Control Space Reduction and Real-Time Accurate Modeling of Continuum Manipulators Using Ritz and Ritz-Galerkin Methods

To address the challenges with real-time accurate modeling of multi-segment continuum manipulators in the presence of significant external and body loads, we introduce a novel series solution for variable-curvature Cosserat rod static and Lagrangian dynamic method. By combining a modified Lagrange polynomial series solution, based on experimental observations, with Ritz and Ritz-Galerkin methods, the infinite modeling state space of a continuum manipulator is minimized to geometrical position of a handful of physical points (in our case two). As a result, a unified easy to implement vector formalism is proposed for the nonlinear impedance and configuration control. We showed that by considering the mechanical effects of highly elastic axial deformation, the model accuracy is increased up to 6%. The proposed model predicts experimental results with 6-8% (4-6 [mm]) mean error for the Ritz-Galerkin method in static cases and 16-20% (12-14 [mm]) mean error for the Ritz method in dynamic cases, in planar and general 3D motions. Comparing to five different models in the literature, our approximate solution is shown to be more accurate with the smallest possible number of modeling states and suitable for real-time modeling, observation and control applications

Operational Strategies for Continuum Manipulators

We introduce a novel, intuitive user interface for continuum manipulators through the use of various joystick mappings. This user interface allows for the effective use of continuum manipulators in the lab and in the field. A novel geometric approach is developed to produce a more intuitive understanding of continuum manipulator kinematics. Using this geometric approach we derive the first closed-form solution to the inverse kinematics problem for continuum robots. Using the derived inverse kinematics to convert from workspace coordinates to configuration space coordinates we develop a potential-field path planner for continuum manipulators

Arm Robot Manipulator Design and Control for Trajectory Tracking; a Review

Arm robot manipulator heavily applied in industries ranging from welding, pick-and-place, assembly, packaging, labeling, etc. Trajectory planning and tracking is the fundamental design of an arm robot manipulator. The trajectory is set and determined to satisfy a certain criterion effectively and optimally. Optimization of robot trajectory is necessary to ensure the good quality product and to save energy, and this optimization can be provided by the right modeling and design. This paper presents a review study of arm-robot manipulator design and control for trajectory tracking by investigating the modeling of an arm robot manipulator starting from kinematics, dynamics and the application of the more advanced methods. The idea of this paper comes from the popularity of inverse kinematics among students

Control Space Reduction and Real-Time Accurate Modeling of Continuum Manipulators Using Ritz and Ritz-Galerkin Methods

To address the challenges with real-time accurate modeling of multisegment continuum manipulators in the presence of significant external and body loads, we introduce a novel series solution for variable-curvature Cosserat rod static and Lagrangian dynamic methods. By combining a modified Lagrange polynomial series solution, based on experimental observations, with Ritz and Ritz-Galerkin methods, the infinite modeling state space of a continuum manipulator is minimized to geometrical position of a handful of physical points (in our case two). As a result, a unified easy to implement vector formalism is proposed for the nonlinear impedance and configuration control. We showed that by considering the mechanical effects of highly elastic axial deformation, the model accuracy is increased up to 6%. The proposed model predicts experimental results with 6%-8% (4-6 mm) mean error for the Ritz-Galerkin method in static cases and 16%-20% (12-14 mm) mean error for the Ritz method in dynamic cases, in planar and general three-dimensional motions. Comparing to five different models in the literature, our approximate solution is shown to be more accurate with the smallest possible number of modeling states and suitable for real-time modeling, observation, and control applications

Dynamic Active Constraints for Surgical Robots using Vector Field Inequalities

Robotic assistance allows surgeons to perform dexterous and tremor-free procedures, but robotic aid is still underrepresented in procedures with constrained workspaces, such as deep brain neurosurgery and endonasal surgery. In these procedures, surgeons have restricted vision to areas near the surgical tooltips, which increases the risk of unexpected collisions between the shafts of the instruments and their surroundings. In this work, our vector-field-inequalities method is extended to provide dynamic active-constraints to any number of robots and moving objects sharing the same workspace. The method is evaluated with experiments and simulations in which robot tools have to avoid collisions autonomously and in real-time, in a constrained endonasal surgical environment. Simulations show that with our method the combined trajectory error of two robotic systems is optimal. Experiments using a real robotic system show that the method can autonomously prevent collisions between the moving robots themselves and between the robots and the environment. Moreover, the framework is also successfully verified under teleoperation with tool-tissue interactions.Comment: Accepted on T-RO 2019, 19 Page