90 Figure 4.19: Shape control of a heterogeneous deformable object: (a) shape control using a position-based control approach, (b) shape control using the proposed controller. 170 Figure 6.22: Comparison between a simulation without feedback control (first column), a simulation with feedback control (second column) and an experimental trial with bovine liver (third column).
INTRODUCTION
- Introduction
- Dissertation Contributions
- Review of Deformable Object Modeling
- Mass-Spring Systems
- Finite Element Method
- Finite Difference Method
- Boundary Element Method
- Finite Volume Method
- Organization of the Dissertation
- Publications from the Dissertation
- Summary
A positional-based proportional-integral (PI) controller was developed to control the movement of the robot fingers. In Chapter II, the motivation and goals of the shape control task of a deformable object are discussed.
AUTONOMOUS SHAPE CONTROL OF A DEFORMABLE OBJECT16
Issues and Prior Research
- Automated Handling Systems
- Modeling and Simulation of Deformable Objects
- Robotic Interaction Control with Deformable Objects
- Interaction under Combined Vision and Tactile Sensing
- Shape Morphing in Computer Graphics Applications
- Review of End-effectors for Deformable Objects
- Review of Objects’ Shape Description and Representation
In our work, we model a deformable object with a physics-based mass-spring-damper system to represent the shape of the object. In our work, it is possible to control the shape of a deformable object while simultaneously manipulating the object.
Modeling of System Dynamics
- Deformable Object Dynamics Based on Rheological Model
- Manipulators Dynamics
- Coupled Dynamics of Multiple Manipulators and a Deformable Object
We also define p02 is the position vector of the origin of the coordinate system of the object. The dynamics of the first set of mass points is written by replacing z with p as
Summary
Equation (2.8) can be used to design the control law for the manipulators and Equation (2.6) can be integrated to find the position of the internal mass points and the boundary mass points that are not interacted by the manipulators. The movements of these mass points are affected by the reaction forces generated as a result of the interaction.
SHAPE CONTROL BY OPTIMIZATION-BASED PLANNING
Introduction
Therefore, we introduce robustness into the shape change controller that can operate in the presence of model uncertainty. The chapter is structured as follows: A mathematical description of the problem is given in section 3.2.
Mathematical Description of the Problem
The total object shape error is defined as the sum of the shape error at each actuation point, expressed as . Note that the above definition of shape error assumes a discrepancy in each contact point location between the initial shape and the final desired shape.
Design of the Shape Controller
- Optimization-Based Control Approach
- Robustness Analysis
Therefore, we obtain the desired x and y coordinates on the desired curve by entering the i values into the parametric representation of the ellipse. The additional control term, Δv, is used to overcome the potentially destabilizing effect of modeling uncertainty (~e,t).
Simulation and Discussion
The initial, desired, and final shapes of the deformable object when controlling the shape from circle to ellipse and from circle to square are shown in Figures 3.5 and 3.6. The time responses of the root-mean-square shape error at the actuation points when controlling the shape from circle to ellipse and from circle to square with 36 contact points are shown in Figures 3.12(a) and 3.13(a).
Summary
A suitable controller will need to be introduced for stability of the needle tip on the desired target. The positioning of the needle tip at the desired target location is shown in Figure 6.18 (black line).
SHAPE CONTROL BY ESTIMATION-BASED PLANNING
Introduction
The remainder of this chapter is organized as follows: we repeat the mathematical description of the problem for completeness in Section 4.2. A shape Jacobian containing the local shape information for the desired object is formulated in section 4.3.
Mathematical Description of the Problem
It makes sense to pose the above problem of controlling the shape of a deformable object by controlling its boundary. So the problem becomes: given the desired shape and the current shape of the plane object, and given the number of activation points, find a control action such that
Shape Representation and Shape Jacobian
- Shape Representation
- Shape Jacobian
It is necessary to map the movement of contact points located on the border. The shape Jacobian contains information about the end effectors and curve features that describe the desired shape of the object.
Design of the Shape Controller
- Estimation-Based Control Approach
- Robustness Analysis
Therefore, all manipulators in the system follow the movement of the object to reach the desired end locations according to the following control law. In our current case it is zero, because we assume that the final shape of the desired curve is constant in the given time.
Simulation Results
The initial, desired, and final shapes of the deformable object when the shape is controlled from the circle to the ellipse and from the circle to the square are shown in Figures 4.4 and 4.5 for all four cases. The time responses of the root mean square shape error at the actuation points when controlling shape from circle to ellipse and from circle to square with 36 contact points are shown in Figures 4.12(a) and 4.13(a).
Advantages and Limitations
In the first scenario, we use a geometry-based shortest distance method to find the reference contact locations of the contact points in the desired shape of the object, and then perform the task of changing the shape using an action DP control. The final object shape obtained based on our proposed method is shown in Figure 4.19(b).
Summary
The needle emerges from a hole in the robot's face plate, as shown in Figure 6.7. We have also developed a robust controller that works in the presence of model uncertainty of the needle curvature.
TARGET POINT MANIPULATION INSIDE A DEFORMABLE
Introduction
To control the position of the internal target point in a deformable object, suitable contact points on the surface of the object are required. Thus, we present a new passivity-based non-collocated controller for the robotic fingers to ensure safe and precise positional control of the internal target point.
