Source-linked AI summary
Stair Climbing Stabilization of the HRP-4 Humanoid Robot using Whole-body Admittance Control
Stéphane Caron, Abderrahmane Kheddar, Olivier Tempier
TL;DR
Humanoid stair climbing is difficult to perform robustly and untethered in industrial environments. The paper extends DCM-based walking stabilization with quadratic-program wrench distribution and whole-body admittance combining end-effector and CoM strategies. HRP-4 dynamically climbed 18.5 cm industrial steps at Airbus Saint-Nazaire, with tracking improvements reported from combining the admittance strategies.
Problem
Untethered humanoid stair climbing remains rare, while industrial deployments require robust stabilization in environments shared with human coworkers.
Method
The controller combines DCM feedback, quadratic-program wrench distribution, and whole-body admittance acting through both end-effectors and the CoM.
Results
HRP-4 dynamically climbed an industrial staircase with 18.5 cm steps, reproducing the performance over two weeks and climbing without safety ropes in later experiments.
Takeaways & Limitations
Combining end-effector and CoM admittance strategies improved DCM and ZMP tracking in simulation and supported the demonstrated stair-climbing controller.
Takeaways & Limitations
The stabilizer has interacting gains, and unmodeled flexibility below the foot ankles and touchdown impacts remain future-work questions.
Abstract
from arXiv · showhide
We consider dynamic stair climbing with the HRP-4 humanoid robot as part of an Airbus manufacturing use-case demonstrator. We share experimental knowledge gathered so as to achieve this task, which HRP-4 had never been challenged to before. In particular, we extend walkingstabilization based on linear inverted pendulum tracking by quadratic programming-based wrench distribution and a whole-body admittance controller that applies both end-effector and CoM strategies. While existing stabilizers tend to use either one or the other, our experience suggests that the combination of these two approaches improves tracking performance. We demonstrate this solution in an on-site experiment where HRP-4 climbs an industrial staircase with 18.5 cm high steps, and release our walking controller as open source software.
I. INTRODUCTION
Humanoid stair climbing remains difficult to perform untethered in industrial environments, where robust stabilization is important for robot and coworker safety. This work combines DCM-based wrench control with simultaneous end-effector and CoM admittance strategies, and demonstrates the approach on HRP-4.
- Motivation: Industrial stairs are a key mobility challenge because they connect manufacturing work areas, while untethered humanoid stair climbing remains rare.Robust stabilization is needed to reduce fall risks in shared workspaces.
- Motivation: Existing position-controlled robots typically apply admittance control either at the end-effectors or at the CoM.The paper investigates applying both strategies simultaneously.
- Contribution: Preliminary stair-climbing simulations and experiments suggest that combining end-effector and CoM admittance improves tracking performance.
- Controller: The controller uses DCM feedback to compute desired contact wrenches and whole-body admittance control to realize them on a position-controlled robot.
- Demonstration: The demonstration targets dynamic stair climbing by HRP-4, which had not previously been shown climbing stairs dynamically, using 18.5 cm steps at Airbus Saint-Nazaire.The controller is also released as open-source software.
A. Linear Inverted Pendulum Mode
The Linear Inverted Pendulum Mode simplifies humanoid walking dynamics by assuming constant CoM height, enabling DCM-based stabilization around a walking-pattern reference. This simplification reduces available balance-recovery strategies and contact-wrench dimensions.
- Model assumptions: The Linear Inverted Pendulum Mode assumes constant CoM height above a horizontal surface, simplifying the Inverted Pendulum Mode dynamics.The model turns the variable scaling factor into a constant and characterizes the contact wrench by the ZMP position.
- Model assumptions: LIPM-based stabilization sacrifices height-variation recovery and reduces the contact wrench from six dimensions to two.These two force coordinates can control two position coordinates, such as horizontal CoM position or floating-base roll and pitch.
- DCM feedback: The DCM is defined as ξ = c + ˙c/ω and decomposes LIPM dynamics into coupled first-order systems.Controlling the DCM is sufficient for locomotion because the CoM converges to it without direct control.
- DCM feedback: An integral term removes steady-state error, while a derivative term can damp potential oscillations.The implementation uses a leaky integrator whose exponential moving average does not wind up by construction.
- DCM feedback: The commanded ZMP accounts for unmodeled admittance-control delay and is equivalent to a commanded net contact wrench.This links DCM feedback to the wrench target later realized by the whole-body controller.
- DCM feedback: DCM feedback combines walking-pattern feedforward with feedback correcting CoM position and velocity deviations from reference.The controller uses proportional feedback around the desired DCM and ZMP trajectories.
