Dismantling Hexapod’s Locomotion
Have you ever seen a non-alive spider crawling somewhere? Well, this kind of robot is getting more and more popular in technology. I am going to break apart the basic steps/requirements of a hexapod’s locomotion and explain why they are so efficient.
Hexapod’s characteristics
Limbed robots like hexapods have several advantages in their locomotion. First of all, they have higher mobility when compared to others. They can move over rough terrain and overcome obstacles, making them useful for a wide range of applications, such as search and rescue, agriculture, and exploration. They also show to be very versatile. Their multiple legs can be used for a variety of tasks, including manipulating objects, climbing walls, and digging. Then finally, and super crucial, they operate with higher stability. Limbed robots maintain stability on rough terrain and when faced with unexpected obstacles. This makes them useful for tasks where balance is important, such as carrying payloads over difficult terrain. These robots are today known as the most efficient because more than 50% of the Earth’s surface cannot be navigated using wheels or tracks alone.
Although very useful, this kind of robot has obviously its disadvantages. They are often very complex than wheeled or tracked robots because they require more sensors and control systems to coordinate the movement of multiple legs. This makes them more difficult to design, build, and maintain. In addition, they consume huge amounts of power in little time Since they require power to move their legs, meaning each joint, gets limited endurance and range, making them less suitable for some applications. Finally, they are often very expensive to build, due to their complexity and the need for more advanced control systems, and numerous parts.
Structure:
Legged robots consist of one or more limbs connected to a central frame or body. These are multiple sections connected to one another using either revolute, prismatic, or spherical joints.
Each joint type has its own advantages and trade-offs. For example, revolute joints (also known as hinge joints) are easy to design and control, but they have limited mobility and can only move on one axis. Prismatic joints (also known as slider joints) provide linear motion and are useful for extending or retracting a leg, but they are not as versatile as revolute joints. Spherical joints provide the greatest range of motion, but they are more complex and expensive to design and manufacture. The choice of leg joint depends on the specific needs of the robot, such as its desired range of motion, payload capacity, and cost constraints.
The morphology of these legs is inspired by bio-structures as in reptilian and mammalian legs, usually named coxa, femur, and tibia. The most efficient number of legs has been established to be 6 each with 3 joints, summing up to 18 degrees of freedom. Anything beyond this number, the complexity and hardware costs outweigh the aforementioned advantages.
End effector’s placement
A hexapod, like any robot with multiple limbs, needs to use inverse kinematics to determine the joint angles required to achieve a desired position or movement in space. Inverse kinematics involves solving a set of equations that relate the position and orientation of the end effector (e.g., the foot) to the joint angles of the robot.
For example, if a hexapod needs to move in a certain distance and direction, we use inverse kinematics to calculate the exact joint angles required for each leg to achieve the desired movement, to then have the end effector (lep tip) exactly where wanted.
Formulas:
Using an example of a three-joint leg, we can set red, blue, and green for each joint variable used from now on.
To determine the position of the end effector, we can have X3 and Y3 as its coordinates of it, being θ1 the angle of joint one. On this XY plane, we can’t determine any other variable because the leg parts can be tilted on the z-axis. Here already, the θ1 angle can be determined using:
Now for the rest of the angles, we need to switch to the side view:
Here, it is finally possible to define each leg’s part length: a1, a2, and a3. And the other joint angles: θ2 and θ3. Notice that is defined by an extension from the femur. But isn’t possible to determine the leg end-effector coordinates, because the leg can be tilted on the XY plane.
To calculate both θ2 and θ3, it is helpful to imagine two triangles, usually, a right triangle is essential to make things simpler:
Here we name β1, β2, and β3 the handiest angles on the image, from the two triangles. And r1, r2, and r3 to each edge of the right triangle.
Now we can calculate the following:
Notice that r1 on the top view is:
So, now r1 one can finally be determined as:
And the rest of the other variables as:
This way there are all the equations for all the joint variables to use in the code.
Locomotion
Once the joint angles of the hexapod are calculated, the locomotion of the hexapod proceeds by coordinating its legs in a specific pattern. To walk in any pattern the robot obeys a leg cycle.
A leg cycle is a combination of raising and placing a leg. It has two phases: the swing phase and the stance phase. During the swing phase, the leg traverses from the initial position to the final one through the air, as shown by the blue dashed line. During the stance phase, the leg end effector is in contact with the ground while the leg traverses from the final position to the initial position, moving the robot in the opposite direction to the red arrow:
This walking pattern depends on the gait used, which can be a tripod gait, a wave gait, a ripple gait, etc.
In the tripod gait, for example, the hexapod moves three legs at a time while the other three remain in contact with the ground, which is the most stable. The three legs that move will typically be the front and rear legs on one side of the hexapod and the middle leg on the opposite side.
To initiate the pattern, the hexapod first lifts one set of the three legs off the ground, move them forward (for example) and then place them back down. Right after the other set of legs remain on the ground and moves backward (for example), and maintains stability. This movement is then repeated continuously.
The wave gait involves moving legs in a wave-like pattern, while the remaining legs support the robot’s weight. In wave gait, only 1 leg is in the swing phase at a time while the other 5 legs are in the stance phase. Ripple gait involves a rolling motion, where each leg moves in succession, which requires precise control and is less stable on uneven terrain. The locomotion speed of the ripple gait is slower than the tripod gait, but it is faster than the wave gait, since 2 legs from opposite sides are in the swing phase by 180 degrees offset, at a time:
Further steps
To control the movement of the hexapod, each leg is connected to a central controller that coordinates the movement of all the legs. The controller can use gyroscopes, accelerometers, and compasses, to provide information on the robot’s orientation and help maintain balance. In addition, force sensors and tactile sensors can also be implemented to detect contact with surfaces and obstacles. And stereo cameras or LIDAR/Ultrasound sensors to make the best path decisions.
All of these sensors work together with the control systems to coordinate the movement of the robot’s multiple legs. The control systems typically use a combination of algorithms and feedback loops to adjust the movements of each leg in real time based on the input from the sensors. By continuously monitoring and adjusting the robot’s movements, these systems enable the hexapod to move smoothly and efficiently over a wide variety of surfaces and terrains.
Hexapod and its applications
Hexapod robots, with their six legs and stable platforms, have found applications in various fields. One of the most promising areas is search and rescue, where hexapods can navigate difficult terrains and reach inaccessible areas to locate survivors in disaster situations.
These robots can also be used in agriculture for tasks such as monitoring crops, collecting data, and spraying pesticides.
In exploration, hexapods have been used to explore remote areas of the planet or other planets, such as the Mars rover.
Hexapods have also found uses in military and defense applications, such as reconnaissance and surveillance missions.
The versatility of hexapods makes them suitable for various industries, including manufacturing, mining, and transportation, to name a few.
References:
- Introduction to Robotics: Mechanics and Control by John J. Craig
- Robot Modeling and Control by Mark W. Spong, Seth Hutchinson, and M. Vidyasagar
- Robotics: Modelling, Planning, and Control by Bruno Siciliano and Lorenzo Sciavicco
- Inverse Kinematics tutorial by Khan Academy (https://www.khanacademy.org/computing/computer-programming/programming-robots/robotics/v/inverse-kinematics)
- Inverse Kinematics tutorial by Angela Sodeman (https://youtu.be/D93iQVoSScQ)
