HMC-Policy: Meta-Control for Contact-Rich Robots

• HMC-Policy is a high-level meta-control policy that allocates heterogeneous low-level control modalities for contact-rich loco-manipulation.
• It integrates position, impedance, and hybrid force-position control via a soft routing mixture-of-experts to enable continuous torque-space blending.
• A two-stage training pipeline, combining large-scale position-only and scarce force-aware data, improves robustness and generalization in real-world tasks.

Searching arXiv for the HMC-Policy paper and closely related material. HMC-Policy is a policy architecture for contact-rich humanoid loco-manipulation that learns to allocate control authority across heterogeneous low-level control modalities rather than emitting a single monolithic action stream. In the formulation introduced in "HMC: Learning Heterogeneous Meta-Control for Contact-Rich Loco-Manipulation" (Wei et al., 18 Nov 2025), it is the learning component of a broader Heterogeneous Meta-Control framework, paired with HMC-Controller. The central premise is that contact-rich manipulation cannot be handled reliably by purely positional control alone, particularly under varying payloads, compliance requirements, and phase-dependent interaction dynamics. HMC-Policy therefore combines position, impedance, and hybrid force-position control within a mixture-of-experts-style routing architecture, trained from both large-scale position-only demonstrations and smaller force-aware datasets (Wei et al., 18 Nov 2025).

1. Conceptual definition and system role

HMC-Policy is the high-level policy layer in a two-part system composed of HMC-Policy and HMC-Controller (Wei et al., 18 Nov 2025). HMC-Policy predicts controller-specific actions together with routing weights, while HMC-Controller converts those heterogeneous controller outputs into executable torques and blends them in torque space. This division of labor is central to the method: the policy is not a direct torque policy in the usual end-to-end sense, but a heterogeneous control allocator over multiple control profiles (Wei et al., 18 Nov 2025).

The control profiles explicitly represented are position, impedance, and hybrid force-position control (Wei et al., 18 Nov 2025). This makes HMC-Policy a meta-control policy in the literal sense that it learns which control regime should dominate at each instant and to what extent. The paper frames this as an answer to a recurrent failure mode in real-world robot imitation learning: abundant demonstrations exist for position-only behavior, but contact-rich tasks often require controlled compliance and force regulation that purely positional policies handle poorly (Wei et al., 18 Nov 2025).

A plausible implication is that HMC-Policy should be understood less as a new low-level controller than as a structured policy layer for controller composition. The architecture is therefore closer to control-policy arbitration than to classical single-head behavioral cloning.

2. Control modalities and torque-space execution

HMC-Controller provides the execution substrate on which HMC-Policy operates (Wei et al., 18 Nov 2025). The paper defines several primitive controllers.

Pure position control uses a standard PD form:

$$\boldsymbol{\tau} = K_p (\mathbf{q}_d - \mathbf{q}) + D_p (\dot{\mathbf{q}}_d - \dot{\mathbf{q}})$$

Joint-space impedance control adds compliance and gravity compensation:

$$\boldsymbol{\tau} = K_q (\mathbf{q}_d - \mathbf{q}) + D_q (\dot{\mathbf{q}}_d - \dot{\mathbf{q}}) + \tau_{gravity}$$

Cartesian-space impedance control is given by:

$$\boldsymbol{\tau} = J^\top \left[ K_x (\mathbf{x}_d - \mathbf{x}) + D_x (\dot{\mathbf{x}}_d - \dot{\mathbf{x}}) \right] + \tau_{gravity}$$

Hybrid position-force control is defined as:

$$\boldsymbol{\tau} = J^\top \bigg[ S_p \Big( K_x (\mathbf{x}_d - \mathbf{x}) + D_x (\dot{\mathbf{x}}_d - \dot{\mathbf{x}}) \Big) + S_f (\mathbf{f}_d - \mathbf{f}) \bigg] + \tau_{gravity}$$

where $S_p$ and $S_f$ are selection matrices for the position-controlled and force-controlled subspaces (Wei et al., 18 Nov 2025).

