When we use our arms we don’t consciously think about the type of motion we use to reach above our head or open a door. The motion starts automatically when our brain aims at a target. Controlling a robot arm is different: A robot’s motions are mathematically calculated, and each type of movements must be purposefully selected when programming or ‘jogging’ a robot.

The fundamental types of robot motions are Joint, Linear, and Circular moves. They are the most basic and simplistically defined, while some robot controllers support other definitions, such as spline motions which involve more complex curves, or combined linear and circular motions like a drilling operation.

Joint moves are defined in the so-called Joint space (details below) and the other two in the Cartesian space. Joint motions are not controlled moves, where Cartesian motions follow trajectories defined in the Cartesian space. Let’s explore these types of motions and the differences between Cartesian space and Joint space in robotic control.

1. Joint Motion

A joint motion, sometimes referred to as Point-to-Point motion, is defined in a robot’s Joint space. This means the robot moves its joints independently to achieve a target position. It’s an easier way for robots to move, as each joint just achieves its own goal while all of them move simultaneously. The robot decides which trajectory to use for this type of motion, and the trajectories can look unnatural in the Cartesian space we perceive them. As long as the joint limits are respected, reaching any target is guaranteed in this space. For a 6-axis manipulator arm, the end-effector trajectory curves because of the revolving joints, and the robot performs better in speed compared to a linear move. The drawback is that the trajectory can be unpredictable unless only one joint is used.

2. Linear Motion

A linear motion is defined in the Cartesian space and it requires the end-effector to follow a straight line for a certain displacement. We have explained that Cartesian or gantry robots are designed to make linear moves along the X, Y, and Z axes, and this is in 3 degrees of freedom (DoFs) defined by the (X, Y, Z) coordinates. For a 6-axis robot arm, the end-effector is able to move in 6 degrees of freedom (DoFs) achieving a position as well as an orientation in 3D. This type of motion requires multiple joints to move in coordination. Each joint contributes to positioning the end-effector to follow a linear path and reaching a 6DoF target at the end. The speed of linear moves may be affected or limited by the mechanical design of a robot.

3. Circular Motion

A circular motion requires a robot’s end-effector to follow a circular trajectory. The motion can be along part of or a complete circle, and it is used in operations where a controlled curve is required. Circular motions, like linear motions, are also defined in the Cartesian space and require coordination of multiple joints to maintain a smooth end-effector trajectory. For 6DoF robot arms, performing a circular move also means that the end-effector can turn or rotate its orientation, as well as following a circular path. An auxiliary point is needed to define the curvature of a trajectory.

Cartesian Space vs Joint Space

Robots can operate within two types of coordinate spaces: Cartesian space and Joint space. The 3D Cartesian space is defined by a Cartesian coordinate system where a robot can translate its end-effector position linearly (defined by X, Y, and Z coordinates) and rotate its end-effector orientation (generally defined by roll, pitch, and yaw parameters) in any direction. Movements and targets have up to 6 DoFs in this 3D space.

Joint space refers to the motion of robot joints collectively, each of which has its own range of motion between minimum and maximum limits. When a robot moves in this space, the joints move independently. The DoFs in a Joint space equal the number of joints or axes a robot has. So a 6-axis robot also has 6 degrees of freedom in Joint space (as well as in Cartesian space), and a target is defined by the values for each joint, from J1 to J6.

Robot Configurations

When we control a robot we must pay attention to robot configurations. They refer to the mechanical arrangements of a robot’s joints and segments at any target pose. For example, the below two configurations of a 6-axis robot arm result in the same target pose, that is, the same end-effector position and orientation in 3D.

This happens when a 3D target is defined in the Cartesian space, with X, Y, Z, roll, pitch, and yaw parameters, but not in a robot’s Joint space. We have mentioned that when a robot performs a joint motion, the trajectory can be unpredictable. This is because the robot can end up in one of the multiple configurations when each joint moves to its goal, perhaps choosing the most convenient route, with no regard to any configuration ‘limit’. Traditionally, linear motions do not have the multi-configuration problem but this has changed (for a reason) – we’ll explain this in our next blog on robot singularities.

For a 6-axis robot arm, there are typically 8 configurations for any target pose. It is important to manage configurations when we control or program a robot. Selecting a stable configuration helps to avoid abrupt moves that could disrupt the task or even be dangerous to the surrounding environment.

Have you ever experienced this kind of behaviour when controlling a robot? Moving to a point only a small distance away suddenly causes a change of configuration. See in the picture the robot has chosen to travel a long way to reach a nearby target.

To summarise, we have compiled a list of useful statements below. For a 6-axis robot arm:

• When a target is defined in 3D Cartesian space, there can be multiple robot configurations for this target.
• There can be only one configuration if a target is defined in the Joint space.
• When a robot performs a joint move, its configuration can change during the move.
• When a robot performs a linear move, reaching a ‘within range’ target may be impossible because the robot controller does not allow the change of configuration.

Conclusion

Controlling and programming an industrial robot involves selecting the appropriate motion type depending on the task. While joint moves can offer speed and simplicity (note: ‘simplicity’ from a robot’s point of view), linear and circular moves give strict path control required for most automation tasks. Understanding the differences between these motion types and spaces is key to optimising the performance and accuracy of industrial robots, ensuring that they perform efficiently in various manufacturing or automated environments.