Robot Path Planning for 2D Drawing on Non-Planar 3D Surfaces
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Solution Overview
Problem
Existing robot drawing systems are limited to planar surfaces and face challenges in mapping 2D drawing paths to 3D surfaces without distortion, and navigating large non-planar canvases due to manipulator reach limitations, requiring mobile platforms that complicate navigation planning.
Innovation Solution
A method and apparatus for generating a robot path by identifying a drawing pose set, projecting surface points onto an xy-plane, determining coverage and bounding circles, and creating a translation path using a manipulator and mobile platform to draw 2D images on non-planar 3D surfaces with minimal distortion.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Area of stationary object
If a manipulator is used to draw on a large non-planar surface, then the drawing area is increased, but the reach distance limitation restricts the canvas size
Solution Approach 1:
The robot system is divided into two functional components: a mobile platform that handles navigation and positioning, and a manipulator that handles drawing operations. This segmentation allows the mobile platform to move to different locations on large canvases while the manipulator maintains its drawing capability within its reach distance, effectively overcoming the reach limitation.
Solution Approach 2:
The system transitions from a fixed-base manipulator operating in 3D space to a mobile platform-based system that adds temporal dimension to the drawing process. The mobile platform moves the manipulator to different positions on the canvas over time, enabling coverage of large non-planar surfaces that would be inaccessible to a fixed manipulator.
2Area of stationary object
If a mobile platform is added to extend reach, then the drawing area is increased, but navigation planning complexity increases
Solution Approach 1:
The system performs preliminary actions by pre-computing the mapping between 2D drawing paths and 3D surface coordinates, and pre-planning the mobile platform's navigation path based on the target canvas geometry. This preliminary preparation simplifies the real-time control complexity during actual drawing operations.
Solution Approach 2:
A path planning module serves as an intermediary between the high-level drawing commands and the low-level mobile platform control. This intermediary component translates drawing requirements into navigation paths, managing the complexity of coordinating mobile platform movement with manipulator drawing actions.
3Adaptability or versatility
If 2D drawing path is mapped to 3D surface, then drawing on non-planar surfaces is enabled, but distortion occurs in the drawn image
Solution Approach 1:
The system transforms the drawing problem by changing the parameter space from direct 3D surface coordinates to a 2D parametric domain that represents the surface geometry. By working in this transformed parameter space and applying appropriate mapping transformations, the system enables drawing on various surface types while minimizing distortion through mathematical correction.
Solution Approach 2:
The system creates a parametric model (copy) of the target 3D surface geometry, which serves as an intermediate representation. The 2D drawing path is first mapped to this parametric model, and then transferred to the actual 3D surface. This copying approach allows for distortion analysis and correction in the virtual parametric space before physical execution.
Data Source
AI summary
A method of generating a robot path is provided. The method includes identifying a drawing pose set for a manipulator included in a robot in order to draw a two-dimensional (2D) image on a three-dimensional (3D) target surface, setting a profile curve by projecting surface points of the 3D target surface onto an xy-plane, determining coverage circles of the manipulator that are capable of covering all surface points of the profile curve, deriving bounding circles for a mobile platform of the robot mounting the manipulator, corresponding to each of the determined coverage circles, and generating a translation path of the robot for drawing the 2D image on the 3D target surface based on the derived bounding circles.