A Concurrent Framework for Constrained Inverse Kinematics of Minimally Invasive Surgical Robots.

Minimally invasive surgery has undergone significant advancements in recent years, transforming various surgical procedures by minimizing patient trauma, postoperative pain, and recovery time. However, the use of robotic systems in minimally invasive surgery introduces significant challenges related to the control of the robot's motion and the accuracy of its movements. In particular, the inverse kinematics (IK) problem is critical for robot-assisted minimally invasive surgery (RMIS), where satisfying the remote center of motion (RCM) constraint is essential to prevent tissue damage at the incision point. Several IK strategies have been proposed for RMIS, including classical inverse Jacobian IK and optimization-based approaches. However, these methods have limitations and perform differently depending on the kinematic configuration. To address these challenges, we propose a novel concurrent IK framework that combines the strengths of both approaches and explicitly incorporates RCM constraints and joint limits into the optimization process. In this paper, we present the design and implementation of concurrent inverse kinematics solvers, as well as experimental validation in both simulation and real-world scenarios. Concurrent IK solvers outperform single-method solvers, achieving a 100% solve rate and reducing the IK solving time by up to 85% for an endoscope positioning task and 37% for a tool pose control task. In particular, the combination of an iterative inverse Jacobian method with a hierarchical quadratic programming method showed the highest average solve rate and lowest computation time in real-world experiments. Our results demonstrate that concurrent IK solving provides a novel and effective solution to the constrained IK problem in RMIS applications.

Creating Better Collision-Free Trajectory for Robot Motion Planning by Linearly Constrained Quadratic Programming.

Many algorithms in probabilistic sampling-based motion planning have been proposed to create a path for a robot in an environment with obstacles. Due to the randomness of sampling, they can efficiently compute the collision-free paths made of segments lying in the configuration space with probabilistic completeness. However, this property also makes the trajectories have some unnecessary redundant or jerky motions, which need to be optimized. For most robotics applications, the trajectories should be short, smooth and keep away from obstacles. This paper proposes a new trajectory optimization technique which transforms a polygon collision-free path into a smooth path, and can deal with trajectories which contain various task constraints. The technique removes redundant motions by quadratic programming in the parameter space of trajectory, and converts collision avoidance conditions to linear constraints to ensure absolute safety of trajectories. Furthermore, the technique uses a projection operator to realize the optimization of trajectories which are subject to some hard kinematic constraints, like keeping a glass of water upright or coordinating operation with dual robots. The experimental results proved the feasibility and effectiveness of the proposed method, when it is compared with other trajectory optimization methods.