CoopPush: Multi-Domain Cooperative Approaches

• CoopPush is a term describing cooperative coordination challenges across domains, including RL benchmark environments, multi-robot pushing, LLM-guided contact selection, and IoT communication.
• In reinforcement learning settings, CoopPush benchmarks isolate state-dependent inter-action dependencies using factored multi-head action spaces that require coordinated particle movements.
• In robotics and IoT, CoopPush frameworks tackle hybrid control and resource allocation challenges to ensure efficient, seamless multi-agent cooperation under shared constraints.

Searching arXiv for "CoopPush" and closely related papers to ground the article. “CoopPush” is not a single, universally fixed technical term in the arXiv literature. Recent usage spans several distinct problem classes: a lightweight benchmark environment for complex-action reinforcement learning, a collaborative planar pushing framework for multi-robot manipulation, an LLM-guided method for contact-point selection in cooperative object transport, and a frame-level coexistence model for pull and push communication in IoT access (Flavin et al., 25 Jun 2026, Tang et al., 2024, Steinkrüger et al., 9 Oct 2025, Cavallero et al., 2024). This suggests that the term functions less as a standardized acronym than as a recurring label for cooperative systems in which coordinated action is necessary to achieve a shared objective.

1. Terminological scope and principal usages

The main recent usages of “CoopPush” are technically heterogeneous. In one line of work, it is a controlled benchmark designed to isolate state-dependent inter-action dependence in factored action spaces. In another, it denotes the broader robotics problem of multiple robots pushing a common object through clutter. In a third, it is associated with contact-point selection for cooperative pushing along a preplanned path. In a fourth, it appears as a natural label for cooperative coexistence of pull-based and push-based wireless access modes (Flavin et al., 25 Jun 2026, Tang et al., 2024, Steinkrüger et al., 9 Oct 2025, Cavallero et al., 2024).

Usage	Domain	Core object
CoopPush benchmark	RL / action factorization	Cooperative push environment with particles, boulders, and landmarks
Cooperative planar pushing	Multi-robot manipulation	Hybrid planning and control for polytopic objects
ConPoSe for cooperative pushing	Multi-robot transport	LLM-guided contact-point selection
Pull/push coexistence	IoT wireless access	Shared slotted frame for WuD queries and push traffic

A plausible implication is that “CoopPush” should be interpreted contextually rather than canonically. In the RL paper, it is an environment name. In the robotics papers, it refers to cooperative pushing as a physical transport problem. In the IoT paper, it refers to a coexistence framework in which “pull” and “push” communication share the same frame resources.

2. CoopPush as a benchmark for factored action spaces

In “Revisiting Action Factorization for Complex Action Spaces” (Flavin et al., 25 Jun 2026), CoopPush is one of two new benchmark environments introduced to isolate “particular challenges such as state-dependent inter-action dependence.” The environment contains three entity types—particles, boulders, and landmarks—and particles must push boulders because boulders do not move by themselves. Reward is obtained when a boulder overlaps a landmark it has not visited before. The paper describes both sparse goal reward and dense shaping based on the change in distance between each boulder and its nearest unvisited landmark.

The state is fully observable and concatenates all entity positions,

$s \in \mathbb{R}^{2(N_p + N_b + N_l)}.$

The paper explicitly notes that, despite its cooperative interpretation, the environment is treated as a single-agent MDP with a high-dimensional, multi-head action space, because full observability collapses the cooperative Dec-POMDP formulation to a standard MDP (Flavin et al., 25 Jun 2026).

The action space is provided in continuous, discrete, and hybrid forms. In the continuous version, each particle takes a 2D action

$(\delta_x, \delta_y) \in [-1,1]^2,$

with movement capped at magnitude $1.0$. In the discrete version, each particle chooses among 9 discrete actions: no-op and 8 directions. For Default CoopPush, the paper studies

$$\mathcal{D}_9 \times \mathcal{D}_9 \times \mathcal{D}_9 \times \mathcal{D}_9,$$

