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Adaptive Whole-Body MPC with Optimal Posture Planning for Humanoid Robots under Unknown Payloads

Manh Cuong Nguyen, Duc Cuong Vu, Viet Anh Vu, Duc Tuan Pham, Toan Nguyen, Minh Hiep Phung, Ngo Anh Vien, Minh Nhat Vu

arXiv:2610.12972v1cs.RO

TL;DR

Humanoid lifting must preserve balance even when payload properties are unknown and alter system dynamics. The paper combines centroidal MPC, adaptive fuzzy torque compensation, and waypoint-based posture planning; simulation and hardware validations report balance maintenance across lifting and loco-manipulation scenarios.

  • Problem

    Humanoid robots must maintain balance while lifting payloads whose properties are not known in advance and can perturb robot dynamics.

    Source: §I · p. 1, B. Adaptive Fuzzy Control (AFC) for… · p. 3

  • Method

    The framework combines centroidal MPC and whole-body control with an adaptive fuzzy compensator and waypoint-based posture planning subject to CoM stability constraints and joint limits.

    Source: §I · pp. 1–2

  • Results

    MuJoCo and real-world validations across stationary lifting and dynamic loco-manipulation scenarios demonstrated the framework’s effectiveness in maintaining whole-body balance.

    Source: §VI · p. 8

  • Takeaways & Limitations

    In the 7 kg lifting-and-walking experiment, stable locomotion was maintained without retuning the fuzzy parameters for walking.

    Source: 2) Lifting and Walking · p. 8

    The current fuzzy logic is heuristic and reactive, motivating future work on learning-based optimization of compensation strategies.

    Source: §VI · p. 8

Abstract

from arXiv · show

Humanoid robots performing lifting and material-handling tasks must maintain balance despite unknown and varying payloads. However, payload uncertainty significantly affects whole-body dynamics and may destabilize conventional controllers. We propose an adaptive whole-body control architecture that integrates three components: (i) a centroidal model predictive controller (MPC) that generates dynamically feasible reference motions, (ii) an adaptive fuzzy balance controller that compensates for payload-induced model mismatch by generating corrective torques distributed across the supporting-leg joints, and (iii) a waypoint-based optimal posture planner built on a triple-integrator model that produces smooth sit-to-stand and stand-to-sit trajectories satisfying center-of-mass (CoM) stability constraints, joint limits, and whole-body feasibility requirements. Together, these components enable stable lowering, grasping, lifting, carrying, and placing behaviors under significant payload uncertainty. Extensive simulation and hardware experiments demonstrate that the proposed framework improves balance robustness and reduces tracking degradation during posture transitions and lifting tasks compared to non-adaptive baselines.

I. INTRODUCTION

Unknown payload properties complicate balance and whole-body coordination during humanoid lifting. The paper combines centroidal MPC, adaptive fuzzy compensation, and optimized posture transitions, then validates the framework in simulation and experiments.

I. INTRODUCTION

  • The illustrated task proceeds through lowering, grasping and lifting, walking while carrying the payload, and controlled placement.The figure describes pitch regulation during lowering and adaptive fuzzy control to constrain CoM deviation throughout the task.Source: Figure 1 · p. 1
  • Unknown mass distributions can alter robot dynamics and shift the CoM, while lifting posture transitions require complex whole-body coordination.The introduction identifies these uncertainties as sources of potential instability and as challenges for accurate modeling and control.Source: §I · p. 1
  • Adaptive fuzzy control generates compensation torques for CoM regulation and pelvic stability, while the posture planner produces smooth transitions subject to CoM stability and joint limits.The compensation torques are mapped to supporting-leg joints; the planner uses a triple-integrator waypoint model.Source: §I · p. 2
  • The proposed architecture integrates centroidal MPC with whole-body control and fuzzy regulation for stability under unknown and varying payloads.MPC generates dynamically feasible CoM motion and contact-force references; the whole-body layer tracks them under kinematic and dynamic constraints.Source: §I · pp. 1–2
  • The paper reports simulation and experimental validation of the proposed method.The introduction does not provide specific outcome metrics in these passages.Source: §I · p. 2

II. RELATED WORKS

The related-work discussion identifies gaps in posture-transition planning under uncertain payloads and in combining fuzzy compensation with predictive control. It then introduces the control architecture and robot dynamics model.

