Task Prioritization

Ranking a robot's simultaneous goals by importance so lower-priority tasks can never disturb higher-priority ones.

Redundant robots — those with more joints than a task strictly needs, such as 7-axis arms or humanoids — often have to satisfy several goals at once: reaching a target, staying balanced, avoiding joint limits, keeping a natural posture. Task prioritization ranks these goals into a hierarchy. Yoshihiko Nakamura and colleagues proposed Jacobian-pseudoinverse-based task-priority redundancy control in 1987, and Bruno Siciliano and Jean-Jacques Slotine generalized it to an arbitrary number of tasks in 1991. The core formula is q̇ = J₁⁺ẋ₁ + (I − J₁⁺J₁)q̇₀: J₁ is the primary task's Jacobian (mapping joint velocity to task velocity), J₁⁺ is its pseudoinverse, and the term (I − J₁⁺J₁) projects the secondary task's desired joint velocity q̇₀ into the null space of the primary task, guaranteeing it can't disturb the primary task's result. This differs from a weighted sum of tasks, where the tasks compromise with each other — strict prioritization instead guarantees the higher-priority task always wins. Modern whole-body controllers commonly implement this with hierarchical quadratic programming, which can also handle inequality constraints.

ExampleA humanoid reaching for a cup: the first priority keeps its center of mass within the support region so it doesn't fall, the second priority moves the hand to the cup, and the third keeps the joints near a comfortable posture. When reaching for the cup conflicts with balance, the controller sacrifices some reaching accuracy rather than balance.

Also called

Prioritized Task Control, Task-Priority Control, Multi-Task Priority Control

Related

Null Space · Null-Space Control · Kinematic Redundancy · Jacobian Pseudoinverse · Hierarchical Quadratic Programming · Whole-Body Control

Sources

Nakamura, Hanafusa, Yoshikawa: Task-Priority Based Redundancy Control of Robot Manipulators (IJRR 1987)
Siciliano, Slotine: A general framework for managing multiple tasks in highly redundant robotic systems (ICAR 1991)