💻 computer science

Partial Motion Imitation for Learning Cart Pushing with Legged Manipulators

This paper proposes a partial imitation learning framework that transfers a robust locomotion policy to legged robots for cart pushing by training a loco-manipulation policy to imitate only lower-body motions, thereby achieving stable and accurate mobile manipulation across diverse terrains and simulators.

Original authors: Mili Das, Morgan Byrd, Donghoon Baek, Sehoon Ha

Published 2026-03-30

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Mili Das, Morgan Byrd, Donghoon Baek, Sehoon Ha

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you have a four-legged robot dog that is also an arm. Your goal is to teach it to push a shopping cart down a hallway, following a specific winding path, without tripping over its own feet or dropping the cart handle.

This is a tricky job. If the robot focuses too much on pushing, it might stumble. If it focuses too much on walking, it might drop the cart. This paper presents a clever new way to teach the robot how to do both at the same time.

Here is the breakdown of their solution, using some everyday analogies:

The Problem: The "Too Many Cooks" Dilemma

Usually, when engineers teach robots new tricks, they use a method called "Reinforcement Learning." Think of this like training a dog with treats. You tell the robot, "Good job if you push the cart," and "Bad job if you fall."

But for a robot that has to walk and push, this is like trying to teach a dog to walk on a tightrope while juggling. If you just give it general instructions, it gets confused. It might learn to walk, but it will drop the cart. Or it might learn to push, but it will walk like a drunk penguin and fall over.

The Solution: The "Partial Imitation" Trick

The authors realized that walking and pushing are actually two different skills that need to happen at the same time. Instead of teaching the robot everything from scratch, they used a two-step "copycat" strategy.

Step 1: The Walking Master
First, they taught the robot only how to walk. They threw it into a virtual gym with slippery floors, uneven ground, and random bumps. The robot learned to walk perfectly, developing a smooth, stable "gait" (the rhythm of its steps).

Analogy: Think of this as training a professional dancer. They learn perfect balance, footwork, and rhythm on a stage.

Step 2: The "Lower-Body" Ghost
Next, they wanted the robot to push the cart. Instead of teaching it to walk and push all at once, they told the robot: "You don't need to learn how to walk again. Just copy the footwork of the Dancing Master you learned in Step 1. But your arms? Your arms are free to do whatever they need to do to push the cart."

They used a special AI tool called a "Partial Adversarial Motion Prior."

Analogy: Imagine the robot is wearing a "ghost suit" of the walking master. The ghost suit forces the robot's legs to move exactly like the master's legs. However, the robot's arms are not wearing the suit. The arms are free to reach out, grab the cart handle, and push. The robot doesn't have to worry about balance; the "ghost legs" handle that. The robot just focuses on the pushing.

Why This is Better Than Other Methods

The paper tested this against three other ways of training:

The "No Help" Method: Just telling the robot to push and walk without any copying.
- Result: The robot learned to push, but it walked like a drunk penguin. When they tried it in a different simulation (a different "world"), it fell over immediately.
The "Full Copy" Method: Telling the robot to copy everything the master does, including the arms.
- Result: This was too strict. The robot's arms were forced to stay in the exact position of the walking master, which meant it couldn't reach the cart handle properly. It was like trying to juggle while your arms are glued to your sides.
The "Hierarchical" Method: Using one brain for walking and a separate brain for pushing, but they don't talk to each other well.
- Result: It was okay, but when the robot slipped, the walking brain didn't know to adjust the pushing brain. It was like having a driver and a navigator who aren't on the same radio channel.

The Winner: The "Partial Imitation" method (the ghost suit for legs only) worked best. The robot walked with the stability of a pro dancer but used its free arms to push the cart smoothly.

The Results

They tested this in two different video game engines (IsaacLab and MuJoCo).

In the training world: The robot pushed the cart perfectly along winding paths.
In the new world (Sim-to-Sim transfer): When they moved the robot to a completely different physics engine (like moving a video game character from Mario to Grand Theft Auto), the other methods failed and fell over. The "Partial Imitation" robot kept walking steadily and pushing the cart, proving it learned a robust skill, not just a trick for one specific video game.

The Bottom Line

The paper shows that if you want a robot to do two hard things at once (walk and push), don't try to teach it everything from scratch. Instead, teach it one thing perfectly (walking), and then let it "borrow" that skill while it learns the new thing (pushing) on its own.

It's like hiring a professional walker to carry a heavy box. You don't teach the walker how to carry the box; you just let them walk their perfect walk while they figure out how to hold the box. The result is a stable, efficient, and successful delivery.

1. Problem Statement

The paper addresses the challenge of legged loco-manipulation, specifically the task of a quadrupedal robot with a mounted arm (legged manipulator) pushing a shopping cart along a predefined trajectory.

Core Difficulty: Learning a policy that simultaneously maintains stable locomotion on dynamic terrain and performs precise manipulation (maintaining contact with the cart handle) is difficult.
Limitations of Existing Methods:
- Pure Reinforcement Learning (RL): Requires extensive reward engineering and often leads to unstable locomotion or inefficient gait patterns when trying to learn both tasks from scratch.
- Full-Body Imitation: Standard adversarial imitation learning (imitating the entire robot state) is unsuitable because the optimal arm configuration for locomotion differs from the configuration needed to push a cart. Forcing the arm to mimic a reference locomotion policy constrains the manipulation task, leading to failure.
- Data Scarcity: High-quality reference datasets for legged loco-manipulation do not exist (unlike humanoid motion datasets).