A. Posture transition for humanoid robot

  • Prior posture-transition work often focuses on locomotion or fixed payloads, leaving waypoint-based MPC planning under uncertain payloads comparatively underexplored.The stated gap concerns smooth, dynamically consistent posture transitions generated in real time.Source: A. Posture transition for humanoid robot · p. 2

B. Adaptive Fuzzy Control (AFC) for humanoid robot

  • Conventional fuzzy controllers offer robustness but lack predictive optimization and constraint handling, while MPC performance may degrade under significant uncertainty.The proposed AFC estimates torque compensation from tracking errors and augments nominal MPC output; its estimation-free rule base maps balance signals to bounded compensation moments without estimating payload mass.Source: B. Adaptive Fuzzy Control (AFC) for… · pp. 2–3

III. ADAPTIVE BALANCING FOR HUMANOID ROBOTS

  • The adaptive balancing section presents the fuzzy-based control framework and identifies its complete system structure in Fig. 2.Source: §III · p. 3

A. Robot Dynamics Modeling

  • The robot model represents a floating base and actuated joints, with rigid-body dynamics, contact wrenches, and holonomic contact constraints.The generalized configuration is partitioned into base and joint coordinates; contact interactions use a stacked contact Jacobian.Source: A. Robot Dynamics Modeling · p. 3

B. Centroidal Dynamics and Full Kinematics

The paper formulates centroidal dynamics using momentum and contact forces, then relates momentum to generalized velocity for planning.

B. Centroidal Dynamics and Full Kinematics

  • Centroidal dynamics are derived at the CoM, with linear and angular momentum represented alongside contact forces and moments, mass, and gravity.Contact positions are expressed relative to the CoM.Source: B. Centroidal Dynamics and Full… · p. 3
  • The centroidal momentum matrix maps generalized velocity to momentum, and the planning state and input comprise momentum and configuration, plus joint velocities and contact wrenches.Source: B. Centroidal Dynamics and Full… · p. 3

C. MPC-based Whole-body Control

The MPC plans motion over a prediction horizon subject to state and input constraints, while inverse dynamics computes joint torques to track the planned motion.

C. MPC-based Whole-body Control

  • The MPC optimization uses stage and terminal costs and state and input constraint sets to plan motion over a prediction horizon.The constraints include contact-wrench, foot-velocity, and joint position and velocity requirements.Source: C. MPC-based Whole-body Control · p. 3
  • Desired joint accelerations use proportional-derivative tracking of the planned joint motion before the corresponding torque command is computed.The floating-base acceleration is computed from the joint acceleration using the robot dynamics.Source: C. MPC-based Whole-body Control · p. 3
  • Inverse dynamics tracks planned accelerations and contact forces without an additional task-space quadratic program or task-weight tuning.The centroidal MPC already handles dynamic feasibility and contact constraints.Source: C. MPC-based Whole-body Control · p. 4

D. Adaptive Fuzzy Inference System

The adaptive fuzzy balance controller uses capture-point error, CoM velocity, and integrated error to estimate compensation moments, then allocates them to leg joints.

D. Adaptive Fuzzy Inference System

  • The controller computes compensation moments to reduce the error between the capture point and support-polygon center and allocates them to leg joints.The capture point is defined under the Linear Inverted Pendulum assumption.Source: D. Adaptive Fuzzy Inference System · p. 4
  • Each axis uses deviation, CoM velocity, and integrated error as fuzzy inputs, with anti-windup clamping to limit the accumulated error.The output is a pitch or roll compensation moment.Source: D. Adaptive Fuzzy Inference System · p. 4
  • The four-layer inference system uses Gaussian membership functions and five linguistic variables for each input.Its rule base has 125 rules per axis, indexed by deviation, velocity, and integral input.Source: D. Adaptive Fuzzy Inference System · p. 4
  • Rule firing strengths use a product t-norm, consequents include an integral effect, and defuzzification produces a scaled, saturated weighted average.The controller computes pitch and roll compensation moments independently.Source: D. Adaptive Fuzzy Inference System · p. 4
  • The hand-crafted symmetric rule base uses expert-tuned parameters shared across experiments, and quantitative comparison with PID is left for future work.The law is described as closely related to a saturated, gain-scheduled PID, with effective gains varying jointly with error, velocity, and integrated error.Source: D. Adaptive Fuzzy Inference System · p. 4

E. Torque allocation

The allocation scheme distributes compensation torque through stance-leg joints, mapping their joint torques to task-space torque at the pelvis.

