Newsletters - MATLAB Digest

Creating a Stewart Platform Model Using SimMechanics

by Natalie Smith and Jeff Wendlandt

Abstract

SimMechanics, in conjunction with Simulink and MATLAB, enables engineers to model complicated mechanical systems, simulate and analyze the models, and develop controllers for the mechanical system. In this technical example, we examine how to use SimMechanics to model physical components, synthesize controllers, and simulate the closed loop performance of a Stewart Platform, a six degrees-of-freedom positioning system. Stewart Platforms are used in many applications for positioning objects.

Various Applications of the Stewart Platform

The Stewart Platform was originally designed in 1965 as a flight simulator, and it is still commonly used for that purpose. Since then, a wide variety of applications have benefited from this design. A few of the industries using the Stewart Platform design include aerospace and defense, automotive, transportation, and machine tool technology, who use the platform to perform flight simulation, handle vehicle maintenance, and design crane hoist mechanisms. The Stewart Platform design is also used for the positioning of satellite communication dishes and telescopes and in applications such as shipbuilding, bridge construction, transportation, and as a drilling platform on the Lunar Rover.

Specifications of the Stewart Platform

The Stewart Platform is a classic example of a mechanical design that is used for position control. It is a parallel mechanism that consists of a rigid body top plate, or mobile plate, connected to a fixed base plate and is defined by at least three stationary points on the grounded base connected to six independent kinematic legs. Typically, the six legs are connected to both the base plate and the top plate by universal joints in parallel located at both ends of each leg. The legs are designed with an upper body and lower body that can be adjusted, allowing each leg to be varied in length. See picture to the right

The position and orientation of the mobile platform varies depending on the lengths to which the six legs are adjusted. The Stewart Platform can be used to position the platform in six degrees of freedom (three rotational degrees of freedom, as well as three translational degrees of freedom). In general, the top plate is triangularly shaped and is rotated 60 degrees from the bottom plate, allowing all legs to be equidistant from one another and each leg to move independently of the others.

Advantages of the Stewart Platform

Engineers and researchers have examined many variants of the Stewart Platform. Most variants have six linearly actuated legs with varying combinations of leg-platform connections. Of the many types of motion control platforms, the Stewart Platform is useful to study because it is a widely accepted design for a motion control device. This is largely because of the system's wide range of motion and accurate positioning capability. It provides a large amount of rigidity, or stiffness, for a given structural mass, enabling the Stewart Platform system to provide a significant source of positional certainty.

The design of the Stewart Platform supports a high load-carrying capacity. Because of the design, the legs carry compression and tension forces, and will not succumb to the undesirable bending force found in other designs. The six legs are spaced around the top plate and share the load on the top plate. This differs from serial designs, such as robot arms, where the load is supported over a long moment arm.

Defining a Control Problem for the Stewart Platform

The problem addressed in this example is to find a method to actuate the six leg forces to properly position the mobile plate of the Stewart Platform given a desired trajectory. For this particular problem, we are given a desired position and orientation of the mobile plate with respect to the fixed base plate. These desired values might change over time. We wish to control the nonlinear plant model of the Stewart Platform and have inputs and outputs to accomplish this. The six leg forces are the inputs into the plant while the outputs are the lengths and velocities of the six legs. Our task is to create a control strategy and design that will make the top plate follow the desired trajectory. We must accomplish this by actuating the six leg forces, sensing the leg lengths and velocities, and reading the desired trajectory.

Traditionally, a common method for designing the controller for the Stewart Platform required manipulating complicated equations that modeled the physical components used to solve the mechanical equations. Then, the engineer had to solve these equations using complex numerical integration techniques. With the advent of computational tools such as dynamic simulation software, it is now possible to easily model and simulate the Stewart Platform mechanics together with the control system.

Constructing a Stewart Platform Model Using SimMechanics

In this article, we will demonstrate how SimMechanics, Simulink, and MATLAB can be used to model and simulate the behavior of the Stewart Platform. SimMechanics will be used to model the mechanical components of the system, and Simulink will be used to model the controller. Using the predefined libraries from SimMechanics, we will be able to model the Stewart Platform without needing to explicitly derive the equations of motion, which can be a tedious and error-prone process.

Modeling the Physical Components with SimMechanics

We will first build the plant model using SimMechanics. The mechanical components of the Stewart Platform consist of a top plate, a bottom plate, and six legs connecting the top plate to the bottom plate. The overall system has six degrees of freedom. Each leg subsystem contains two bodies connected together with a cylindrical joint. The upper body connects to the top mobile plate using a universal joint, and the lower body connects to the base plate using a second universal joint.

Using SimMechanics Body blocks, we model the rigid bodies for the base plate, top plate, and upper and lower legs. Next, we connect the bodies together using SimMechanics Joint blocks.

When beginning to build the physical model of the Stewart Platform, we first need to define attachment points relative to an inertial frame (or world). We define this by using a Ground block from the Bodies Library in SimMechanics. The Ground block acts as a fixed point for attaching system components.

Now we will build the legs of the Stewart Platform by connecting the Ground block to the Universal Joint block, and connecting that to a Body block to create the lower leg. Next, we add another Body block to represent the upper leg. Then we use a Cylindrical Joint block to connect the lower leg to the upper leg, enabling the entire leg to adjust its length by moving in one translational and one rotational degree of freedom. Next, we simply add another Universal Joint block connected to the Upper Leg Body block, which will ultimately be attached to the top plate.

Linear actuation of the Stewart Platform is accomplished by varying the lengths of the legs. To move the legs, we use a Joint Actuator block from the Sensor & Actuators Library in SimMechanics. This joint actuator is used to control the translational degree of freedom of the cylindrical joint. (The rotational degree of freedom is unconstrained.) A force signal will be created and used for actuation, rather than using the displacement. This enables us to create a more realistic model of the Stewart Platform where hydraulic actuators can be used to apply force between the upper and lower legs. We are also sensing the length of the leg with a Joint Sensor block from the Sensors & Actuators Library to extract the position and velocity, which will be used by the controller.

By creating a library subsystem of the leg component, we can easily create six instances of the legs of our Stewart Platform model. Now we can connect each of the joints connected to the upper part of each of our six legs to one Body block that will be our top plate. This represents the plant portion of our Stewart Platform model, which will accept inputs of actuation of the top plate as well as the force, position, and velocity signals.

Part 2