The crucial systems-level choice is torque-space blending. HMC-Controller computes the torque command of each controller at the same timestamp and then combines them through a soft weighted average, followed by low-pass filtering for continuity and stability (Wei et al., 18 Nov 2025). If HMC-Policy predicts controller outputs $a_{t,i}$ and routing weights $g_{t,i}$, the blended action is:

$\hat{a}_t = \sum_{i=1}^{N} g_{t,i} \cdot a_{t,i}$

This is not hard switching between modes. The paper explicitly contrasts soft blending with discrete controller switching, which can induce torque discontinuities, unstable contacts, and unsafe interaction behavior (Wei et al., 18 Nov 2025). In that sense, torque-space blending is not merely an implementation detail; it is a core stability mechanism.

3. Policy architecture

HMC-Policy is formulated as a heterogeneous behavioral cloning system over trajectories

$\tau = \{(o_t, a_t, g_t)\}_{t=1}^T$

where $$\boldsymbol{\tau} = K_q (\mathbf{q}_d - \mathbf{q}) + D_q (\dot{\mathbf{q}}_d - \dot{\mathbf{q}}) + \tau_{gravity}$$0 contains multi-sensory observations, $$\boldsymbol{\tau} = K_q (\mathbf{q}_d - \mathbf{q}) + D_q (\dot{\mathbf{q}}_d - \dot{\mathbf{q}}) + \tau_{gravity}$$1 is a unified action vector spanning the attributes of all controller types, and $$\boldsymbol{\tau} = K_q (\mathbf{q}_d - \mathbf{q}) + D_q (\dot{\mathbf{q}}_d - \dot{\mathbf{q}}) + \tau_{gravity}$$2 is a soft routing state satisfying

$$\boldsymbol{\tau} = K_q (\mathbf{q}_d - \mathbf{q}) + D_q (\dot{\mathbf{q}}_d - \dot{\mathbf{q}}) + \tau_{gravity}$$3

(Wei et al., 18 Nov 2025).

A key representational device is the unified action vector. Controller-specific quantities such as end-effector commands, impedance stiffness values, and force vectors are embedded into a common action space, and irrelevant fields are zero-padded when a demonstration does not use them (Wei et al., 18 Nov 2025). This allows heterogeneous demonstrations to be consumed within a single supervised training objective.

The architecture contains four principal components (Wei et al., 18 Nov 2025):

1. A shared Transformer trunk. Visual and proprioceptive inputs are tokenized as

$$\boldsymbol{\tau} = K_q (\mathbf{q}_d - \mathbf{q}) + D_q (\dot{\mathbf{q}}_d - \dot{\mathbf{q}}) + \tau_{gravity}$$4

and passed to a Transformer trunk

$$\boldsymbol{\tau} = K_q (\mathbf{q}_d - \mathbf{q}) + D_q (\dot{\mathbf{q}}_d - \dot{\mathbf{q}}) + \tau_{gravity}$$5

2. Modality-specific expert heads, one per control profile:

$$\boldsymbol{\tau} = K_q (\mathbf{q}_d - \mathbf{q}) + D_q (\dot{\mathbf{q}}_d - \dot{\mathbf{q}}) + \tau_{gravity}$$6

These predict controller-specific action profiles.

3. A soft router:

$$\boldsymbol{\tau} = K_q (\mathbf{q}_d - \mathbf{q}) + D_q (\dot{\mathbf{q}}_d - \dot{\mathbf{q}}) + \tau_{gravity}$$7

The final action is then

$$\boldsymbol{\tau} = K_q (\mathbf{q}_d - \mathbf{q}) + D_q (\dot{\mathbf{q}}_d - \dot{\mathbf{q}}) + \tau_{gravity}$$8

4. A Whole-Body Control commander:

$$\boldsymbol{\tau} = K_q (\mathbf{q}_d - \mathbf{q}) + D_q (\dot{\mathbf{q}}_d - \dot{\mathbf{q}}) + \tau_{gravity}$$9

which outputs high-level whole-body commands such as base velocity, base height, and waist posture (Wei et al., 18 Nov 2025).

