Simulation-Based Design of Robotic Systems Shadi Mohammad Munshi* & Erik Van Voorthuysen School of Mechanical and Manufacturing Engineering, The University of New South Wales, Sydney, NSW 2052 shadimunshi@hotmail.com, erikv@unsw.edu.au Abstract: The design of novel robotic joints and manipulators requires the integration and synthesis of knowledge and information from a number of different sources and disciplines including mechanics, control theory, tribology, reliability and manufacturability. In order to increase the likelihood of a successful design in a shorter period of time, a simulation-based methodology is proposed and is currently being employed in the design of a low-cost but high performance pneumatic manipulator. The methodology is based on an iterative process of system modifications leading to improved successful designs of robotic systems. Pneumatic actuation has been exploited in the past decades as a low cost alternative to electrical and hydraulic actuation. Understanding the behavior of these systems with different controllers will assist to expand their applications, especially in robotics. A challenge that the simulation model addresses is to understand the performance of pneumatic cylinders operated with two different valve configurations, in this case, a single 5/3 way proportional valve and a configuration of 4 3/2 way low cost electrical on/off solenoid valves. These valves act as the main control elements in the system. A simulation program using Matlab/Simulink was developed and tested with a PD controller to test the performance of a 6 DOF robot manipulator actuated using a single pneumatic cylinder, as the driving force, for each joint. The simulation model is based on several physical laws describing the pneumatic system as the valve(s) open and close providing pressure difference between the two chambers causing the pneumatic cylinder to actuate. Preliminary designs arising from the models are manufactured using Rapid-Prototyping technology. These components are subsequently experimentally tested and the resulting experimental data is fed back into the simulation model. This design methodology can be used for system fine tuning; design feature modifications and multi variable optimization such as accuracy, speed and force control. Keywords: Simulation, Simulation-based design, Rapid Prototyping, Pneumatic cylinder, Modularity, Re-configurability, Manipulator, Controller, Design, Valve configurations, Performance, Accuracy, Precision, Flexibility, Compactness. 1. INTRODUCTION The ability to design and modify changes in the design without actually having to build the system is desirable Simulation is the process of designing a model of a real especially when different components are to be selected or imagined system and conducting experiments with for optimized performance. This greatly helps to make that model to understand the behavior of the system or the process economically feasible. In particular, all evaluate strategies for its operation (Smith 1999). It has robotic systems run with controllers which need to be been used for many purposes including technology, tested for consistency, reliability and accuracy. safety engineering, testing, training, education and entertainment. Along with the rapid growth of computers, hardware and software, the ability of simulating complex systems in shorter periods of time can be carried out. In robotic system designs, simulation has become an important factor when planning and modifying new or existing systems, thereby gaining an insight into the behavior and response to changing conditions and courses of action of system components resulting in higher efficiencies, optimized performance and realistic views of a system s end product. In this study, a simulation-based methodology is proposed for the design of a low-cost, high performance modular pneumatic manipulator actuated using two different types of valves, a 5/3 proportional valve and 4 3/2 on/off solenoid valves. Furthermore, prototype manipulator parts are designed and manufactured using Rapid Prototyping for experimental purposes in order to obtain data which can be fed back into the simulation module resulting in higher module accuracy. This method can be used to design any system with established mathematical models and relationships of *Shadi Munshi is a graduate teaching assistant at Umm Al-Qura University and is currently a PhD Scholar