Issues and Prior Research
Cutkosky [106] discussed that the size and shape of the object have less influence on the choice of grasp than on the tasks to be performed after examining a variety of human grasps. Anderson and Spong [111] published the first solid result by passivating the system using scattering theory.
Mathematical Description of the Problem
In our current case, we assume that the number of positioned points is one, since we are trying to control the position of the target. So we need to control the position of the target by applying only unidirectional pressure.
Deformable Object Modeling
Problem Statement: Given the number of activation points, the initial target and the desired locations, you need to find suitable contact locations and arrange the action so that the aiming point is positioned at the desired location by checking the boundary points of the object with minimal force. To formulate the optimal contact locations, we model the deformable object using discrete networks of mass-spring-damper systems.
Framework for Optimal Contact Locations
A physically feasible grip configuration can be achieved if the surface normals at three contact points positively span the plane so that they do not all lie in the same half-plane [117]. Therefore, a feasible capture can be achieved if the pairwise angles satisfy the following constraints.
Design of the Controller
- Target Position Control
- Passivity-Based Control
The desired target velocity along the direction of drive of the i-th robot finger is given by. The trajectory generator essentially calculates the desired target velocity along the direction of propulsion of the robot fingers.
Simulation and Discussion
The robot finger forces generated by the PI controller are shown in Figure 5.11 and the POs fall to negative as shown in Figure 5.12. The POs become positive during the interaction between the robot fingers and the object, as shown in Figure 5.18.
Summary
We present the robust controller, which will work robustly in the presence of needle modeling uncertainty. The curvature of the needle path is obtained by fitting a circle through the data points.
ROBOT-ASSISTED FLEXIBLE NEEDLE INSERTION
Introduction
A thinner needle diameter results in less tissue damage and reduces the potential for postdural puncture headache (PDPH) in spinal anesthesia [130]. Section 6.3 presents a brief overview of the steerable needle and its kinematic model for completeness.
Issues and Prior Research
Thus, the targeting procedure is complicated by the bending of the needle shaft and the target displacement due to the tissue deformation. Tip-based steering can be achieved by using either a pre-bent tip [150] or a bevel to create asymmetric forces that bend the needle during insertion.
Review of Bevel Steering Kinematic Model
Axial rotation of the needle rotates the tip frame around its own z-axis and redirects the plane in which the needle travels. Let q be the vector of six generalized coordinates needed to determine the kinematics of the needle.
Controllability Analysis
To verify the controllability at a point, we consider the linear approximation of the system (6.7) at an equilibrium point while the input is equal to zero. To test the controllability of the above non-linear system we make use of the Lie algebra rank condition.
Problem Formulation
By making use of the fact that can be modified by the control input u2, it can be shown that the system is locally and also globally controllable as long as it avoids the singularity condition. Problem (Accessing a Target): Given a feasible target point pd3 located within a deformable tissue, design a feedback controller u such that the needle tip can be positioned to the desired target location from any feasible access point.
Coordinate Transformation and Feedback Control
Now the goal is to find a control law such that the error between the actual needle tip and the desired target, eppd, converges to zero along a feasible path when the base of the needle is driven. Our control goal is to design an appropriate state feedback controller so that the point of the.
Continuous-Discrete Extended Kalman Filter (EKF)
Therefore, we develop an estimator to estimate full states from the measured data that can work in the presence of measurement noise and process noise. The continuous-discrete extended Kalman filter differs from the more traditional linear class of Kalman filters in many respects, but the main difference lies in the inability to prove the stability of the nonlinear filtering process.
Robustness Analysis
The performance of the control action can be improved if we include the deformable tissue model, the properties of the needle and their interaction during the input to the control law [176]. The additional control term, Δv, is used to overcome the destabilizing effect of the modeling uncertainty (~e).
Experimental Testbed
- Magnetically Tracked Needle
- Robotic Actuation Unit
- Phantom Material
- System Architecture
The translational motion of the entire carriage, shown in Figure 6.6, is driven by a spindle in the lower right corner. Also shown are the center support shaft and the linear bearing that slides on it, and the two linear guides that support the lower corners of the carriage.
Results and Discussions
- Curvature Obtained from Experimental Data and Validation with Model
- Numerical Simulation Results
- Experimental Results
Experimental data of the needle path as it cuts through the tissue is shown in Figure 6.10 for the case shown in Figure 6.9(a). The needle tip has been successfully positioned at the desired target location, as shown in Figure 6.18 (blue line).
Summary
CONCLUSION AND FUTURE DIRECTIONS
Shape Control of Deformable Object
Two different planning approaches were investigated to find desired contact points on the final shape of the deformable object. Therefore, the movements of the manipulators were controlled using a proportional-derivative controller as the initial object was deformed to its desired shape.
Control of an Internal Target Point of a Deformable Object
Motivated by the work presented in [179] and the references therein, we investigate how many actuation points and their locations are required to efficiently accomplish the desired shape change task.
Control of a Flexible Bevel-Tip Steerable Needle
A port is passive if the sign of the product is positive (ie, f.v0), which means that power is flowing into the grid system. A port is active if the sign is negative (ie, f.v0), which means power is flowing from the grid system.
