Forward kinematics determines the end-effector position or pose from known joint values, while inverse kinematics finds joint values that achieve a specified end-effector state. Engineers use these complementary calculations to translate between task-space requirements and coordinated joint motion. Their results provide the basis for selecting feasible waypoints and generating movement that reaches the intended task states accurately.
Joint-space interpolation coordinates changes in individual joint variables, whereas Cartesian interpolation focuses on how the end effector moves through positions or poses. The choice depends on whether consistent joint coordination or task-space motion is more important. Comparing these approaches helps engineers produce motion that is smooth, accurate, and appropriate for operations such as assembly, machining, or welding.
Velocity and acceleration limits constrain how quickly joints and the end effector can move or change speed, while jerk limits control how abruptly acceleration changes. Applying these limits makes a planned motion more feasible and smooth. The resulting trajectory can reduce undesirable motion and support safer, more controlled operation when multiple joints move together.
Three important evaluation measures are tracking error, smoothness, and computational cost. Tracking error indicates how closely the robot follows the planned motion, while smoothness reflects the quality of changes in movement. Computational cost shows how demanding the planning method is. Considering all three helps engineers compare methods for precision, cycle time, and adaptability.
Engineers begin by specifying task positions or poses and identifying the states the robot must reach. They then apply forward or inverse kinematics, choose joint-space or Cartesian waypoints, and interpolate motion between those waypoints. Velocity, acceleration, and sometimes jerk limits are applied before evaluating tracking error, smoothness, and computational cost.
Planned motion supports accurate assembly, machining, welding, and material handling. In each case, coordinated joint movement helps the end effector reach required task states while limiting undesirable motion. Evaluating trajectory quality can guide improvements in precision, safety, cycle time, and adaptability, making trajectory planning relevant to both industrial robots and research platforms.