C. Contact Wrench Distribution
Contact wrench distribution allocates the DCM-derived net wrench among foot contacts while representing contact wrenches in suitable spatial frames.
- Contact wrench distribution: Foot-force control requires distributing the net wrench among contacts, unlike CoM admittance control that uses the net wrench directly.The stabilizer also saturates the DCM-derived wrench to respect feasibility constraints such as keeping the ZMP inside its support area.
- Contact wrench distribution: The distribution formulation uses spatial vector algebra to express the net and individual foot contact wrenches in inertial, sole, and ankle frames.Left and right foot wrenches are defined in both sole-center and ankle frames.
1) Constraints:
The wrench-distribution quadratic program enforces contact stability and minimum contact pressure, with constraints covering friction, support area, yaw moment, and contact switching behavior.
- Constraints: In double support, the wrench-distribution QP imposes contact-stability and minimum-pressure constraints at each contact.The minimum pressure threshold avoids sending low-pressure targets to the foot-force controller.
- Constraints: The 16×6 contact-wrench-cone matrix encodes Coulomb friction, center-of-pressure support area, and net yaw-moment boundaries.A small pressure threshold such as 15 N is selected through the resultant-pressure basis vector.
- Constraints: Low-pressure targets can make fixed-gain admittance control oscillate around contact switches.The minimum-pressure constraint addresses this behavior by avoiding such targets.
- Constraints: DCM feedback gains can be selected by pole placement using an estimate of admittance-control delay.The delay is treated as relevant when tuning the feedback response.
2) Costs:
The controller prioritizes realizing the desired net wrench, then reducing ankle torques and regularizing pressure transfer, while whole-body admittance realizes these force targets through position-controlled motion.
- Costs: The QP cost prioritizes matching the desired net contact wrench, then minimizing ankle torques and regulating the pressure ratio.The prescribed pressure ratio varies from ρinit ∈ {0, 1} at the beginning of double support to 1 − ρinit at its end.
- Costs: Pressure-ratio regularization smooths force-output discontinuities when contacts are added or removed.The cost weights approximate a lexicographic order: 10000 for net-wrench matching, 100 for ankle-torque minimization, and 1 for pressure ratio.
- Whole-body admittance: Whole-body admittance tracks DCM-derived and distributed force targets while following the walking pattern’s position targets.This controller provides the force-feedback layer for the position-controlled robot.
- Whole-body admittance: Ankle admittance control tracks a desired center of pressure using commanded ankle roll and pitch and measured contact wrench.The target CoP is supplied by the wrench-distribution QP; damping control is shorthand for first-order admittance control.
- Whole-body admittance: Higher CoP admittance gains make the foot roll or pitch faster in response to lateral or sagittal CoP deviations.The resulting angular velocities are clamped to 0.2 rad/s.
- Whole-body admittance: The CoP formulation remains meaningful when foot pressure-difference tracking is degraded, and it can be extended with integral and derivative wrench terms.Under accurate pressure-difference tracking, CoP and desired-torque formulations are equivalent.
B. Foot force difference control
Foot force difference control regulates relative foot pressure during double support and implicitly increases CoM compliance. This allows the robot to respond to lateral pushes by lifting the leg opposite the push, rather than only tilting its feet.
- Foot force difference control regulates pressure transfer by lifting the foot with excess pressure and lowering the other foot.Its damping term is tuned by the admittance gain Aδfz.
- The controller adds vertical drift compensation to recover the walking pattern’s average foot altitude.The compensation uses a frequency gain T_vdc^-1 set to 1 Hz in practice.
- The velocity formulation of foot force difference control is chosen for the inverse-kinematics implementation while preserving the position formulation’s behavior.
- Foot force difference control increases CoM compliance by lifting the leg opposite a lateral push, producing CoM displacement toward that leg.With foot damping control alone, the robot instead resists the push by tilting its feet.
C. CoM Admittance Control
CoM admittance control adjusts the commanded CoM acceleration according to the difference between measured and distributed ZMP. Combined with end-effector control, it improves DCM and ZMP tracking in step-climbing simulation.
- Admittance control at the CoM is distinguished from Honda’s model ZMP control because it applies CoM accelerations continuously rather than only after ZMP-constraint saturation.
- CoM admittance control adds a correction to feedforward CoM acceleration based on measured and distributed ZMP.The measured ZMP comes from the net contact wrench, while the distributed ZMP comes from the wrench-distribution QP.
- Higher CoM admittance gains make the CoM accelerate faster toward the measured ZMP and move it back toward the desired ZMP.
