SOMA: Stack-of-Objects Manipulation using a Quadruped Robot

Stergios E. Bachoumas; Panagiotis Artemiadis

cs.ROOct 14, 2026

SOMA: Stack-of-Objects Manipulation using a Quadruped Robot

Authors: Stergios E. Bachoumas, Panagiotis Artemiadis

Abstract

Executing heavy-duty physical manipulation in unpredictable environments remains a major challenge for quadrupedal robots lacking dedicated manipulators. This paper presents SOMA, a hierarchical reinforcement learning framework for whole-body non-prehensile manipulation of multi-object stacks using a quadruped robot. Unlike traditional methods restricted to two-dimensional planar pushing, SOMA integrates explicit robot base-height control, unlocking full three-dimensional pushing strategies. This capability enables the quadruped to manipulate complex payload stacks as a unified system while preventing relative sliding or tipping of upper layers. The architecture factorizes control into a high-level manipulation policy using a Simplified Structured State Space Sequence (S5) encoder to reason over long-horizon temporal history and predict bounded target tracking commands via Beta distributions, and a low-level locomotion policy that dynamically adapts leg stance configurations. In extensive simulation benchmarks, SOMA achieves a $90.3\%$ success rate for single-object reposing and up to $90.1\%$ for dynamic two-box stacks under stringent error margins ( $0.05\text{ m}$ position error, $1^\circ$ orientation error). Finally, we validate zero-shot sim-to-real transfer on a Unitree Go1 quadruped robot across diverse payload masses and geometries, demonstrating active base-height adjustments to maintain traction and balance during heavy pushing tasks.

Figures & tables

Fig. 1 : Overview of SOMA : A quadrupedal robot performing non-prehensile push manipulation on a multi-body stack of independent, unattached objects. SOMA reasons about contact height and physical parameters to push stacked payloads without destabilizing them during movement.

Component	Mathematical Formulation	Weight ( $w$ )
$r_{\text{dist,rb}}$	$\exp(-\lVert\mathbf{p}_{R}-\mathbf{p}_{B}\rVert_{2}/\sigma_{r})$	$0.25$
$r_{\text{dist,bg}}$	$\exp(-\lVert\mathbf{p}_{G}-\mathbf{p}_{B}\rVert_{2}/\sigma_{g})$	$2.0$
$r_{\text{orient,bg}}$	$\exp(-\|\tilde{\psi}\|/\sigma_{\psi})\cdot\mathbb{I}_{\lVert\mathbf{p}_{G}-\mathbf{p}_{B}\rVert\leq 0.1}$	$10.0$
$r_{\text{push}}$	$\exp\left(\mathbf{r}_{x}\cdot\mathbf{v}_{B}-1\right)\cdot\delta_{BG}$	$500.0$
$r_{\text{success}}$	$\sum_{k=1}^{3}w_{\text{stage},k}\mathbb{I}_{\|\tilde{\psi}\|\leq\|\tilde{\psi}_{k}\|}\cdot\mathbb{I}_{\lVert\mathbf{p}_{G}-\mathbf{p}_{B}\rVert\leq\tilde{d}_{k}}$	$0.1$
$r_{\text{rate}}$	$\sum_{k=1}^{12}w_{\text{rate},k}(\mathbf{a}_{k,t}-\mathbf{a}_{k,t-1})^{2}$	$-0.001$

TABLE I : Reward and Penalty Formulations and Weights

Fig. 2 : Manipulation success rate across varying box heights and widths for a $12\,\text{kg}$ payload. The policy maintains a $\sim 90\%$ success rate across mid-range geometries. Performance drops to $82\%$ for tall, narrow boxes prone to tipping, while wider bases sustain the $90\%$ success rate due to increased stability against overturning moments.

Fig. 3 : Manipulation success rates across varying box dimensions ( $0.3^{3},0.4^{3},0.5^{3}\,\text{m}$ ) and masses ( $4,8,12\,\text{kg}$ ) under strict convergence criteria ( $\tilde{\psi}<1^{\circ}$ heading error, $\tilde{d}<0.05\,\text{m}$ position error). The proposed S5 SOMA framework (blue) consistently outperforms baseline models (MLP, GRU, and S5), demonstrating superior out-of-distribution generalization.

Side length (m)	$M_{\text{bot}}\ \|\ M_{\text{top}}$ (kg)	%Success	%StackFail	%Other
$0.3$	$4\ \|\ 4$	72.4	12.1	15.5
	$6\ \|\ 4$	71.4	9.1	23.5
	$\mathbf{8\ \|\ 4}$	77.5	4.9	17.6
$0.4$	$4\ \|\ 4$	80.1	7.6	12.3
	$6\ \|\ 4$	87.1	2.7	10.2
	$\mathbf{8\ \|\ 4}$	90.1	1.0	8.9

TABLE II : Termination analysis for the two stacked boxes push experiments.

Fig. 4 : Robot validation of SOMA double-stack loco-manipulation. ( Top & Middle ): Execution sequence showing initial approach ( $0\text{--}9\,\text{s}$ ), base-object contact alignment ( $15\,\text{s}$ ), stack relocation ( $23\,\text{s}$ ), fine correction ( $29\,\text{s}$ ), and task completion ( $32\,\text{s}$ ). ( Bottom left ): Base-object positional error converging below $0.05\,\text{m}$ in all four trials. ( Bottom center ): Yaw error converging within $\pm 5^{\circ}$ . ( Bottom right ): Active base-height lowering during contact pushing to maximize contact stability.

