Cartesian Parallel Manipulator Modeling, Control and Simulation

Ayssam Elkady, Galal Elkobrosy, Sarwat Hanna, and Tarek Sobh's book chapter on robotic parallel manipulators

Cartesian control of redundant robots

A Cartesian-space position/force controller is presented for redundant robots. The proposed control structure partitions the control problem into a nonredundant position/force trajectory tracking problem and a redundant mapping problem between Cartesian control input F is a set member of the set R(sup m) and robot actuator torque T is a set member of the set R(sup n) (for redundant robots, m is less than n). The underdetermined nature of the F yields T map is exploited so that the robot redundancy is utilized to improve the dynamic response of the robot. This dynamically optimal F yields T map is implemented locally (in time) so that it is computationally efficient for on-line control; however, it is shown that the map possesses globally optimal characteristics. Additionally, it is demonstrated that the dynamically optimal F yields T map can be modified so that the robot redundancy is used to simultaneously improve the dynamic response and realize any specified kinematic performance objective (e.g., manipulability maximization or obstacle avoidance). Computer simulation results are given for a four degree of freedom planar redundant robot under Cartesian control, and demonstrate that position/force trajectory tracking and effective redundancy utilization can be achieved simultaneously with the proposed controller

Autonomous space processor for orbital debris

The development of an Autonomous Space Processor for Orbital Debris (ASPOD) was the goal. The nature of this craft, which will process, in situ, orbital debris using resources available in low Earth orbit (LEO) is explained. The serious problem of orbital debris is briefly described and the nature of the large debris population is outlined. The focus was on the development of a versatile robotic manipulator to augment an existing robotic arm, the incorporation of remote operation of the robotic arms, and the formulation of optimal (time and energy) trajectory planning algorithms for coordinated robotic arms. The mechanical design of the new arm is described in detail. The work envelope is explained showing the flexibility of the new design. Several telemetry communication systems are described which will enable the remote operation of the robotic arms. The trajectory planning algorithms are fully developed for both the time optimal and energy optimal problems. The time optimal problem is solved using phase plane techniques while the energy optimal problem is solved using dynamic programming

Dynamics and control of flexible manipulators

Flexible link manipulators (FLM) are well-known for their light mass and small energy consumption compared to rigid link manipulators (RLM). These advantages of FLM are even of greater importance in applications where energy efficiency is crucial, such as in space applications. However, RLM are still preferred over FLM for industrial applications. This is due to the fact that the reliability and predictability of the performance of FLM are not yet as good as those of RLM. The major cause for these drawbacks is link flexibility, which not only makes the dynamic modeling of FLM very challenging, but also turns its end-effector trajectory tracking (EETT) into a complicated control problem. The major objectives of the research undertaken in this project were to develop a dynamic model for a FLM and model-based controllers for the EETT. Therefore, the dynamic model of FLM was first derived. This dynamic model was then used to develop the EETT controllers. A dynamic model of a FLM was derived by means of a novel method using the dynamic model of a single flexible link manipulator on a moving base (SFLMB). The computational efficiency of this method is among its novelties. To obtain the dynamic model, the Lagrange method was adopted. Derivation of the kinetic energy and the calculation of the corresponding derivatives, which are required in the Lagrange method, are complex for the FLM. The new method introduced in this thesis alleviated these complexities by calculating the kinetic energy and the required derivatives only for a SFLMB, which were much simpler than those of the FLM. To verify the derived dynamic model the simulation results for a two-link manipulator, with both links being flexible, were compared with those of full nonlinear finite element analysis. These comparisons showed sound agreement. A new controller for EETT of FLM, which used the singularly perturbed form of the dynamic model and the integral manifold concept, was developed. By using the integral manifold concept the links’ lateral deflections were approximately represented in terms of the rotations of the links and input torques. Therefore the end-effector displacement, which was composed of the rotations of the links and links’ lateral deflections, was expressed in terms of the rotations of the links and input torques. The input torques were then selected to reduce the EETT error. The originalities of this controller, which was based on the singularly perturbed form of the dynamic model of FLM, are: (1) it is easy and computationally efficient to implement, and (2) it does not require the time derivative of links’ lateral deflections, which are impractical to measure. The ease and computational efficiency of the new controller were due to the use of the several properties of the dynamic model of the FLM. This controller was first employed for the EETT of a single flexible link manipulator (SFLM) with a linear model. The novel controller was then extended for the EETT of a class of flexible link manipulators, which were composed of a chain of rigid links with only a flexible end-link (CRFE). Finally it was used for the EETT of a FLM with all links being flexible. The simulation results showed the effectiveness of the new controller. These simulations were conducted on a SFLM, a CRFE (with the first link being rigid and second link being flexible) and finally a two-link manipulator, with both links being flexible. Moreover, the feasibility of the new controller proposed in this thesis was verified by experimental studies carried out using the equipment available in the newly established Robotic Laboratory at the University of Saskatchewan. The experimental verifications were performed on a SFLM and a two-link manipulator, with first link being rigid and second link being flexible.Another new controller was also introduced in this thesis for the EETT of single flexible link manipulators with the linear dynamic model. This controller combined the feedforward torque, which was required to move the end-effector along the desired path, with a feedback controller. The novelty of this EETT controller was in developing a new method for the derivation of the feedforward torque. The feedforward torque was obtained by redefining the desired end-effector trajectory. For the end-effector trajectory redefinition, the summation of the stable exponential functions was used. Simulation studies showed the effectiveness of this new controller. Its feasibility was also proven by experimental verification carried out in the Robotic Laboratory at the University of Saskatchewan

Study of Motion Control of A Flexible Link

20th century has witnessed massive upsurge in the use of manipulators in several industries especially in space, defense, and medical industries. Among the types of manipulators used, single link manipulators are the most widely used. A single link robotic manipulator is nothing but a link controlled by an actuator to carry out a particular function such as placing a payload from point A to point B. For low power requirements single link manipulators are made up of light weight materials which require flexibility considerations.Flexibility makes the dynamics of the link heavily non-linear which induces vibrations and overshoot. In this project initially the dynamic model of rigid flexible manipulator is explained, then the state space model of the manipulator system is incorporated into MATLAB. The link flexibility is studied by a single beam FEmodel, where expressions for kinetic and potential energyare employed to derive the torqueequation.The 3 flexible link equations are coupled in terms of 3 variables, θ, Ø and v. The tip angle is finally given aslvfor flexible case whereas for the rigid manipulator the tip angle is same as the hub angle θ. Thereforeaccurate computation of v is very important. The joint flexibility is excluded from analysis.Several comparisons were made between the rigid and flexible link for torque requirement. The relation between the trajectory and hub angle is also plotted in a graph.Finally a PD controller taking the errors and its derivative is designed based on the rigid link dynamics

Modeling and Robust PD Compensation of Two-Link Flexible Manipulator

The Two Link Flexible manipulator (TLFM) is a two-input-two-output, highly nonlinear and unstable system. Therefore, modeling and control system design of such a system is a challenging task. To this end, first, to establish a non-linear mathematical model of the TLFM, its kinematic and dynamic motions are analyzed through assumed mode method. Then a linearized model about equilibrium point at origin is obtained from this nonlinear model via “linmod/linearize” command in MATLAB. Next, for this linearized model a two-loop robust PD controller is designed via root locus based loop shaping approach. The controller obtained thus is employed for the nonlinear system and the robustness results are verified