$$\mathcal{D}_9 \times \mathcal{D}_9 \times \mathbb{R}^2 \times \mathbb{R}^2,$$

and

$$\mathbb{R}^2 \times \mathbb{R}^2 \times \mathbb{R}^2 \times \mathbb{R}^2.$$

For Independent CoopPush, the corresponding spaces are

$\mathcal{D}_9 \times \mathcal{D}_9,$

$\mathcal{D}_9 \times \mathbb{R}^2,$

and

$\mathbb{R}^2 \times \mathbb{R}^2.$

A central design feature is the presence of two layouts, Default and Independent. In the Independent setting, there is not enough time to push the other particle’s boulder, so the optimal action for one particle is mostly independent of the other particle’s behavior. In the Default setting, interactions matter: if the left particles are pushing a boulder to the right, the right particles should move out of the way rather than obstructing progress. The environment can also emphasize continuous precision by adjusting δ_t and num_physics_steps; lower control frequency and more physics steps make precision-based continuous control more valuable (Flavin et al., 25 Jun 2026).

CoopPush is used in a cross-sectional study spanning PPO, SAC, and DQN across multiple factorization methods, including independent networks, shared encoder, VDN, QPLEX, Joint, and Auto-Regressive. The paper’s broad conclusion is that factorization strategy matters more than whether the action space is discrete, hybrid, or continuous. It further reports that VDN-PPO and PPO-MIX, which use a branching critic to assign credit to multi-headed PPO, out-perform all other tested PPO factorizations, while auto-regressive action factorization reaches the highest performance overall. Native continuous SAC outperforms discrete and hybrid algorithms, albeit at increased computational cost (Flavin et al., 25 Jun 2026).

3. CoopPush as collaborative planar pushing in cluttered scenes

In “Collaborative Planar Pushing of Polytopic Objects with Multiple Robots in Complex Scenes” (Tang et al., 2024), “CoopPush” refers to a complete collaborative pushing framework for moving a polygonal object through a cluttered 2D environment with multiple mobile robots. The object and obstacles are known a priori, the robots are homogeneous, and the object must remain collision-free together with the robot team. The paper emphasizes two main difficulties: hybrid switching among different contact modes and under-actuation due to constrained contact forces.

The contact-force constraints are stated as

$$0 \le f_n^{n} \le f_{n,\max}, \qquad 0 \le |f_n^{t}| \le \mu_c f_n^{n},$$

which induce a mode-dependent feasible wrench set. Under a quasi-static assumption, the object dynamics are written as

$(\delta_x, \delta_y) \in [-1,1]^2,$0

with

$(\delta_x, \delta_y) \in [-1,1]^2,$1

and the equilibrium condition

$(\delta_x, \delta_y) \in [-1,1]^2,$2

To evaluate whether a desired generalized velocity is feasible under a mode $(\delta_x, \delta_y) \in [-1,1]^2,$3, the paper defines

$(\delta_x, \delta_y) \in [-1,1]^2,$4

If $(\delta_x, \delta_y) \in [-1,1]^2,$5, the motion is feasible.

The framework has three principal components. First, it uses multi-directional feasibility estimation, checking not only a desired velocity but a set of six directions in velocity space and aggregating them through

$(\delta_x, \delta_y) \in [-1,1]^2,$6

Second, it employs a keyframe-guided hybrid search algorithm, KG-HS, which decomposes a guiding path into arc segments and assigns parameterized modes. For a fixed generalized velocity $(\delta_x, \delta_y) \in [-1,1]^2,$7, the object follows an arc if $(\delta_x, \delta_y) \in [-1,1]^2,$8 and a straight line if $(\delta_x, \delta_y) \in [-1,1]^2,$9, with arc radius

$1.0$0

The search objective is

$1.0$1

Third, it uses a nonlinear MPC to track the planned trajectory online and compensate for slip, disturbance, and model mismatch (Tang et al., 2024).

