Robot Arm Positioning with Polar Coordinates and Redundancy Limits
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Solution Overview
Problem
Conventional methods for determining possible positions of a robot arm are inefficient in accounting for platform-specific kinematic redundancies and boundary conditions, limiting precise placement within a robot cell.
Innovation Solution
A method that defines target positions and orientations for a robot arm's tool center point in polar coordinates, determining possible positions of the robot arm's frame by intersecting geometric constraints with boundary conditions, using a mobile carrier device with omnidirectional wheels to freely move and position the arm within a robot cell.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional methods are used to determine robot arm positions, then the calculation process is simpler, but the ability to account for platform-specific kinematic redundancies and boundary conditions is insufficient
Solution Approach 1:
The patent transforms the problem from Cartesian coordinates to spherical coordinates, changing the parameter system to naturally accommodate the mobile platform's kinematic redundancies. This coordinate transformation allows the method to handle boundary conditions and platform movements more effectively while maintaining computational feasibility.
Solution Approach 2:
The patent introduces a new dimensional approach by using spherical coordinates (radial distance, polar angle, azimuthal angle) instead of traditional 3D Cartesian coordinates. This dimensional change enables the method to separately handle the mobile platform's position and orientation, thereby resolving kinematic redundancy issues.
2Adaptability or versatility
If the robot arm is constrained to fixed positions, then the positioning is more stable, but the operational flexibility is reduced
Solution Approach 1:
The patent makes the robot arm's base mobile rather than fixed, allowing the carrier vehicle to move freely within the workspace. This dynamic base position, combined with spherical coordinate representation, enables the system to adapt to different operational scenarios while maintaining positioning stability through the mathematical framework.
Solution Approach 2:
The patent creates a universal positioning method that works for both fixed and mobile bases. The spherical coordinate system and boundary condition approach can handle various base configurations, making the method universally applicable to different robot arm setups while maintaining operational flexibility.
Data Source
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AI summary
The method involves fixing a target position and a target orientation in a space of tool center points (8) assigned to robotic arms (7) or an end effector fastened at the robotic arms. A reference coordinate system (K-Ref) is assigned with polar coordinates. Potential positions of frames (9) of the robotic arms are determined in the space and in the polar coordinates of the reference coordinate system based on geometry of the robotic arms so that the tool center points set the fixed target position and the target orientation.