each component in the system. Matlab/Simulink software was used for simulation as it provides simple block to block connections for building the model. The simulation-based design methodology for the robotic system was approached by means of defining the mathematical model of the system, finding the relationships between components for block connections and building the equations into Simulink. 2. DEFINING THE SYSTEMS MATHEMATICAL MODEL Before the simulating process, the system components to be simulated need to be defined. These components include the actuator or force element (Pneumatic cylinder), the commanding device (proportional/ solenoid valve(s)) and the feedback sensing element (position, pressure, force) which, all together, form the system to be modeled. Starting with the commanding device (proportional/ solenoid valve(s)), the mathematical model is derived by using the mass flow rate through an orifice (thin plate) depending on the type of valve. In this example only the 5/3 proportional valve is shown. For this valve, one input and one output port is activated at any one time making the commanding system operate as two orifices. The input to the system is from a proportional directional control valve (FESTO MPYE-5-1/8-HF- 010-B) operating at voltages from 0-10 volts (or current from 4-20mA). This valve controls the flow rate of air to and from the actuator chambers proportionally with the change in voltages. For this valve: Pu, Pd and A(u) are dependent on the input voltage (u) as follows: If (2) where: P atm is the atmospheric pressure and P sys is the system pressure to the valve. Furthermore, using the energy conservation law and the ideal gas state equation the relationship between the pressure flow rates and the piston displacement can be derived as: ; (1) for chamber a, and (3) for chamber b (4) where: P u and P d are the upstream & downstream pressures K,R,T are constants and A(u) is the surface area of the orifice as a function of input voltage to the valve. Newton s second law of motion is further applied to figure 1 to obtain the dynamic equation of the actuator, with friction forces considered, forming the following equations:
Figure 1: Filling stage of chamber A and the forces acting upon the actuator 3. SIMULATION USING MATLAB/SIMULINK Where: F sf, F cf and C vf are friction constants is the velocity of the piston is the acceleration of the piston (5) Friction constants F sf, F cf and C vf are calculated from experiments for the pneumatic cylinder used and fed back into the simulation model. Equations (1),(2),(3),(4) and (5) are used for simulating the pneumatic actuator and valve with a controlled input voltage applied to the valve by means of feeding back pneumatic piston displacement, velocity, acceleration and/or force with required set-points for each whenever required. Expanding the system, robotic joints were designed to actuate depending on the movements of pneumatic cylinders. Each joint includes a similar controllable pneumatic system with its own unique set points and control variables. These set-points are specified from another system containing the Denavit-Hartenberg parameters. These represent the transformation matrices between the consecutive joints of the robotic manipulator thus solving the kinematics of these manipulators. For simulating the actuator and valve, the system parameters are set, including initial conditions for. From the initial conditions, equation (1) and (2) can be used to calculate. Following, are computed through equations (3) and (4). Furthermore, are calculated by integrating. From equation (5), is calculated then is integrated to get and integrated again to get. Finally, the new results are fed back to calculate and so on, until the desired position is reached (Ning and Bone 2005). Figure 2 displays a simulink model of the pneumatic actuator along with the valve and controller. Each joint for the manipulator is made up of a pneumatic system and is further attached to a second system containing the kinematics and dynamic effects of manipulators interacting through the set-points and actual positions (y) of each joint. For each joint, various control methods could be tested for consistency before actually building any system using the simulation module. A cyclic coordinate descent (CCD) control algorithm (Mukundan 2009) was chosen for the controller of a modular manipulator with a decentralized control system (Vittor 2003) having each joint detect its path to the goal point in real-time without the aid of a central controller.