The paper states a completeness result under mild assumptions: if the mode set is sufficient and the guiding path is collision-free, then KG-HS finds a feasible hybrid plan in finite steps. It also reports simulation results in three $1.0$2 cluttered scenes with 3 robots, a $1.0$3 target object, PyBullet at $1.0$4, NMPC at $1.0$5, and intermediate goal update at $1.0$6. The three scenarios were solved with planning times $1.0$7, $1.0$8, and $1.0$9; execution times $$\mathcal{D}_9 \times \mathcal{D}_9 \times \mathcal{D}_9 \times \mathcal{D}_9,$$0, $$\mathcal{D}_9 \times \mathcal{D}_9 \times \mathcal{D}_9 \times \mathcal{D}_9,$$1, and $$\mathcal{D}_9 \times \mathcal{D}_9 \times \mathcal{D}_9 \times \mathcal{D}_9,$$2; mode switches $$\mathcal{D}_9 \times \mathcal{D}_9 \times \mathcal{D}_9 \times \mathcal{D}_9,$$3, $$\mathcal{D}_9 \times \mathcal{D}_9 \times \mathcal{D}_9 \times \mathcal{D}_9,$$4, and $$\mathcal{D}_9 \times \mathcal{D}_9 \times \mathcal{D}_9 \times \mathcal{D}_9,$$5; and average tracking errors $$\mathcal{D}_9 \times \mathcal{D}_9 \times \mathcal{D}_9 \times \mathcal{D}_9,$$6, $$\mathcal{D}_9 \times \mathcal{D}_9 \times \mathcal{D}_9 \times \mathcal{D}_9,$$7, and $$\mathcal{D}_9 \times \mathcal{D}_9 \times \mathcal{D}_9 \times \mathcal{D}_9,$$8 (Tang et al., 2024).

In comparative evaluation, the key table reports KG-HS success rate 1.00, tracking error 0.03, control cost 2241, smoothness 0.31, planning time 13.21 s, execution time 44.31 s, and end error 0.14. The paper further reports successful hardware experiments in a $$\mathcal{D}_9 \times \mathcal{D}_9 \times \mathcal{D}_9 \times \mathcal{D}_9,$$9 workspace using 3 LIMO robots, with total times about $$\mathcal{D}_9 \times \mathcal{D}_9 \times \mathbb{R}^2 \times \mathbb{R}^2,$$0 and $$\mathcal{D}_9 \times \mathcal{D}_9 \times \mathbb{R}^2 \times \mathbb{R}^2,$$1, $$\mathcal{D}_9 \times \mathcal{D}_9 \times \mathbb{R}^2 \times \mathbb{R}^2,$$2 and $$\mathcal{D}_9 \times \mathcal{D}_9 \times \mathbb{R}^2 \times \mathbb{R}^2,$$3 modes, and average tracking errors $$\mathcal{D}_9 \times \mathcal{D}_9 \times \mathbb{R}^2 \times \mathbb{R}^2,$$4 and $$\mathcal{D}_9 \times \mathcal{D}_9 \times \mathbb{R}^2 \times \mathbb{R}^2,$$5 (Tang et al., 2024).

4. CoopPush as cooperative object pushing via contact-point selection

In “ConPoSe: LLM-Guided Contact Point Selection for Scalable Cooperative Object Pushing” (Steinkrüger et al., 9 Oct 2025), the relevant sense of CoopPush is cooperative object pushing by multiple simple robots, with the main technical problem being contact-point selection rather than low-level force control. The setting is 2D cooperative pushing in a workspace $$\mathcal{D}_9 \times \mathcal{D}_9 \times \mathbb{R}^2 \times \mathbb{R}^2,$$6 with static obstacles. A homogeneous multi-robot system of $$\mathcal{D}_9 \times \mathcal{D}_9 \times \mathbb{R}^2 \times \mathbb{R}^2,$$7 round differential-drive robots pushes an object $$\mathcal{D}_9 \times \mathcal{D}_9 \times \mathbb{R}^2 \times \mathbb{R}^2,$$8 along a preplanned path

$$\mathcal{D}_9 \times \mathcal{D}_9 \times \mathbb{R}^2 \times \mathbb{R}^2,$$9

and the object pose is

$$\mathbb{R}^2 \times \mathbb{R}^2 \times \mathbb{R}^2 \times \mathbb{R}^2.$$0

Each robot pushes at a boundary contact point $$\mathbb{R}^2 \times \mathbb{R}^2 \times \mathbb{R}^2 \times \mathbb{R}^2.$$1 along the inward normal direction.