2. Methodology

The authors propose a Partial Adversarial Motion Prior (Partial AMP) framework, which decouples locomotion style learning from manipulation adaptation. The training occurs in two stages:

Stage 1: Robust Locomotion Policy Training

Goal: Train a reference policy ( $\pi_{ref}$ ) to walk stably on rough terrain.
Setup: The robot (Unitree Go2 + WidowX arm) is trained in simulation (IsaacLab) using Proximal Policy Optimization (PPO).
Techniques: Extensive domain randomization (friction, mass, disturbances) and terrain randomization (rough terrain, slopes) are applied. The arm is kept in a neutral position or moved minimally to focus on leg stability.
Output: A robust locomotion policy that generates a dataset of state transitions ( $D_{ref}$ ) representing stable, cyclic walking gaits.

Stage 2: Partial Adversarial Motion Prior Training

Goal: Train the final loco-manipulation policy ( $\pi$ ) to push the cart while maintaining the stable gait learned in Stage 1.
Partial Imitation: Instead of imitating the full robot state, the authors introduce a projection function $\phi(\cdot)$ $ϕ (\cdot)$ that maps the state to a lower-dimensional representation containing only lower-body kinematics (base motion, hip/thigh/calf joint positions and velocities).
- Excluded: Arm joint states and end-effector states are excluded from the imitation signal.
Adversarial Training: A discriminator ( $D_\psi$ $D_{ψ}$ ) is trained to distinguish between the projected state transitions of the reference policy and the current policy.
- Style Reward: The discriminator output provides a "style reward" ( $r_{style}$ ) that encourages the lower body of the manipulator policy to mimic the stable gait of the reference.
- Task Reward: A separate reward ( $r_{task}$ ) is used for cart pushing (tracking velocity, maintaining contact, minimizing slip).
Final Objective: The policy is optimized to maximize the weighted sum of the task reward and the style reward. This allows the upper body to adapt freely to the cart while the lower body remains stable.

High-Level Control

To enable long-horizon path following, a Stanley controller (standard in autonomous driving) is used as a high-level planner. It generates velocity and yaw rate commands based on the cart's position relative to the desired path, which are then fed as inputs to the low-level learned policy.

3. Key Contributions

Partial Imitation Learning Framework: A novel approach that transfers locomotion styles from a simpler task to a complex loco-manipulation task by imitating only the lower-body motions, avoiding the constraints of full-body imitation.
Robust Sim-to-Sim Transfer: Demonstrated successful transfer from the training environment (IsaacLab) to a different physics engine (MuJoCo) without retraining, a significant challenge in legged robotics.
Comprehensive Baseline Comparison: The method is rigorously compared against:
- No Imitation (Pure RL).
- Full-Body AMP (Standard imitation).
- Hierarchical RL (Fixed lower body, learned upper body).
Stress Testing: Extensive evaluation under varying physical parameters (friction, mass, damping) showing superior robustness compared to baselines.

4. Experimental Results

The experiments were conducted on a Unitree Go2 quadruped with a WidowX arm pushing a cart.

Performance Metrics: Survival rate, tracking errors (linear velocity, angular velocity, heading), and end-effector (EE) errors.
IsaacLab (Training Env): All methods achieved high survival rates (~97-100%), but Partial AMP showed the most regular trotting gait and stable end-effector motion.
MuJoCo (Sim-to-Sim Transfer):
- Partial AMP (Ours): Achieved 94.4% survival rate with low tracking errors. It maintained stable trotting and consistent contact with the cart.
- No AMP: Dropped to 63.6% survival. The robot exhibited unstable "bounding" gaits and frequent foot slips.
- Full AMP: Performed worst (31.6% survival). Overfitting to the reference arm position caused the end-effector to lose contact with the cart handle.
- Hierarchical RL: Achieved 66.0% survival but failed to push the cart effectively due to the rigid lower-body policy.
Robustness: Partial AMP was the only method to satisfy success criteria (survival >30%, velocity error <0.5) across a wide range of randomized physical parameters (slide friction, mass scaling, wheel damping).
Path Tracking: The integrated system successfully tracked complex trajectories (BeatPath, RiverPath, SincPath) with mean cross-track errors ranging from 0.01m to 0.12m.

5. Significance

This work provides a scalable solution for mobile manipulation in unstructured environments. By recognizing that locomotion stability and manipulation flexibility have conflicting requirements, the authors successfully decoupled them using partial state imitation.

Practical Impact: The ability to push objects (like carts) is critical for warehouse logistics and retail automation.
Methodological Insight: The paper demonstrates that "full" imitation is not always better; selectively imitating specific body parts (lower body for stability) while allowing others (upper body) to learn via reward signals is a more effective strategy for complex whole-body control tasks.
Future Directions: The authors note that while the system is robust, it currently lacks visual feedback. Future work aims to integrate vision for obstacle avoidance and active contact recovery (re-grasping if the cart handle is lost).