Experiment Type	Side Length ( m )	$M_{\text{bottom}}\mid M_{\text{top}}$ ( kg )
Small Box	$0.3\mid-$	$4\mid-$
Big Box	$0.4\mid-$	$6\mid-$
Double Stack 1	$0.3\mid 0.3$	$4\mid 2.5$
Double Stack 2	$0.4\mid 0.3$	$6\mid 2.5$
Double Stack 3	$0.4\mid 0.3$	$6\mid 4$

TABLE III : Stack object size and mass configuration for each experiment conducted.

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Legged manipulators extend robotic capabilities beyond static manipulation by integrating agile locomotion with versatile arm control. However, achieving precise manipulation while maintaining coordinated locomotion remains a major challenge. This work presents a hierarchical reinforcement learning framework for dynamic pick-and-place tasks using a quadruped equipped with a 6-DOF robotic arm. The framework incorporates an explicit mass estimation module enabling adaptive whole-body control for objects with varying weights. In simulation, the system achieves an 86.05% success rate with payloads up to 2.3 kg. The approach is further validated through real-world experiments across six representative scenarios with controlled variations in object physical properties (size and mass) and task heights. Specifically, within a wide vertical workspace ranging from ground level to 1.1~m-high tabletops, the system demonstrates an average success rate of 73.3% for payloads up to 1.3 kg, with an average execution time of 4.06 s. Unlike prior works that handle lightweight objects and execute pick-and-place motions with slow, piecewise motions, the proposed framework exploits concurrent locomotion and manipulation for dynamic, continuous execution. These results demonstrate the potential of quadrupedal mobile manipulators for adaptive, whole-body pick-and-place with heavier payloads and extended workspaces.

Moonkyu Jung, Jiseong Lee, Zhengmao He +8

Robotics and Artificial Intelligence Lab, KAIST, Daejeon, South Korea · Thrust of Robotics and Autonomous Systems, The Hong Kong University of Science and Technology (Guangzhou), Guangzhou, China

Mobile Manipulation Whole-Body Control Robotic Manipulation

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Oct 5, 2026

Transporting Unsecured Stacked Payloads with a Quadrupedal Robot via Multi-Objective Reinforcement Learning

Transporting unsecured payloads with legged robots over uneven terrain requires balancing locomotion performance and payload stability, since aggressive motion can destabilize the payload even when the robot remains stable. We study quadrupedal transportation of unsecured stacked boxes on an edgeless torso-mounted board without dedicated payload sensors or active carrier mechanisms. To address this trade-off, we propose Payload-Adaptive Multi-Objective Reinforcement learning for Transportation (PAMORT). PAMORT trains a multi-objective base policy conditioned on a preference vector that weights locomotion and payload-stability reward groups, then trains a weight adjuster on the frozen policy to adapt this preference online from proprioception. In simulation, PAMORT achieves comparable or better overall transportation success than a corresponding single-objective baseline across different payload configurations, including an unseen three-box stack, despite training only with two boxes. Real-world experiments on a Unitree Go2 demonstrate zero-shot transfer to slopes and steps at or beyond the training difficulty, with mean success rates of 0.850 for PAMORT and 0.675 for the baseline across eight tasks. These results demonstrate robust unsecured-payload transportation with online adaptation of the locomotion--payload trade-off from proprioceptive information.

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Fujitsu Limited, Kawasaki, Japan

Multi-Objective Reinforcement Learning Robot Policy Adaptation Robotics RL for Legged Locomotion Quadruped Locomotion

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Oct 16, 2026

Reinforcement Learning Based Multi-Terrain Adaptive Whole-Body Control for a Quadruped Manipulator

Legged robots equipped with manipulators offer promising capabilities for loco-manipulation tasks in unstructured environments. However, achieving task-consistent end-effector behavior during locomotion remains challenging due to terrain-induced disturbances and the strong coupling between locomotion and manipulation, particularly for small-scale quadruped platforms. A reinforcement-learning based whole-body control framework is proposed for quadruped loco-manipulation on complex terrain. The proposed framework combines a hybrid task representation with task-prioritized whole-body learning to coordinate locomotion and manipulation while preserving task-consistent end-effector behavior. A lightweight quadruped manipulator platform is further developed to validate the proposed framework on a small-scale quadruped system. Real-world experiments demonstrate successful deployment on complex terrains such as slopes up to 30 degrees, stairs, and deformable terrain. These results demonstrate the feasibility of deploying learned whole-body control policy for quadruped loco-manipulation in real-world environments and highlight the importance of task-consistent whole-body coordination for terrain-adaptive loco-manipulation.

Yanzhou Jin, Fei Suo, Chang Liu +5

Graduate School of Engineering, The University of Tokyo, Japan. · Department of Micro-Nano Mechanical Science and Engineering, Nagoya University, Nagoya, 464-8603, Japan. · Department of Mathematics and Informatics, Ecole Centrale de Lyon, France.

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Abstract

Non-Prehensile Robotic Manipulation

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