SOMA: Quadruped Robot Pushes Stacked Objects Without an Arm, Hits 90% in Simulation

A quadruped robot trained with hierarchical reinforcement learning can now locate, approach, and reposition stacked objects using only its body — no arm, no grasping, no leg-tip manipulation — while maintaining the stack's structural integrity at a 90.1% success rate, according to a new paper from the University of Delaware posted to arXiv.

The system, named SOMA (Stack-of-Objects Manipulation using a Quadruped Robot), tackles a problem central to robotic logistics: how to move unstable, multi-layer loads on a legged platform without a dedicated arm, which adds weight, mechanical complexity, and a potential single-point-of-failure that reduces the robot's operational range. In simulation, SOMA matches the stack-manipulation performance of arm-equipped mobile platforms at a fraction of the hardware cost — a comparison that directly challenges one of the default assumptions in warehouse robotics design.

Pushing in 3D Rather Than Across a Table

Most prior work on non-prehensile robot manipulation — moving objects without gripping them — has been confined to planar pushing: the robot and its payload remain at the same height while the robot nudges items laterally across a surface. That constraint reflects a hardware reality: a robot with no height-variable contact surface cannot change the geometry of its interaction with a stack, and so cannot influence whether the top object tips relative to the bottom.

SOMA breaks from that constraint with a single key mechanism: explicit control of the quadruped's base height during the manipulation task. By raising or lowering its body while pushing, the robot changes the contact angle against the stack, allowing it to steer upper objects independently from lower ones and suppress the relative sliding or tipping that causes stacks to fail mid-maneuver.

That capability matters in real warehouse or logistics settings, which are rarely flat and uniform. Stacks arrive at different heights, on uneven surfaces, and at varying orientations. A system limited to lateral contact has limited use against that variety; one that can adjust its contact geometry vertically is substantially more capable across the full range of conditions.

How the Hierarchical RL Framework Is Structured

SOMA uses a two-layer reinforcement learning architecture in which the levels of the hierarchy handle different timescales of the task.

The high-level policy is responsible for goal tracking. It receives observations about the target object's position and orientation and outputs commands that direct the robot toward the manipulation goal. Rather than producing raw motor signals, this policy generates bounded tracking commands enforced through Beta distribution outputs. Beta distributions naturally constrain their output to a defined interval, avoiding the hard-clipping operations that can destabilize RL training gradients when action bounds are imposed rigidly.

Temporal reasoning — the ability to integrate information across many prior time steps — is handled by an S5 encoder embedded in the high-level policy. S5, or Simplified Structured State Space Sequence, is a sequence model published at ICLR 2023 that extends earlier structured state space architectures by replacing many independent single-input/single-output systems with a single multi-input multi-output formulation, processed via efficient parallel scans. In long-horizon robot manipulation, this matters because the policy must reason about whether an approach is working not from a single frame but from the accumulated dynamics of many interaction steps — whether the stack is drifting, whether contact is being maintained, whether the robot's positioning is accumulating error. S5 provides that kind of compact long-range temporal memory without the gradient-vanishing problems that afflict standard recurrent networks on extended sequences.

The low-level policy handles locomotion, translating the high-level command stream into moment-by-moment leg stance adjustments. The Unitree Go1 platform used for hardware validation — a 12-kilogram robot with 12 degrees of freedom capable of up to 3.7 meters per second — must maintain stable footing while its body is actively repositioning to sustain pushing contact with a shifting stack. The two-policy design keeps that leg-control problem decoupled from the manipulation goal-tracking problem.

How SOMA Compares to Arm-Equipped Alternatives

In simulation, SOMA achieves 90.3% success for single-object repositioning tasks (position error below 5 centimeters and orientation error below one degree) and 90.1% success for dynamic two-object stacks where the upper object can shift relative to the lower during manipulation.

Those numbers sit close to the best available arm-equipped comparison, though the evaluation criteria differ. Dadiotis et al., publishing at ICRA 2025, reported 91.35% simulation success for a mobile manipulator — a legged robot carrying a dedicated robotic arm — on a related class of stack-manipulation tasks, measured at a position tolerance of 10 centimeters and orientation tolerance of 10 degrees. SOMA's thresholds are stricter: 5 centimeters for position and 1 degree for orientation. The roughly 1.2 percentage point difference in reported success rates therefore reflects non-equivalent criteria, and direct cross-system comparison requires caution.

Pedipulation, the approach of using leg-tip contact for fine manipulation, offers a separate arm-free path developed by ETH Zurich and others. But pedipulation requires precise foot placement near small objects and constrains the robot's locomotion posture while manipulating — it is a different capability than body-based pushing and is less suited to moving heavy or large payloads that exceed the force limits of leg-tip contact. Earlier non-prehensile systems such as HeRD operate in 2D simulation environments only, without the height-variable contact that SOMA's architecture provides.

Zero-shot sim-to-real transfer — policies trained entirely in simulation deployed directly to hardware without fine-tuning — was validated on the physical Unitree Go1 across a range of payload masses and geometries, confirming that the trained policies survive the reality gap for at least the tested conditions.

The Economic Argument for Arm-Free Manipulation

The case for an arm-free approach in logistics is direct: equipping a quadruped with a commercial robotic arm adds cost, weight, and a failure mode that reduces both locomotion range and operational uptime. For tasks bounded to repositioning — sorting, staging, retrieval from floor-level positions — an arm provides reach and fine-motor capability that the task does not require.

SOMA's body-based pushing also opens capability in spaces where arm-equipped robots cannot operate: narrow aisles, low-ceiling storage environments, and configurations where the arm's reach envelope conflicts with structural obstacles. A robot that uses its torso as the primary contact surface has a smaller and more predictable physical footprint, which matters in dense warehouse layouts designed before robotic manipulation was in scope.

Read more: Robot AI policies that fix their own hardware errors

Simulation Results, Stack-Scaling Limits, and What Comes Next

The paper's quantitative success rates are simulation-derived. The zero-shot hardware validation on the physical Unitree Go1 demonstrates policy transfer but does not provide equivalent quantitative success statistics for multi-object stacks specifically. Real-world contact dynamics — surface texture variation, vibration, material compliance in cardboard or plastic containers — are routinely underrepresented in simulation, and their effect on stack stability during body-based pushing is not yet characterized.

The current framework is also bounded to two-object stacks and geometrically regular payloads. Extending to three or more layers introduces a qualitatively harder problem: maintaining the structural integrity of intermediate stack elements requires coordinating contact with multiple surfaces simultaneously, a challenge the current hierarchical architecture does not address.

That limitation defines the clearest next research problem: whether body-height control and a deeper policy architecture can handle taller stacks, or whether the manipulation complexity of three-plus layers creates a natural boundary where even a lightweight stabilization end-effector becomes justified — not for grasping, but for suppressing upper-layer motion while the body pushes below. The answer to that question will determine whether whole-body pushing scales to the full range of warehouse stack configurations or remains a capable but bounded complement to arm-equipped manipulation.