- In step-climbing simulation, combining CoM admittance with foot damping improves both DCM and ZMP tracking without apparent conflict with end-effector control.The comparison uses an 18.5 cm step and contrasts Acom,x = 0, Acom,y = 0 with Acom,x = 20, Acom,y = 10.
- Whole-body inverse kinematics simultaneously tracks contact, CoM, swing-foot, chest, pelvis, and joint-configuration tasks.The task list prioritizes foot contact, followed by CoM and swing-foot tracking, then posture and regularization objectives.
- The inverse-kinematics solver uses acceleration-based tracking laws for these tasks.
IV. EXPERIMENTS
The controller was implemented in the mc_rtc framework and tested on the HRP-4 humanoid robot.
- The controller was implemented in the mc_rtc framework and evaluated experimentally on the HRP-4 humanoid robot.
A. Demonstration environment
The on-site demonstration used a five-step Airbus factory staircase with 18.5 cm risers. HRP-4 dynamically climbed it repeatedly, while the controller tracked disturbances and met the robot’s real-time control budget.
- The Airbus demonstration staircase had five steps, each 24 cm long and 18.5 cm high.
- A cable-driven parallel robot served as a remotely operated safety crane during preliminary experiments with varying step heights.Four of its eight actuators were used, with cables attached to a shoulder-mounted holder.
- 18 s was the demonstrated climbing time, using 1.4 s single-support and 0.2 s double-support durations.
- DCM and ZMP tracking performance were reported for the factory-staircase climb.
- 1.0 ± 0.4 ms was the overall controller-cycle runtime, fitting within HRP-4’s 5 ms control loop.The inverse-kinematics QP took 0.4 ± 0.1 ms, and the wrench-distribution QP took 0.3 ± 0.1 ms during double support.
- Swing-foot clearance and CoM-height variations disturbed DCM and ZMP tracking during stair climbing.Delaying CoM lift mitigated the disturbance but increased knee torques.
C. Practicalities
The HRP-4 stair-climbing experiments combined simulation, hardware adjustments, and stabilization improvements to demonstrate dynamic climbing over 18.5 cm steps in an industrial setting. The reported system remains constrained to double-support stair climbing, with several stabilization and mechanical issues left for future work.
- Experimental tools: Choreonoid enabled fast, realistic controller testing that reproduced most phenomena encountered during physical trials.The authors report better realism and real-time performance than V-REP or Gazebo.
- Power and hardware: A 5 A power-supply current limit caused servo-off during the second, most knee-torque-intensive swing phase.After increasing the threshold, peak current reached up to 13 A and estimated peak power was around 750 W.
- Experimental boundary: The reported experiment used double-support phases at each step rather than the planned one-foot-per-step gait.A mechanical transmission issue prevented the right leg from reproducing the left-leg motions even at lower step heights.
- Prior stair-climbing results: Prior humanoid demonstrations covered smaller steps with HRP-series stabilizers or higher steps using slower, quasi-static, or paused motions.Examples include HRP-2 at 10 and 15 cm, HRP-4 at 24 cm without stabilization, and 23 cm steps during the DARPA Robotics Challenge.
- Experimental demonstration: 18.5 cm steps were climbed dynamically by HRP-4 at the Airbus Saint-Nazaire industrial site.The experiment applied the resulting stabilization controller in an industrial environment.
- Open issues: The stabilizer requires interacting gain tuning, while unmodeled ankle flexibility and touchdown impacts remain open problems.Lower foot CoP admittances permit higher DCM feedback gains before instability.
APPENDIX
The walking pattern generator uses a predictive quadratic program to shape ZMP and CoM behavior over a finite horizon, while state estimation supplies the floating-base and CoM quantities needed for control. Its objectives and constraints prioritize reference tracking, smoothness, and terminal consistency.
- Pattern-generation objective: The predictive QP minimizes weighted ZMP deviation, CoM velocity deviation, and CoM jerk.The respective weights are 1000, 10, and 1.
- Pattern-generation constraints: The QP constrains ZMPs to support polygons and imposes terminal ZMP and DCM consistency with the reference trajectory.The terminal conditions require both quantities to end on zideal(T).
- Prediction and reference update: T = 1.6 s is the predictive horizon, with a 100 ms sampling period.The predictive controller updates the CoM reference and its derivatives through open-loop integration.
- State estimation: A Kalman filter estimates floating-base orientation, an anchor-point assumption estimates translation, and forward kinematics derives CoM position from joint encoders.CoM velocity is obtained by low-pass filtering, while foot flexibilities are not yet included.