Figure 2: Simulink model of a pneumatic system (actuator and valve) converted to forces acting on the cylinders and fed to the pneumatic system of each joint. Figure 3: Angle or distance error for CDD control a) Revolute b) Rotary c) Prismatic The main idea of CCD is for each joint to minimize the angle between the joint & end-effector and the joint & goal point. Figure 3 illustrates the angle or distance errors for different joints with knowledge of the goal and end-effector points of the manipulator. For a revolute joint the error angle is calculated as θ2- θ1; for the rotary joint it is the angle between the shortest distance from the end-effector to the normal of the module and between the shortest distance from the goal point to the normal of the module, reflected on the module surface; and for the prismatic joint, the error is calculated as the difference in height between the goal point and the end-effector reflected on the module surface as well. These angles are then fed to the pneumatic system as set-point errors for correction. Figure 4: CCD Control algorithm for detecting positions Forward kinematics was applied to convert joint angles into Cartesian coordinates for the calculations of current positions of each joint and the manipulators endeffector coordinates enabling real-time error angle (or distance) calculations for each joint as shown in figure 4. To simulate a more realistic model, the dynamics of robotic manipulators were constructed estimating the joint torques caused by gravity, inertial, centrifugal and coriolis forces (Xiao 2008). The torque values are then where: D is the acceleration related inertia matrix term H is the coriolis and centrifugal terms C is the gravity terms τ is the driving torque applied on each link The CCD control algorithm can be further modified for path tracking by substituting the goal point with a generated path to obtain any demands in maneuverability around the environment of the manipulator. Simulation works as a great refining tool for better designs. Model parameters can be estimated and tuned for design improvements as in testing different actuators with different specifications or even tuning of joint module mass to meet required system behaviors. Design parameters, as controller gains, can also be automatically tuned to meet the rise time and overshoot constraints resulting in improved system performances and reduced system costs. Physical parameters can be calibrated as well using test data to increase model accuracy. Furthermore, system parameters can be recorded, visualized and used for Finite Element analysis (FEA) & design modification. Such parameters include the dynamic effects of forces and torques on moving objects. As part of a case study, the design was optimized by testing two different valve types and two different pneumatic cylinders. Friction parameters for these physical systems were calibrated and re-entered into the simulation model for better model accuracies. Different external mass loads were tested for optimizing the controller. Besides that, the controller was further tuned for optimal gains ending up with faster and more stable system control. Simulation not only helps in refining and tuning system parameters in the modular manipulator designed but can also aid in the selection of modules for a specific application. An application can be modeled and tested with different joint connections as the robot is designed in a modular way. In addition, a virtual motion of the modular manipulator is available for modifying and seeking the optimal path planning method. This methodology is shown in figure 5. It is based on an iterative process of system modifications running in three phases, a design phase (part design), a post design
phase (assembly phase) and an acceptance testing phase. Final Product Figure 5: Simulation-based Design process of Robotic Systems Further extensions of this methodology can complex process design such as materials handling and automation. For simulating automated assembly lines and layouts it is important to define the right constraints for each process. These processes can also be visualized in three dimensions using the virtual reality toolbox accompanied with the Matlab/Simulink package. 4. CONCLUSION A simulation-based design method for robotic systems has been developed for a pneumatically actuated manipulator using Matlab/Simulink as the programming software. This method is based on several physical laws describing a pneumatic system and placing it as the driving force for a 6DOF manipulator. A modular manipulator was designed and simulated with three types of changeable joints, revolute, rotational and prismatic. With the assistance of kinematics transforming from joint space to task space, enabled a cyclic coordinate descent (CCD) algorithm along with a decentralized modular approach to be used for the manipulation of the robotic arm. Novel designs were successfully manufactured using Rapid-Prototyping technology for experiments. Simulation can provide many advantages to the design process of any robotic system. Whether it involves planning a new design or modifying an existing one, simulation serves as a tool for visualizing, understanding the behavior of a modeled system with a preferred design. Having that in mind, manipulation can be assured for safety by predicting motion behaviors and constructing new methods or constraints for unbehaved movements. Furthermore, robotic system controllers can be altered, achieving higher efficiencies and optimized performances. Beyond that, simulation can act as an economic solution to component selection as in valves with highest performance and lowest cost. REFERENCES [1] Smith, R. D. (1999)." Simulation: The Engine Behind the Virtual World". [2] Ning, S. and G. M. Bone (2005). "Development of a nonlinear dynamic model for a servo pneumatic positioning system", Niagara Falls, ON, Canada, Institute of Electrical and Electronics Engineers Computer Society, Piscataway, NJ 08855 1331, United States. [3] Mukundan, R. (2009). "A robust inverse kinematics algorithm for animating a joint chain." International Journal of Computer Applications in Technology 34(4): 303 308. [4] Vittor, W., Furukawa (2003). "Modular Decentralized Control of Fruit Picking Redundant Manipulator." [5] Xiao, J. (2008) " Introduction to Robotics Manipulator Dynamics".