Matt Strong

Matt Strong

CS PhD at Stanford University

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PolyMorphWBC: Whole-Body Control from End-Effector Trajectories for Quadrupedal Mobile Manipulation across Arm Morphologies with Extended Reach

Heng Li, Yang Li, Yifan Duan, Ren Fang, Matao Duan, Wenhao Yu, Lu Zhang, Jianmin Ji, Yanyong Zhang

November 2026

TL;DR A learned hierarchy turns a short end-effector trajectory into coordinated arm and leg motion for a Go2 quadruped carrying arms from four kinematic families, including targets beyond the arm's fixed-base reach. On held-out arms and trajectories in IsaacLab it completes 93.95% of trajectories with 2.30 cm mean position error.

What they do

Visuomotor and VLA policies increasingly output short end-effector (EE) trajectories. On a quadruped with an arm, someone still has to decide when and how the base should move, and that depends on which arm is mounted. PolyMorphWBC takes the EE trajectory as its only task-level command and generates the base motion itself, with one learned controller reused across arms.

How it works

  • Hierarchy. A coordinator (10 Hz) reads a 1 s preview of 7 EE poses and outputs a base command: planar velocity, yaw rate, pitch and height offsets. Arm-specific IK tracks the current target, and a frozen PPO locomotion backend (50 Hz) produces the leg actions.
  • Morphology encoder. The arm’s URDF (joint frames, axes, limits, link masses and inertias) is encoded into an embedding pretrained to predict TCP position and the arm-induced wrench, then frozen. It conditions both coordinator and backend.
  • Residual-wrench feedback. The backend also sees the wrench computed from arm link masses and accelerations, plus a short history of how the base responded.
  • Training. IsaacLab, 1024 procedurally generated arms from four families (anchors: ARX X5, PiPER, compact xArm6, compact MICO) and 100k procedural trajectories.

Results

  • Held-out arms and trajectories: 93.95% completion, 2.30 cm and 4.81° mean error; 94.83% on trajectories reaching more than 1 m ahead of the starting base.
  • Anchor arms excluded from training: 99.30% (ARX X5), 99.27% (xArm6), 93.16% (PiPER), 86.62% (MICO) completion.
  • In MuJoCo against UMI-on-Legs: 1.38-2.04 cm and 2.01-2.38° error versus 4.77-7.31 cm and 22.72-76.57°.
  • Removing morphology conditioning cuts completion by 9.90 points (curved wrist) and 2.59 (offset wrist), under 1 point for the other two families.

Limitations

It assumes a known arm model, smooth low-speed EE trajectories and a single Go2 base. The hardware runs (teleoperation and pi0 pick-and-place on a Go2 with an ARX X5) are demonstrations without reported success rates, and contact-rich manipulation is left to future work.

Figures

From Figure 1: A shared control hierarchy maps short-horizon EE trajectories to arm and base motion. (a) The four rep...
From Figure 1: A shared control hierarchy maps short-horizon EE trajectories to arm and base motion. (a) The four representative arms have different fixed-base workspaces. (b) Base motion lets the EE follow trajectories beyond the arm's initial reach (schematic).
From Figure 2: (a) The coordinator turns an EE trajectory preview into a base command, arm-specific IK tracks the cur...
From Figure 2: (a) The coordinator turns an EE trajectory preview into a base command, arm-specific IK tracks the current target and the locomotion backend produces leg actions. (b) The morphology encoder is pretrained with kinematic and residual-wrench supervision, then frozen. (c) The backend is trained with PPO on sampled base commands. (d) The coordinator is trained last, with encoder and backend frozen.
From Figure 3: EE-trajectory tracking on Go2-ARX5 in MuJoCo for a vertical circle, vertical square, horizontal rectan...
From Figure 3: EE-trajectory tracking on Go2-ARX5 in MuJoCo for a vertical circle, vertical square, horizontal rectangle and horizontal base orbit. Black dashed: commanded; blue: PolyMorphWBC; orange: UMI-on-Legs. Arrows show the EE z-axis.
From Figure 4: Real-world runs on a Go2-ARX5. (a) EE-commanded teleoperation: straight arrows are the commanded EE mo...
From Figure 4: Real-world runs on a Go2-ARX5. (a) EE-commanded teleoperation: straight arrows are the commanded EE motion, curved marks the base motion the controller adds. (b) Extended-reach pick-and-place driven by pi0. Only EE motion is commanded in both.
Abstract

Quadrupedal mobile manipulators can extend their manipulation workspace by coordinating the mounted arm with the mobile base. At the task level, short-horizon end-effector (EE) trajectories provide an interface for specifying the desired manipulation motion without prescribing how it should be realized by the arm and base. However, executing such trajectories remains challenging because the controller must determine when and how the base should move, and this decision depends on the mounted-arm morphology. We therefore present PolyMorphWBC, a hierarchical controller that takes an EE trajectory as the sole task-level motion command and generates coordinated arm--base motions across four families of 6-DoF mounted arms, with extended-reach trajectories beyond the initial fixed-base reach. Within PolyMorphWBC, a trajectory-conditioned coordinator determines the base motion from previewed EE targets, while arm-specific Inverse Kinematics (IK) tracks the current target, and a frozen locomotion backend executes the resulting motion. Cross-arm reuse is enabled by a Unified Robot Description Format (URDF)-derived morphology conditioning, together with online residual-wrench feedback. We train PolyMorphWBC on procedurally generated arms and structured trajectories within and beyond fixed-base reach. In IsaacLab, it achieves 93.95% completion with 2.30cm position error and 4.81° orientation error on held-out trajectories and arm morphologies. In MuJoCo evaluation against UMI-on-Legs, PolyMorphWBC reduces EE position error by 69--72% and orientation error by 91--97% across four within- and extended-reach trajectories. On a physical Go2--ARX5 system, we demonstrate language-conditioned extended-reach pick-and-place using EE trajectories from pi_0 without vision-language-action (VLA)-generated base commands.

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