization. This allows the controller to process trajectory data in manageable chunks rather than requiring all future data at once, reducing peak memory requirements while maintaining the benefits of look-ahead planning.
Solution Approach 2:
The method uses a limited look-ahead horizon rather than considering the entire remaining trajectory. This partial action approach provides sufficient predictive capability to improve tracking performance while keeping data requirements and computational load within practical limits.
Data Source
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AI summary
A method for minimizing tracking errors in dynamic systems including obtaining desired trajectory data of the dynamic system, obtaining a set of constraints on at least one of the desired and actual trajectories of the dynamic system, obtaining a set of uniform or non-uniform rational B-splines having known original B-spline basis functions but unknown B-spline coefficients, applying a trajectory optimization process to the desired trajectory data including applying forward filtering to B-spline basis functions and utilizing the original and filtered B-spline basis functions to select optimal coefficients of the B-splines, and outputting an optimal motion command signal in response to the trajectory optimization process to the dynamic system such that a resultant actual trajectory is substantially equal to the desired trajectory while satisfying the set of constraints on the at least one of the desired and actual trajectories.