3Sigma wanted to create a high-fidelity model of a gyropode robot, Geeros, which could be used by students to learn about robotic design and programming. Using traditional design tools, the complex mathematical equations used in the model were extremely difficult to calculate and manage.
3Sigma selected the powerful combination of MapleSim and Maple to automatically generate and manage the equations for the model.
Using MapleSim and Maple, 3Sigma created a high-fidelity model that would have been too difficult to develop otherwise. The company achieved greater accuracy and gained considerable time savings in the design, test and build of Geeros. The students are now able to visualize the symbolic nature of the underlying equations providing them with a greater learning opportunity.
3Sigma is a company that specializes in automation and robotics. Recently, 3Sigma set out to design Geeros, a customizable, self-balancing gyropode robot. Geeros was designed as an educational robot that students can use to learn about piloting, programming, and modifying robots. The robot’s motion can be controlled using a host computer and the instructions are transmitted instantly to the robot via a wireless connection, providing the students with real-time results in a practical application.
The base of a gyropode robot is an electric vehicle with a platform and two wheels. The robot’s servomechanism is an automatic controller that uses error-sensing negative feedback to improve performance. For Geeros, a proportional-integral-derivative (PID) controller was used because students are usually already familiar with this type of controller. Geeros was built using Arduino, the easy-to-use, open-source electronic prototyping platform. Sensors and actuators can easily be added or replaced in Geeros, making the robot fully customizable.
(Learn more about MapleSim’s powerful symbolic math engine.)
In designing Geeros, Nicolas Gachadoit, Principle and Chief Engineer at 3Sigma, immediately chose to employ Maplesoft’s MapleSim and Maple to support a model-based system-level design of the robot. As a former employee of Maplesoft, Gachadoit was well aware of the benefits offered by this unique software combination.
MapleSim and Maple provided 3Sigma with distinct advantages over traditional tools. First, the complex mathematical equations used in the design of a gyropode are extremely difficult to manage by hand. Traditionally, the engineer chooses to use a simpler set of equations to represent the model, resulting in less accurate simulations of the behavior. However, using MapleSim and Maple, the model equations are automatically generated and managed by the software. As a result, 3Sigma was able to create a more accurate gyropode model with less effort, giving them higher fidelity simulation results and making it easier for them to test their design.
In addition to automatically generating the equations of motion, MapleSim and Maple allow the engineer to view, analyze, and manipulate those equations. In this case, because they wanted to use a PID controller to control the robot, the engineer transformed the system of non-linear equations into a matrix representation of the linearized equations. This was done quickly and error-free using a single command. The linearized equations remain symbolic, so that the friction, inertia, resistance, and other factors remain as parameters that the engineers, and ultimately the students themselves, can vary and see the resulting changes of behavior.
Due to the advantages provided by Maple and MapleSim, 3Sigma was easily able to design, test, and build the Gyropode robot. “Using the powerful combination of Maple and MapleSim, we were able to create a high-fidelity model that would have been too difficult to develop if we had to perform all the calculations by hand,” says Gachadoit. “As a result, we were able to achieve considerable time savings in the development of our gyropode model, designing it in a fraction of the time normally required for such a complex system, and with much greater accuracy. As well, the symbolic nature of the underlying equations gave us the ability to provide students with the means to easily modify a variety of parameters in the controller and see the change in how the robot actually behaves, which helps them deepen their understanding of the factors going into robotic design.”
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