In this chapter, we present the design, simulation, and control of a hexapod robot using tools available in MATLAB software. In addition, we design and implement a dynamic model (using the Simscape Multibody™ toolbox) as well as a three-dimensional model of the robot, using Virtual Reality Modeling Language (VRML), that help to visualize the robot’s walking sequence.
This three-dimensional model is interconnected with the Simscape Multibody™ blocks using MATLAB’s virtual reality blocks. Apart from this, and following specific requirements, we design and implement a Proportional–Integral–Derivative controller in order to obtain a pre-established displacement for the robot that, thanks to the developed computer simulations, proved to be satisfactory.
Special emphasis is put in obtaining a modular representation of the dynamic model of the studied robot because it will permit to design more sophisticated nonlinear controllers in future works, allowing a good dynamic behavior of the robot in front of environmental perturbations, an issue that will become evident through computer simulations of its displacement.
Success in designing a hexapod robot lies fundamentally in the structure of chosen legs. The main aspects of a hexapod robot’s displacement are ruled by physical limitations of their legs. It is of paramount importance to choose a leg whose design provides the maximum possible range of movements and that does not pose unnecessary constraints that can affect the movement of the robot.
Direct Kinematics of a Hexapod Robot:
In order to obtain the kinematics of the studied robot, it is necessary to use the Denavit-
Hartenberg algorithm, applying it to a leg of the hexapod robot. This robot is formed by a
symmetrical structure composed of six identical legs, having three degrees of freedom (DOF).
Inverse kinematics is the process of determination of the angles in terms of the coordinates for the leg’s desired position in the Cartesian system. Unlike the problem posed by direct kinematics, the procedure for getting the equations is strongly dependent on the robot’s configuration, making it a complex procedure because it is very difficult to obtain systematically those equations, even plainly impossible. Inverse kinematics, in this case, is obtained through geometrical considerations based on the leg’s shape.
DYNAMICS OF THE HEXAPOD ROBOT
The problem of obtaining a robot’s dynamic model is one of the more complex aspects in the field of robotics, and it is necessary for achieving the following objectives: design and evaluation of robot’s dynamic control, sizing of actuators, evaluation of the robot’s mechanical structure, and motion simulation of the robot design.
HEXAPOD ROBOT MODEL AND SIMULATIONS
Hexapod Robot Model:
In order to carry out a modeling and further simulation of a hexapod robot, it is necessary to take into account the robot’s physical characteristics (mass, dimensions of thorax, measures of links, and the inertia matrix). In this case, we will employ the model developed which details the robot’s size, as well as the other parameters. However, some parameter modifications will be made, trying to get as close as possible to real conditions. Basically, we will employ the robot geometry.
When observing the complexity of obtained expressions, it becomes evident that the greater the number of DOF a robot has, the more difficult is to find the equations, more computer resources are consumed, and longer time and greater effort are spent trying to obtain them.
As previously mentioned, an expression for the individual dynamics of a single leg of the hexapod robot is relatively easy to obtain, nevertheless the hexapod robot has six legs, that is a total of 18 DOF, therefore making the simulation more complex. That is why we employed a MATLAB tool called Simscape Multibody™, which has the advantage to perform simulations using blocks that represent links and joints (rotational or prismatic), as if the robot was being assembled.
CONCLUSIONS AND FUTURE DEVELOPMENT
Obtaining a dynamic model for a hexapod robot can be a laborious and complex task (espe‐cially when the robot has several DOF), which makes Simscape Multibody™ a powerful and easy-to-use tool for this purpose. We do not need to obtain an explicit dynamic model when using Simscape Multibody™ because such model is elaborated by means of blocks that represent links and joints, therefore consuming little time in the implementation of computer simulations. The development of a model in three dimensions and its further simulation help to visualize the design and possible problems that a real robot could confront (if the robot already exists or if it is going to be built).
PID controllers are not the most suitable devices to perform position control for this kind of
robots; however, it is necessary to remark that the aim of our work was not to design a controller that could allow precise control, but getting the robot to respond in a quick and acceptable manner to input references. Special emphasis has been put in obtaining a modular representation of the dynamic model of the studied robot because it will permit to design more sophisticated nonlinear controllers in future works, allowing a good dynamic behavior of the robot in front of environmental perturbations, an issue that will become evident through computer simulations of its displacement.
In the near future, a robot of this kind will be designed and built, which will permit to
implement algorithms for intelligent control, such as neural nets, fuzzy logic, and/or adaptive control. Additionally, not only the locomotion of the hexapod robot will be developed but also its artificial vision systems.
Authors: Claudio Urrea | Luis Valenzuela | John Kern