Surgical Robot Inverse Kinematics Under Joint Motion Limits
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Solution Overview
Problem
Robotic systems for minimally-invasive surgery face challenges in converting user commands into precise joint motions due to physical constraints such as joint position, velocity, and acceleration limits, which can lead to sub-optimal or unachievable solutions during teleoperation.
Innovation Solution
The implementation of iterative inverse kinematics that decouples linear and angular motion solutions, handles all limits in a single solution, and uses a bounded Gauss-Seidel solver with successive-over-relaxation to clamp intermediate solutions to hardware limits, ensuring accurate and controlled motion of surgical robotic systems.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If an exact inverse kinematic solution is computed without considering hardware limits, then mathematical accuracy is improved, but the solution becomes unachievable when joint position, velocity, or acceleration limits are violated
Solution Approach 1:
The patent applies preliminary action by incorporating hardware limits (joint position, velocity, and acceleration bounds) into the inverse kinematic formulation before solving. The Gauss-Seidel iterative solver uses these pre-defined limits to guide the solution process, ensuring that the computed joint commands remain within achievable ranges while still accurately tracking the desired end-effector motion.
2Reliability
If hardware limits are strictly enforced in the inverse kinematic solution, then solution achievability is improved, but motion accuracy deteriorates when limits are reached
Solution Approach 1:
The patent applies dynamics by using an iterative Gauss-Seidel solver that dynamically adjusts joint commands based on current state and limit constraints. The successive over-relaxation technique allows the solution to adaptively balance between achieving the desired motion and respecting hardware limits, maintaining accuracy wherever possible while ensuring achievability.
Solution Approach 2:
The iterative nature of the Gauss-Seidel solver provides continuous feedback between the desired motion and hardware constraints. Each iteration refines the joint commands by comparing the current solution against the limits and adjusting accordingly, allowing the system to recover accuracy while remaining within achievable bounds.
3Device complexity
If a simple inverse kinematic solver is used, then computational complexity is reduced, but the ability to handle multiple simultaneous limits deteriorates
Solution Approach 1:
The patent applies segmentation by breaking down the complex inverse kinematic problem with multiple simultaneous limits into manageable iterative steps. The Gauss-Seidel solver processes each joint and its associated limits in sequence during each iteration, making the complex multi-constraint problem tractable while maintaining comprehensive limit handling capability.
Data Source
AI summary
Various approaches to solve for inverse kinematics may be used for teleoperation of a surgical robotic system. In one approach, an iterative solver solves for the linear component of motion independently from solving for the angular component of motion. One solver may be used to solve for both together. In another approach, all limits (e.g., position, velocity, and acceleration) are handled in one solution. Where a limit is reached, the limit is used as a bound in the intermediate solution, allowing solution even where a bound is reached. In another approach, a ratio of limits of position are used to create a slow-down region near the bounds to more naturally control motion. In yet another approach, the medical-based teleoperation uses a bounded Gauss-Siedel solver, such as with successive-over-relaxation.