The Fast Calibration Algorithm And Kinematic-free Control Method For A Novel Deformable Manipulator

Coexisting,Cooperative,Cognitive Robots(Tri-Co Robots)would be the breakthrough technology that bring great influence to the world and would be the enabling technology for the next generation of robotics.As the typical representation of Tri-co Robots,service robots work in unstructured environment with challenges of complex dynamic environment and various tasks.Moreover,service robots have to share space with humans and interact with humans.Therefore,dexterous manipulation and safe interaction are the inherent properties for service robots.It is hard for traditional rigid-link manipulators to meet the requirements of Tri-co Robots due to their rigid links,which would result in fixed workspace and cause damage to the environment and humans.Nowadays,a growing body of work is focused on the soft/continuum manipulators,which offer a number of potential advantages in dexterous manipulation and safe interaction.However,soft/continuum manipulators also have some inherent drawbacks.For instance,they have weaker payload bearing capacity and they are difficult to control.To meet the requirements of dexterous manipulation and safe interaction,we introduce a novel deformable manipulator by combing the rigid and soft mechanism.The rigid link of the manipulator is replaced by a deformable link,which is a series of passive spherical joints connected with each other,with the preload force between socketball surfaces.On one hand,the deformable manipulator can obtain more dexterous workspace by bending its deformable links according to different tasks.On the other hand,it can bear heavier payload than soft manipulator by choosing a proper preload force.We present a static force-based model for the deformable link and use it to predict the load bearing capacity of the deformable link in this dissertation.To address the kinematic control problem with unknown parameters led by bending operations,we propose a fast calibration algorithm and a kinematic-free control framework in this dissertation.The main contributions are summarized as follows:Firstly,a novel deformable manipulator,which is composed of four active joints and two deformable links,is introduced in this dissertation.Moreover,we present a static force-based model for the deformable link and develop a parameter estimation method to estimate the model parameters.Based on this model,we can accurately predict the payload bearing capacity of the deformable link.This job lays a foundation for the fast calibration algorithm and the kinematic-free control method.Secondly,for any revolute joint,the locus of end-effector rotating around this joint axis is a circle lying in a plane,called the plane-of rotation.By using this property,we propose a fast calibration algorithm based on the circular motion of the end-effector.Our method can obtain the kinematic parameter only by measuring the pose of the endeffector.Thus,our method is practical,fast and easy to be applied to a class of serial manipulators with any Degrees-of-Freedoms(DoFs)or any configurations.Thirdly,we propose a kinematic-free control framework based on visual feedback.The key idea of our framework is to estimate the Jacobian matrix between the input and output directly by observing each actuator's effects on the robot's end-effector.Moreover,the estimated Jacobian is evaluated in real time according to visual feedback.Based on the kinematic-free control framework,we propose a hybrid model to implement globally automatic position control by considering hybrid behaviors of the deformable manipulator.Our framework do not rely on any kinematic information.Thus our framework can automatically adapt to kinematic change,which is very difficult for model-based methods.Fourthly,we define an axis-angle space which is bijective to the rotation group SO(3)and propose a modified axis-angle representation method.Based on this representation method,we study the basic concepts about angle distance metric and the geodesic in rotation group.Our method can avoid representational singularity and is helpful to implement global convergence.Thus our method has significant theoretical value.Based on the kinematic-free control framework,we propose a kinematic-free orientation control algorithm by following the geodesic in rotation group.The global convergence of our algorithm is proved in mathematics.The kinematic-free orientation control remains an open problem for traditional methods.Thus our method is a breakthrough to robotic society.Fifthly,we define the problems,which are not required a controlled motion constrained at all three spatial directions,as Incomplete Orientation Constraint Problems(IOCPs).The theory or method aiming for these problems has promising application in a class of tasks with incomplete orientation constraint,which widely exists in ping-pong robot,engraving robot,arc welding robot,and so on.To address the IOCPs,we develop the perpendicular curve theory in rotation group.A given orientation rotating around a given direction forms a curve in rotation group.This curve is also a geodesic in rotation group.We define and give the analytical expressions for the foot of perpendicular and the perpendicular curve from a given orientation to the given curve.We also prove that the angle between the direction of end-effector and the target direction is equal to the geodesic distance from the current orientation of end-effector to the given curve.Based on this result,the control target is transformed from a single orientation to a curve,which is a one-parameter family of orientations.Therefore,our theory gains the chance to find solutions.In conclusion,our theory has significant theoretical value.Based on the kinematic-free control framework,we propose a kinematic-free control method to solve the IOCPs by following the perpendicular curve in rotation group.Our method is highly universal.It can be applied to manipulators with any number of DoFs,not just the manipulators with functional redundancy.It can be applied to manipulators with both known and unknown kinematic parameters.It can not only be applied to rigid-link manipulators and deformable manipulators,but also to soft/continuum manipulators.