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Whole-Body Control: Moving & Working Simultaneously

Duration: 60 min · Level: Advanced · Module: 3. Bipedal Locomotion & Whole-Body Control · Focus: WBC, loco-manipulation, control, QP

Learning objectives

By the end of this lesson you will be able to explain and apply:

  • WBC formulation
  • Task hierarchy example
  • Null-space projection
  • CMU loco-manipulation work (2023-2024)
  • Contact-consistent WBC

Why this matters​

Whole-Body Control (WBC) is the control framework that allows a humanoid to simultaneously maintain balance, walk, and use its arms for manipulation — treating all joints as a unified system.

Overview​

Whole-Body Control (WBC) is the control framework that allows a humanoid to simultaneously maintain balance, walk, and use its arms for manipulation — treating all joints as a unified system. It is the foundation of every useful humanoid task: you cannot fold laundry while standing if your arms and legs are controlled independently.

Key concepts​

Key idea

WBC formulation: hierarchical QP that solves for all joint accelerations simultaneously; high-priority tasks (balance) override low-priority tasks (arm motion) in null space

  • Task hierarchy example: (1) stay balanced, (2) maintain desired CoM trajectory, (3) track arm end-effector goal, (4) minimize joint torques — solved as cascaded QP
  • Null-space projection: arm movements that would disturb balance are projected into the null space of the balance task — arm can move without affecting CoM
  • CMU loco-manipulation work (2023-2024): humanoid carrying objects while navigating; WBC enables stable walking with 10kg payload in extended arms
  • Contact-consistent WBC: explicitly models foot contact forces as optimization variables; handles terrain with varying friction gracefully
  • Computational cost: full WBC QP for 40-DOF humanoid solves in ~0.5ms on modern CPU — fast enough for 2kHz control loop

Check your understanding​

Try to recall each answer before expanding it.

Q1. What do you know about WBC formulation?

hierarchical QP that solves for all joint accelerations simultaneously; high-priority tasks (balance) override low-priority tasks (arm motion) in null space

Q2. What do you know about Task hierarchy example?

(1) stay balanced, (2) maintain desired CoM trajectory, (3) track arm end-effector goal, (4) minimize joint torques — solved as cascaded QP

Q3. What do you know about Null-space projection?

arm movements that would disturb balance are projected into the null space of the balance task — arm can move without affecting CoM

Q4. What do you know about CMU loco-manipulation work (2023-2024)?

humanoid carrying objects while navigating; WBC enables stable walking with 10kg payload in extended arms

Q5. What do you know about Contact-consistent WBC?

explicitly models foot contact forces as optimization variables; handles terrain with varying friction gracefully

References​

  • Whole-Body Control of a Mobile Manipulator Using Hierarchical Tasks — Sentis and Khatib (2005). ICRA 2005
  • LOCO-MANI: Simultaneous Locomotion and Manipulation — Sleiman et al. (2023). ICRA 2023

← Previous: 3.3 Reinforcement Learning for Locomotion · Next: 3.5 Terrain Adaptation & Push Recovery →

Part of Module 3: Bipedal Locomotion & Whole-Body Control.