Robot Pose Trajectory Generalization for Changeable Path Points
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Solution Overview
Problem
Existing robot trajectory learning methods fail to account for geometric constraints of attitude quaternions, leading to low precision in probability modeling and inability to simultaneously generate high-precision robot position and attitude trajectories, limiting adaptability to changing operation scenes.
Innovation Solution
A method combining Gaussian mixture regression, variational Bayesian methods, and attitude quaternion tangent space mapping to construct precise robot pose trajectories, aligning time steps with multi-dimensional dynamic time warping, and optimizing kernelized representation for flexible adaptation to operation path points.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If traditional Gaussian mixture model is used for trajectory learning, then the modeling process is simple, but the precision of probability modeling is low due to ignoring geometric constraints of attitude quaternion
Solution Approach 1:
The patent introduces an intermediary transformation process: attitude quaternions are first mapped to tangent space (an intermediate Euclidean space), where Gaussian mixture modeling is performed, and then the results are transformed back to quaternion space. This intermediary step allows the use of simple Gaussian models while respecting the geometric constraints of quaternions, thereby improving modeling precision without excessive complexity increase.
Solution Approach 2:
The patent changes the parameter space from direct quaternion representation to tangent space representation. By transforming the attitude quaternion parameters into tangent space coordinates, the model can apply standard Gaussian mixture models while implicitly preserving quaternion geometric constraints through the transformation, thus improving precision.
2Productivity
If existing trajectory learning methods are used, then position trajectories can be generated, but the ability to simultaneously generate high-precision robot attitude trajectories is lacking
Solution Approach 1:
The patent segments the pose trajectory into two independent components: position trajectory and attitude trajectory. Each component is modeled separately using Gaussian mixture models - position in Euclidean space and attitude in quaternion tangent space. This segmentation allows both components to be optimized independently for their respective precision requirements while maintaining overall efficiency.
Solution Approach 2:
The patent adds a dimensional transformation layer for attitude representation. Instead of working directly in 4D quaternion space, it maps to a 3D tangent space at each operating point, allowing standard 3D Gaussian models to be applied. This dimensional change enables precise attitude modeling while maintaining computational efficiency.
3Manufacturing precision
If teaching programming is used to ensure high precision completion of tasks, then programming accuracy is improved, but deployment time increases and programming efficiency decreases
Solution Approach 1:
The patent performs preliminary action by pre-computing the Gaussian mixture model parameters (means, covariances, mixing coefficients) from teaching data during an offline training phase. Once the model is trained, generating new trajectories for different operation scenes requires only evaluating the pre-computed model, which is computationally efficient. This separates the time-consuming modeling work from the time-critical trajectory generation task.
Solution Approach 2:
The patent creates a mathematical model (Gaussian mixture model) that copies and generalizes the essential characteristics of taught trajectories. Instead of storing and replaying exact teaching data, the model captures the probabilistic structure of motion patterns, allowing efficient generation of new trajectories that maintain the precision characteristics of the original teachings while adapting to new scenarios.
4Reliability
If robots are programmed for fixed operation scenes to ensure task completion, then task execution reliability is improved, but adaptability to changing operation scenes deteriorates
Solution Approach 1:
The patent introduces dynamics into the trajectory generation system by making the Gaussian mixture model adaptive to different operation scenes. The model can be retrained or adjusted when operation scenes change, allowing the robot to maintain reliable task execution across varying conditions. The probabilistic nature of the model naturally accommodates variations in operation scenarios.
Solution Approach 2:
The patent creates a universal trajectory generation framework based on Gaussian mixture models that can handle multiple operation scenes and task types. By learning the probabilistic structure of motion from teaching data, the single model serves multiple functions - generating trajectories for different operation paths, adapting to scene changes, and maintaining task execution reliability across diverse scenarios.
Data Source
AI summary
Provided is a generalization generation method of industrial robot pose trajectories supporting changeable operation path points, which relates to the field of robot trajectory planning. The method includes: acquiring a plurality of groups of robot end pose trajectories; aligning time steps of the pose trajectories via a multi-dimensional dynamic time warping algorithm; constructing a Gaussian mixture model of robot pose trajectories in combination with a variational Bayesian method and an attitude quaternion tangent space mapping method; calculating reference pose trajectory distribution via a Gaussian mixture regression method; performing kernelized representation on pose trajectory distribution, and solving an optimal hyperparameter of a kernel function by minimizing a root mean square error of a reproduced reference trajectory; and generating the robot end pose trajectories adapted to the operation path points by updating the reference pose trajectory distribution.