Redundant Manipulator Null-Space Control Near Joint Limits
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Solution Overview
Problem
Current surgical robotic systems face limitations in range of motion and dexterity due to joint configurations that become poorly conditioned near minimally invasive apertures, leading to reduced maneuverability and increased complexity in setup and operation.
Innovation Solution
A robotic manipulator arm system with redundant degrees of freedom, utilizing a processor to calculate joint movements within a null-space of the Jacobian, allowing for increased range of motion and improved dexterity by defining position-based constraints and facilitating movements within the null-space to avoid joint limits and collisions.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If the manipulator arm uses a standard joint configuration to position the end effector, then the end effector can reach the desired position, but the joint configurations become poorly conditioned near minimally invasive apertures, reducing range of motion and dexterity
Solution Approach 1:
The patent introduces a null-space dimension to the joint configuration space. By adding redundant degrees of freedom (7 DOF instead of 6), the system creates an additional dimension that allows joints to move along null-space trajectories while maintaining the end effector at the desired position. This extra dimension enables the manipulator to avoid poorly conditioned configurations near apertures while preserving positioning accuracy.
Solution Approach 2:
The patent changes the parameter space by transitioning from a 6-DOF to a 7-DOF configuration. This parameter change allows the system to explore additional configuration space through null-space movements, transforming the joint state parameters while keeping the end effector position constant. The null-space parameter α enables continuous adjustment of joint configurations without affecting end effector positioning.
2Adaptability or versatility
If the manipulator arm is designed with redundant degrees of freedom to improve range of motion, then dexterity increases, but the system complexity and computational requirements increase
Solution Approach 1:
The patent replaces complex mechanical constraint mechanisms with a computational null-space approach. Instead of using mechanical stops, guides, or physical constraints to manage redundant DOF, the system uses software-based null-space projections and Jacobian calculations to control joint movements. This substitution reduces mechanical complexity while maintaining adaptability.
Solution Approach 2:
The redundant degree of freedom serves multiple functions simultaneously: it provides collision avoidance, improves dexterity, enables null-space movements, and maintains end effector positioning. The single additional joint acts as a self-servicing element that benefits the system in multiple ways without requiring separate mechanisms for each function.
3Ease of operation
If the manipulator arm operates near joint limits to access edges of Cartesian-coordinate space, then range of motion is maximized, but the joints become poorly conditioned, reducing maneuverability
Solution Approach 1:
The patent uses preliminary null-space movements to reposition joints into well-conditioned configurations before executing end effector movements that would otherwise require operating near joint limits. The system proactively adjusts joint configurations through null-space trajectories to prevent poor conditioning, rather than reacting after the problem occurs.
Solution Approach 2:
The null-space acts as an intermediary between the end effector position command and the joint configurations. Instead of directly commanding joints to positions that may be poorly conditioned, the system uses null-space projections as an intermediate step to find equivalent configurations that are well-conditioned and maintain the desired end effector position.
4Measurement precision
If the system uses traditional Jacobian-based control for end effector movement, then positioning accuracy is maintained, but the manipulator cannot utilize null-space movements for collision avoidance or improved dexterity
Solution Approach 1:
The patent segments the joint velocity command into two independent components: a null-perpendicular component that ensures accurate end effector positioning, and a null-space component that enables collision avoidance and improved dexterity. This segmentation allows each component to be optimized independently while combining to achieve both positioning accuracy and enhanced maneuverability.
Solution Approach 2:
The patent merges traditional Jacobian-based control with null-space control into a unified control framework. By combining the null-perpendicular Jacobian (for positioning accuracy) with the null-space Jacobian (for maneuverability), the system achieves both end effector positioning precision and the ability to perform collision avoidance and dexterity-enhancing movements simultaneously.
Data Source
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Figure 1B
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AI summary
Devices, systems, and methods for providing increased range of movement of the end effector of a manipulator arm having a plurality of joints with redundant degrees of freedom. Methods include defining a position-based constraint within a joint space defined by the at least one joint, determining a movement of the joints along the constraint within a null-space and driving the joints according to a calculated movement to effect the commanded movement while providing an increased end effector range of movement, particularly as one or more joints approach a respective joint limit within the joint space.