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1. Decoupled Data-Based Approach for Learning to Control Nonlinear Dynamical Systems

   https://doi.org/10.1109/TAC.2021.3108552  

   Wang, Ran; Parunandi, Karthikeya Sharma; Yu, Dan; Kalathil, Dileep; Chakravorty, Suman (August 2021, IEEE Transactions on Automatic Control)

   This paper addresses the problem of learning the optimal control policy for a nonlinear stochastic dynam- ical. This problem is subject to the ‘curse of dimension- ality’ associated with the dynamic programming method. This paper proposes a novel decoupled data-based con- trol (D2C) algorithm that addresses this problem using a decoupled, ‘open-loop - closed-loop’, approach. First, an open-loop deterministic trajectory optimization problem is solved using a black-box simulation model of the dynamical system. Then, closed-loop control is developed around this open-loop trajectory by linearization of the dynamics about this nominal trajectory. By virtue of linearization, a linear quadratic regulator based algorithm can be used for this closed-loop control. We show that the performance of D2C algorithm is approximately optimal. Moreover, simulation performance suggests a significant reduction in training time compared to other state of the art algorithms. 

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2. A sEMG Proportional Control for the Gripper of Patient Side Manipulator in da Vinci Surgical System

   https://doi.org/10.1109/EMBC48229.2022.9871664  

   Yang, Kehan; Meier, Tess B.; Zhou, Haoying; Fischer, Gregory S.; Nycz, Christopher J. (July 2022, 2022 44th Annual International Conference of the IEEE Engineering in Medicine & Biology Society)

   There is a large community of people with hand disabilities, and these disabilities can be a barrier to those looking to retain or pursue surgical careers. With the development of surgical robotics technologies, it may be possible to develop user interfaces to accommodate these individuals. This paper proposes a hand-free control method for the gripper of a patient side manipulator (PSM) in the da Vinci surgical system. Using electromyography (EMG) signals, a proportional control method was tested on its ability to grasp a pressure sensor. These preliminary results demonstrate that the user can reliably control the grasping motion of the da Vinci PSM using this system. There is a strong correlation between grasping force and normalized EMG signal (r= 0.874). Moreover, the gripper can generate a step grasping force output when feeding in a generated step signal. The results in this paper demonstrate the system integration of a research EMG system with the da Vinci surgical system and are a step towards developing accessible teleoperation systems for surgeons with disabilities. Hand-free control for remaining degrees of freedom in the PSM is under development using additional input from the motion capture system. 

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3. A Convex Optimization-based Dynamic Model Identification Package for the da Vinci Research Kit

   https://doi.org/10.1109/LRA.2019.2927947  

   Wang, Yan; Gondokaryono, Radian; Munawar, Adnan; Fischer, Gregory Scott (July 2019, IEEE Robotics and Automation Letters)

   The da Vinci Research Kit (dVRK) is a teleoperated surgical robotic system. For dynamic simulations and model-based control, the dynamic model of the dVRK is required. We present an open-source dynamic model identification package for the dVRK, capable of modeling the parallelograms, springs, counterweight, and tendon couplings, which are inherent to the dVRK. A convex optimization-based method is used to identify the dynamic parameters of the dVRK subject to physical consistency. Experimental results show the effectiveness of the modeling and the robustness of the package. Although this software package is originally developed for the dVRK, it is feasible to apply it on other similar robots. 

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4. An SDP Optimization Formulation for the Inverse Kinematics Problem

   https://doi.org/10.1109/CDC49753.2023.10384035  

   Wu, Liangting; Tron, Roberto (December 2023, IEEE International Conference on Decision and Control)

   Inverse kinematics (IK) is an important problem in robot control and motion planning; however, the nonlinearity of the map from joint angles to robot configurations makes the problem nonconvex. In this paper, we propose an inverse kinematics solver that works in the space of rotation matrices of the link reference frames rather than joint angles. To overcome the nonlinearity of the manifold of rotation matrices $$\mathbf{SO}(3)$$, we propose a semidefinite programming (SDP) relaxation of the kinematic constraints followed by a fixed-trace rank minimization via maximization of a convex function. Along the way, we show that the feasible set of an IK problem is exactly the intersection of a convex set and fixed-trace rank-1 matrices. Thanks to the use of matrices with fixed trace, our algorithm to obtain rank-1 solutions has guaranteed local convergence. Unlike some traditional solvers, our method does not require an initial guess, and can be applied to robots with closed kinematic chains without ad-hoc modifications such as splitting the kinematic chain. Compared to other work that performs SDP relaxation for IK problems, our formulation is simpler, and uses variables with smaller sizes. We validate our approach via simulations on a closed kinematic chain constituted by two robotic arms holding a box, comparing against a standard IK method. 

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5. Iterative Jacobian-Based Inverse Kinematics and Open-Loop Control of an MRI-Guided Magnetically-Actuated Steerable Catheter System

   https://doi.org/10.1109/TMECH.2017.2704526  

   Liu, Taoming; Jackson, Russell; Franson, Dominique; Lombard Poirot, Nate; Criss, Reinhardt Kam; Seiberlich, Nicole; Griswold, Mark A.; Cavusoglu, M. Cenk (May 2017, IEEE/ASME Transactions on Mechatronics)

   This paper presents an iterative Jacobian-based inverse kinematics method for an MRI-guided magnetically-actuated steerable intravascular catheter system. The catheter is directly actuated by magnetic torques generated on a set of current-carrying micro-coils embedded on the catheter tip, by the magnetic field of the magnetic resonance imaging (MRI) scanner. The Jacobian matrix relating changes of the currents through the coils to changes of the tip position is derived using a three dimensional kinematic model of the catheter deflection. The inverse kinematics is numerically computed by iteratively applying the inverse of the Jacobian matrix. The damped least square method is implemented to avoid numerical instability issues that exist during the computation of the inverse of the Jacobian matrix. The performance of the proposed inverse kinematics approach is validated using a prototype of the robotic catheter by comparing the actual trajectories of the catheter tip obtained via open-loop control with the desired trajectories. The results of reproducibility and accuracy evaluations demonstrate that the proposed Jacobian-based inverse kinematics method can be used to actuate the catheter in open-loop to successfully perform complex ablation trajectories required in atrial fibrillation ablation procedures. This study paves the way for effective and accurate closed-loop control of the robotic catheter with real-time feedback from MRI guidance in subsequent research. 

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