The mixture-of-experts character of the system is explicit, but unlike sparse MoE designs with hard gating, HMC-Policy uses soft routing throughout. The paper attributes to this choice improved continuity, better expert utilization under data imbalance, and more stable phase transitions in contact-rich tasks (Wei et al., 18 Nov 2025).

4. Training methodology

A defining feature of HMC-Policy is its two-stage training pipeline, introduced to handle the mismatch between abundant position-only demonstrations and scarce force-aware demonstrations (Wei et al., 18 Nov 2025).

In the first stage, the system is pretrained on large-scale position-only data. All expert heads except the positional expert and the WBC commander are frozen, and the loss is

$$\boldsymbol{\tau} = J^\top \left[ K_x (\mathbf{x}_d - \mathbf{x}) + D_x (\dot{\mathbf{x}}_d - \dot{\mathbf{x}}) \right] + \tau_{gravity}$$0

(Wei et al., 18 Nov 2025).

This stage is intended to give the shared Transformer trunk a strong positional prior and general task representations. In the second stage, all heads are unfrozen, the trunk is trained at a reduced learning rate, and the model is fine-tuned on force-aware and multi-controller demonstrations with the loss

$$\boldsymbol{\tau} = J^\top \left[ K_x (\mathbf{x}_d - \mathbf{x}) + D_x (\dot{\mathbf{x}}_d - \dot{\mathbf{x}}) \right] + \tau_{gravity}$$1

where $$\boldsymbol{\tau} = J^\top \left[ K_x (\mathbf{x}_d - \mathbf{x}) + D_x (\dot{\mathbf{x}}_d - \dot{\mathbf{x}}) \right] + \tau_{gravity}$$2 is a smoothed ground-truth routing label obtained by low-pass filtering teleoperated modality IDs (Wei et al., 18 Nov 2025).

This design addresses what the paper identifies as modality collapse: if trained naively on imbalanced data, the policy tends to converge toward positional behavior and underuse compliance-oriented experts (Wei et al., 18 Nov 2025). The two-stage scheme is reported to improve training stability, gradient flow to all experts, generalization to unseen objects and initial states, and avoidance of modality collapse (Wei et al., 18 Nov 2025).

This suggests that HMC-Policy is not just architecturally heterogeneous but also data-heterogeneity-aware. Its training procedure is a core part of the method, not an auxiliary engineering choice.

5. Task structure, demonstrations, and operational behavior

The demonstration corpus is itself heterogeneous. The paper distinguishes between large-scale position-only demonstrations, which are easier to collect, and fine-grained force-aware demonstrations, which are more difficult but essential for contact-rich behavior (Wei et al., 18 Nov 2025). The unified action space and zero-padding scheme allow both data sources to be incorporated into one imitation-learning pipeline.

Teleoperation is performed with OpenTV at 50 Hz, and a dashboard permits a second operator to switch control modes and adjust parameters such as stiffness online (Wei et al., 18 Nov 2025). The system does not require dedicated physical force sensors during teleoperation; instead, it uses a coarse online estimate of contact forces based on joint torques and position errors, visualized in the 3D scene (Wei et al., 18 Nov 2025).

The paper evaluates the method on a Unitree G1 humanoid robot with two 7-DoF arms, using an Intel RealSense D435i for vision and the Unitree SDK for proprioception (Wei et al., 18 Nov 2025). The benchmark tasks are all contact-rich:

• Wipe Table: requires regulated contact force to remove marker traces without unsafe over-force.
• Lift Bottle with Both Hands: requires stable frictional bimanual coordination and closed-chain interaction.
• Open Drawer: includes hand insertion into a narrow slot, followed by pulling against a magnetic latch, with substantial whole-body balance demands (Wei et al., 18 Nov 2025).

The drawer task is especially informative because it is explicitly multi-phase: insertion benefits from compliance, while pulling benefits from greater stiffness and force generation (Wei et al., 18 Nov 2025). This staged structure is aligned with the architecture’s routing mechanism, and the paper presents routing visualizations showing compliance during insertion and increased stiffness during pulling (Wei et al., 18 Nov 2025). This is offered as evidence that the learned routing is interpretable and phase-dependent.

