Trajectory Time Scaling for Redundant Actuator Constraint Satisfaction
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Solution Overview
Problem
Conventional methods for controlling processing machines with redundant actuators, such as laser processing machines, often fail to guarantee a priori satisfaction of constraints during various patterns, leading to inefficiencies and potential violations of actuator limitations.
Innovation Solution
A method that modifies the time domain of the reference trajectory in real-time, ensuring feasibility by expanding time units between points while preserving the spatial pattern, using sequential processing and invariant sets tailored to different operation modes to satisfy actuator constraints, thereby ensuring optimal trajectory tracking without violating future constraints.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of operation
If frequency separation techniques are used to assign positioning tasks to two actuators, then the positioning task can be distributed between actuators, but the method does not consider actuator constraints such as acceleration or velocity limits and does not guarantee optimal reference trajectories
Solution Approach 1:
The patent transforms the reference trajectory from the spatial domain to the time domain by modifying time parameters. It expands time units between trajectory points and adjusts timing parameters to ensure actuator constraints are satisfied while maintaining the spatial processing pattern. This parameter transformation resolves the contradiction by making the trajectory feasible for the actuators without changing the processing quality.
2Productivity
If Model Predictive Control is used to generate reference trajectories accounting for constraints, then future events can be anticipated and control actions can be optimized, but the receding horizon approach has no guarantee of finding a solution to the optimization problem
Solution Approach 1:
The patent performs preliminary actions by transforming the reference trajectory in the time domain before execution. It expands time units between trajectory points and verifies constraint satisfaction in advance, ensuring that a feasible solution exists before the receding horizon optimization begins. This preliminary time-domain modification guarantees that the MPC will find a solution.
Solution Approach 2:
The patent applies preliminary anti-action by pre-modifying the reference trajectory to prevent future constraint violations. By expanding time units and adjusting timing parameters before optimization, it anticipates and counteracts potential infeasibility issues that would otherwise cause the MPC to fail in finding a solution.
3Reliability
If an initial feasible reference trajectory with terminal equality constraint is used, then the MPC-generated trajectory can be made to coincide with the reference trajectory at the end of each data window, but the loss of performance is significant and a long horizon is required resulting in significant computational complexity
Solution Approach 1:
The patent changes time parameters by expanding time units between trajectory points and modifying the timing structure of the reference trajectory. This parameter transformation allows the system to achieve trajectory coincidence with reduced performance loss and lower computational complexity by working with a longer time horizon that naturally accommodates actuator dynamics.
Data Source
AI summary
An operation of a processing machine with redundant actuators is controlled according to a reference trajectory by selecting, from a set of points forming a segment of the reference trajectory to be processed for a period of time, a subset of points corresponding to a fraction of the period of time. The subset of points is selected such that the redundant actuators are capable to position the worktool at each point in the subset within the period of time and are capable to maintain the worktool at the last point of the subset after the period of time while satisfying constraints on motion of the redundant actuators. The constraints on motion are selected based on the mode of operation of the processing machine. The segment of the reference trajectory is modified in the time domain and the control inputs for controlling the motion of the redundant actuators are determined using the modified segment of the reference trajectory.