E. Torque allocation

  • Compensation is applied through the legs because the arms hold the payload and corrective upper-body motion would disturb the grasp.Source: E. Torque allocation · p. 5
  • The additional stance-leg torque is applied to the low-level controller to enhance CoM-motion robustness and stability.Source: E. Torque allocation · p. 5
  • The mapping Ω(·) relates stance-leg joint torques to task-space torque at the pelvis during stance.The pelvis is treated as the end-effector for this mapping.Source: E. Torque allocation · p. 5

IV. OPTIMAL POSTURE-TRANSITION MOTION PLANNING

This section addresses motion generation for standing posture transitions, including standing up, sitting down, and leaning backward.

IV. OPTIMAL POSTURE-TRANSITION MOTION PLANNING

  • The posture-transition motion planner generates motions for standing up, sitting down, and leaning backward.Source: §IV · p. 5

A. Waypoint Model

The waypoint model represents a three-link planar robot with a discrete-time triple-integrator state and jerk inputs. Its state tracks joint positions, velocities, and accelerations.

A. Waypoint Model

  • The three-link planar robot’s generalized coordinates are the hip, knee, and ankle joint angles.Source: A. Waypoint Model · p. 5
  • A discrete-time triple-integrator model generates smooth joint trajectories using joint positions, velocities, and accelerations as its state.Source: A. Waypoint Model · p. 5
  • The model uses jerk as its input, with the Kronecker product denoted by ⊗.Source: A. Waypoint Model · p. 5

B. Pelvis posture selection mechanism

Pelvis posture selection searches for a feasible horizontal pelvis position for a desired height and pitch. The posture-transition planner then optimizes a smooth trajectory under joint and CoM stability constraints.

B. Pelvis posture selection mechanism

  • For a desired pelvis height and pitch, Algorithm 1 varies horizontal position within the support polygon until inverse kinematics returns a configuration within joint limits, or reports no feasible configuration.Source: B. Pelvis posture selection mechanism · p. 5
  • The inverse-kinematics solution uses a three-link planar robot model, with link lengths and hip-to-ankle distance defining its geometry.Source: B. Pelvis posture selection mechanism · p. 5

C. Posture-transition motion generation

V. EXPERIMENTAL RESULTS

In MuJoCo simulation, the proposed framework maintained whole-body equilibrium during unknown-payload lifting, whereas standard Centroidal MPC without adaptive balance control led to collapse. The experiments cover static lifting and dynamic lifting with load-carrying during locomotion.

V. EXPERIMENTAL RESULTS

  • The experimental platform is a 28-DoF humanoid with seven DoFs per arm and six per leg.Source: §V · p. 6
  • The control structure supports joystick-driven pelvis reference velocities and a separate mode for optimization-based posture transitions.Source: §V · p. 6
  • The centroidal MPC runs at 50 Hz, the adaptive framework at 500 Hz, and the low-level torque controller above 1 kHz.Source: §V · p. 6

A. Simulation validation

  • Without adaptive balance control, standard Centroidal MPC led to collapse under unknown-payload lifting; the proposed framework maintained equilibrium throughout the manipulation cycle.The framework combines compensation torques with feasible waypoints that proactively lower the CoM.Source: A. Simulation validation · p. 6

B. Experiment implementation

1) Lifting:

The lifting experiments report smooth 7 kg posture transitions and recovery to upright with a 10 kg payload, while a 7 kg lifting-and-walking trial maintained stable locomotion. Simulation and hardware validations support the framework’s balance performance across stationary lifting and dynamic loco-manipulation.

1) Lifting:

  • The 7 kg trial achieved smooth posture transitions, while the 10 kg trial required greater control effort, showed small initial oscillations, and returned to the nominal upright position.The 7 kg task included sitting, grasping, lifting, standing, and placing; the 10 kg task began with a bowing posture before grasping.Source: 1) Lifting · p. 6, Figure 7 · p. 7, Figure 8 · p. 7
  • In simulation, standard Centroidal MPC collapsed while Adaptive MPC with posture Transition Generation lowered the posture and maintained balance with an unknown heavy payload.The comparison attributes the standard controller’s failure to uncompensated added mass and the proposed approach’s balance to adaptive posture lowering.Source: Figure 6 · p. 7

2) Lifting and Walking:

  • With a 7 kg load, the robot walked stably for 15 seconds and completed the task; fuzzy parameters were not retuned for walking.The sequence included grasping, lifting, carrying, placing, and recovery to the home position.Source: 2) Lifting and Walking · pp. 7–8, Figure 9 · p. 7

VI. CONCLUSION

  • The conclusion reports balance validation in MuJoCo and on a real-world platform, and identifies learning-based compensation and proactive disturbance observers as future work.The architecture combines Optimal Posture Planning, Whole-Body MPC, and Adaptive Fuzzy Control.Source: §VI · p. 8
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