6. Empirical results, ablations, and limitations

The paper compares HMC-Policy against several baselines: ACT (vanilla), ACT (meta), Stiff Policy, Compliant Policy, HMC w/o soft routing, HMC (from scratch), and the full HMC (ours) system (Wei et al., 18 Nov 2025).

The main success-rate results are as follows (Wei et al., 18 Nov 2025):

Method	Wipe	Lift	Drawer
Stiff Policy	33	67	80
ACT (vanilla)	33	60	40
ACT (meta)	47	67	47
HMC (w/o soft routing)	87	93	80
HMC (ours)	93	93	87

The paper states that experiments on a real humanoid robot show over 50% relative improvement vs. baselines on challenging tasks such as compliant table wiping and drawer opening (Wei et al., 18 Nov 2025). The tabulated results support that claim particularly for wiping and drawer opening, where purely position-centric baselines underperform.

The ablation studies emphasize three points (Wei et al., 18 Nov 2025). First, soft routing improves unseen generalization. For Lift Bottle, the full HMC system attains 93 seen / 80 unseen, compared with 93 / 53 for HMC without soft routing. For Open Drawer, the full method reports 87 / 67 unseen performance for both insertion and pull stages, while HMC without soft routing drops to 80 / 53 and 80 / 47, respectively (Wei et al., 18 Nov 2025). Second, pretraining matters: training from scratch underperforms the two-stage regime, especially on unseen settings. Third, single fixed-controller policies are insufficient for multi-stage contact tasks.

The interpretation offered is concrete. Hard argmax routing can produce abrupt force changes when contact state changes, such as slipping during bottle lifting because the expert transition is too sudden (Wei et al., 18 Nov 2025). Soft routing mitigates this by smoothing controller transitions. Likewise, the drawer task demonstrates why neither pure stiffness nor pure compliance is adequate across all phases (Wei et al., 18 Nov 2025).

The paper does not present an extensive formal limitations section, but several constraints are explicit or implicit (Wei et al., 18 Nov 2025):

• The method still depends on some controller-specific force-aware demonstrations.
• It requires routing supervision derived from smoothed controller IDs.
• The implemented expert set is limited to position, impedance, and hybrid force-position control.
• Teleoperation relies on estimated rather than dedicated force sensing.
• Evaluation is confined to a small set of real-robot contact-rich tasks.

A plausible implication is that scaling HMC-Policy to broader control libraries or longer-horizon task hierarchies would require additional routing structure and supervision schemes beyond those described in the paper.

7. Relation to surrounding research

HMC-Policy belongs to a line of work that embeds structured transformations or routing mechanisms inside larger control or sampling systems rather than treating the policy as a flat function approximator. In robotic control, its nearest point of comparison within the provided literature is not another locomotion method but the broader idea of embedding learned structure into an existing algorithmic substrate.

For example, "Neural Network Field Transformation and Its Application in HMC" (Jin, 2022) uses neural networks to construct constrained, differentiable, invertible gauge-field transformations for Hybrid Monte Carlo, with the aim of improving topological tunneling and reducing force-induced stiffness. The commonality is methodological rather than domain-specific: both approaches place learning inside a rigid algorithmic scaffold instead of replacing that scaffold outright (Jin, 2022).

Likewise, "HMC: Learning Heterogeneous Meta-Control for Contact-Rich Loco-Manipulation" (Wei et al., 18 Nov 2025) is architecturally close to mixture-of-experts systems, but its specialization lies in grounding the experts in physically interpretable controller profiles and executing their mixture in torque space. This distinguishes it from generic policy-mixture methods. The paper’s emphasis on continuous blending, controller-specific action parameterization, and phase-aligned routing suggests an intermediate position between imitation learning, whole-body control, and classical hybrid force-motion control (Wei et al., 18 Nov 2025).

In summary, HMC-Policy denotes a heterogeneous imitation policy that predicts both controller-specific actions and their soft composition over time. Its defining contribution is to couple a Transformer-based mixture-of-experts policy with torque-space controller blending so that a humanoid robot can exploit large-scale position-only demonstrations while retaining the capacity for compliant and force-aware behavior in contact-rich tasks (Wei et al., 18 Nov 2025).