As we all know, many robot companies have launched seven-axis robotic arms

Why release a seven-axis robotic arm? The reason is simple, that is, six axes are enough.

It is also well known that one end posture of a general six-axis robot arm will correspond to several different sets of inverse solutions. However, these sets of inverse solutions are discretely distributed in the configuration space. In general, it is impossible to transform one set of inverse solutions to another set of inverse solutions while ensuring the end pose:

In other words, let the robot end follow a fixed trajectory. If there are some impassable points (obstacles, singular points, etc.) between the two points, then the six-axis robotic arm cannot complete this trajectory.

However, for the seven-axis manipulator, it has one more redundant degree of freedom, there is a continuous inverse solution of no array in the configuration space. In other words, it is possible to avoid singular obstacles while ensuring the end trajectory .

The answer to why make eight- nine-axis manipulators is simple. Seven-axis is enough in most cases. Adding joints will only reduce the rigidity of the entire mechanism.

In short, the seven-axis mechanical arm is a configuration that takes into account both flexibility stiffness. Coincidentally, the human arm also has seven degrees of freedom.

So, we have another question: Why don’t you start with seven axes at the beginning, but mostly start with six axes? The reason is probably because everyone thought that there was no analytical solution to the kinematics of the seven-axis robot arm.

We know that the bottom controller of the robot needs real-time trajectory interpolation. If the end trajectory is interpolated, the inverse kinematics solution needs to be calculated multiple times within a servo cycle (<1ms).

For the tandem manipulator, we may academically use various numerical solutions based on Jacobian iteration: