Maintaining a steady arm1 March 2000
Using computer simulation, engineers at the Pacific Northwest National Laboratory have developed a vibration-free control system for a robot arm 30 feet long. Designed to break down nuclear waste within storage tanks at the Hanford site in Washington state, the computer aided design technique significantly reduced the time and effort necessary, compared with a traditional physical testing approach.
Nuclear waste at the Department of Energy's (DoE’s) Hanford site is currently stored in concrete tanks which are as much as 40 ft (12.2 m) deep. Access is through a 42 in (107 cm) diameter hole in the tank's top. Robotic manipulators are required that can pass through the hole, reach the bottom of the tank and use various tools to break up and remove the waste. The manipulators must have relatively flexible links and low natural frequencies, and this makes them prone to oscillation.
There are no commercial robots currently available that can handle this task. The DoE asked the Pacific Northwest National Laboratory (PNNL) to develop a long-reach robot capable of doing the job. One concept PNNL developed consists of a long-reach manipulator (LRM), used for coarse positioning, with a lighter-duty short-reach manipulator (SRM) mounted on its tip. Sensors and control computers are used to provide feedback control for oscillation damping.
The design process
The most challenging aspect of the design process was developing control strategies to damp out induced oscillations in the beam. The basic idea was to alter the short arm's intended command trajectory to annihilate the oscillations. The problem is challenging partly because the control system must accomplish an additional task, rejecting oscillations, while still meeting the normal requirements of stability, robustness and reliability. Also, the manipulator system is highly nonlinear, making it challenging to develop an accurate model using conventional design tools.
To dampen the oscillations engineers developed control algorithms to generate inertial forces that oppose the oscillations. The algorithms had to address multiple modes of vibration, take complex nonlinear kinematic and dynamic interactions between the LRM and SRM into account and produce damping under a wide range of conditions.
PNNL engineers constructed a half-scale prototype of the proposed design. The test bed consists of a steel beam 15 ft (4.6 m) long by 1 ft (30 cm) high by 0.75 in (1.9 cm), fixed at one end and free to move in a horizontal plane at the other. The free end is supported off the ground by an air bearing that provides a low-friction interface with the floor while restricting any torsion about the beam's longitudinal axis. A six degree of freedom hydraulic manipulator is mounted on the beam at the free-floating end to represent the short-reach manipulator.
The prototype can be used to evaluate the effectiveness of different control strategies. The problem is that it takes a long time to implement and evaluate a control strategy using such physical testing. PNNL engineers would have been able to find a control strategy that worked in most cases, but would have been required to evaluate all reasonable strategies to be confident they had reached the optimum approach.
For this reason, computer simulation was used to evaluate the impact of alternate control strategies. This technique has the benefit of providing a vast amount of data, such as the position, velocity and acceleration at every point in the model at each time step in the simulation. These data can be used in analysis routines to calculate optimum values for control equations. A critical part of the simulation approach is ensuring that it reflects accurately the physical reality. Important issues include accurately modelling the robot arm hydraulic system, capturing the dynamics of the elastic robot link, and interfacing the mechanical model with the software used to develop the control system – in this case Matlab from MathWorks of Natick, US.
PNNL engineers used the Dynamic Analysis and Design System (DADS) mechanical system simulation software from Computer Aided Design Software (LMS CADSI), based in Coralville, US, to model the system. This software allowed engineers quickly to assemble, simulate and animate the basic test bed system. The model included open and closed loop control systems and realistic hydraulic valve and actuator properties. The model also incorporated finite element results that accurately modelled the flexible link.
To design the controllers, PNNL engineers built a DADS model; they then went through a sequence of simulations to exercise individual parts of the system. The DADS model of the robot developed by the engineers consisted of the base of the test bed; the flexible arm; and the rigid bodies, joints, hydraulic elements and control elements. While the actual robot in the test bed was a six degree of freedom device, all joints other than the azimuth joint were held fixed in this analysis. The control elements were used to measure the angles between the manipulator links, compute control error values, and actuate hydraulic servo valves that drive the manipulator. Using appropriate boundary conditions, a modal, finite-element analysis of the beam was performed using ANSYS, from Swanson Analysis Systems, based in Canonsburg, US. Additional runs were made to compute the deflections and modes resulting from static loads. DADS used this modal information to simulate the flexibility of the part throughout its range of motion.
The linearised model was then used to develop constant coefficient differential equations to drive the controller design models (CDMs) - the mathematical models that compute the actuator responses needed to damp vibrations. The step functions developed from the DADS simulation output were applied to the azimuth angle of the SRM and the LRM tip response signals were measured. The responses were then analysed using the Prony analysis program, developed at PNNL in collaboration with the Bonneville Power Administration. The analysis produced optimised linear transfer functions based on the step response of the robotic system. The analysis was performed under a variety of loading conditions to obtain a family of transfer functions.
The technique of sequential loop-closure was used to design the final CDMs. To initiate the control design, the DADS non-linear mechanical model was linearised at an operating point. The CDMs were developed under full load because this represents the highest gain conditions.
Once the control parameters were chosen, their effectiveness was evaluated by simulating their performance combined with another DADS mechanical simulation. The simulation results showed that the control system provided the required level of vibration damping, stability, robustness and reliability. The next step was implementing the control and testing its performance on the prototype robot. The physical test results matched the simulation very closely and again demonstrated the damping capabilities and robustness of the CDMs.
Development of this control system using simulation based design illustrates the effectiveness of this approach. PNNL engineers used simulation based design to develop an optimised control system in a fraction of the time that would have been required using the conventional approach based on physical tests.
Modern engineering modelling tools allow engineers to construct systems of these tools. Using these systems, they can create realistic simulations of controlled mechanical systems. This approach frees engineers from the time consuming and error prone process of manually writing their own equations of motion.