ConPoSe combines zero-shot LLM initialization with local search. The object path is first computed with A* on a costmap and then simplified with Ramer–Douglas–Peucker. The current desired pushing direction toward the next waypoint is

$$\mathbb{R}^2 \times \mathbb{R}^2 \times \mathbb{R}^2 \times \mathbb{R}^2.$$2

The object contour is discretized into a candidate set

$$\mathbb{R}^2 \times \mathbb{R}^2 \times \mathbb{R}^2 \times \mathbb{R}^2.$$3

and the LLM returns

$$\mathbb{R}^2 \times \mathbb{R}^2 \times \mathbb{R}^2 \times \mathbb{R}^2.$$4

where $$\mathbb{R}^2 \times \mathbb{R}^2 \times \mathbb{R}^2 \times \mathbb{R}^2.$$5 is the selected set of contact-point indices and $$\mathbb{R}^2 \times \mathbb{R}^2 \times \mathbb{R}^2 \times \mathbb{R}^2.$$6 is the model’s reasoning text (Steinkrüger et al., 9 Oct 2025).

The LLM proposal is accepted only if two conditions hold. First, the combined pushing direction must lie within tolerance

$$\mathbb{R}^2 \times \mathbb{R}^2 \times \mathbb{R}^2 \times \mathbb{R}^2.$$7

of the target direction. Second, at least $$\mathbb{R}^2 \times \mathbb{R}^2 \times \mathbb{R}^2 \times \mathbb{R}^2.$$8 robots must contribute force in the intended pushing direction. If the proposal is infeasible or suboptimal, the method constructs a 1-swap neighborhood,

$$\mathbb{R}^2 \times \mathbb{R}^2 \times \mathbb{R}^2 \times \mathbb{R}^2.$$9

and scores neighbors according to net direction and total torque. The net force and direction mismatch are computed as

$\mathcal{D}_9 \times \mathcal{D}_9,$0

$\mathcal{D}_9 \times \mathcal{D}_9,$1

where

$\mathcal{D}_9 \times \mathcal{D}_9,$2

A configuration is accepted if

$\mathcal{D}_9 \times \mathcal{D}_9,$3

The paper states that the algorithm terminates after evaluating at most

$\mathcal{D}_9 \times \mathcal{D}_9,$4

pushing configurations (Steinkrüger et al., 9 Oct 2025).

The analytical baseline evaluates

$\mathcal{D}_9 \times \mathcal{D}_9,$5

contact-point combinations, described in the paper as effectively $\mathcal{D}_9 \times \mathcal{D}_9,$6. ConPoSe avoids exhaustive enumeration by starting from an LLM proposal and searching only a limited 1-swap neighborhood. The reported consequence is that selection time stays almost flat as $\mathcal{D}_9 \times \mathcal{D}_9,$7 grows, whereas the analytical baseline took more than an hour for $\mathcal{D}_9 \times \mathcal{D}_9,$8 and several days for $\mathcal{D}_9 \times \mathcal{D}_9,$9. The paper concludes that ConPoSe becomes competitive with or better than analytical selection from about $\mathcal{D}_9 \times \mathbb{R}^2,$0, while also outperforming a naive LLM baseline that uses raw LLM output directly (Steinkrüger et al., 9 Oct 2025).

The experiments were conducted in Webots with TurtleBot 4 robots in a $\mathcal{D}_9 \times \mathbb{R}^2,$1 arena across five scenes. The tested objects were a cuboid $\mathcal{D}_9 \times \mathbb{R}^2,$2, a cylinder of radius $\mathcal{D}_9 \times \mathbb{R}^2,$3, and a T-shape whose horizontal bar is $\mathcal{D}_9 \times \mathbb{R}^2,$4 and vertical bar $\mathcal{D}_9 \times \mathbb{R}^2,$5; all had height $\mathcal{D}_9 \times \mathbb{R}^2,$6 and density $\mathcal{D}_9 \times \mathbb{R}^2,$7. The paper reports selection time $\mathcal{D}_9 \times \mathbb{R}^2,$8, success rate (SR), execution time $\mathcal{D}_9 \times \mathbb{R}^2,$9, number of pushing configurations $\mathbb{R}^2 \times \mathbb{R}^2.$0, and switch time $\mathbb{R}^2 \times \mathbb{R}^2.$1. It notes that the cylinder is the easiest object, reaching $\mathbb{R}^2 \times \mathbb{R}^2.$2 SR in all tested methods in the shape-only evaluation, whereas the T-shape is the hardest, especially when contact switching near concave corners is required (Steinkrüger et al., 9 Oct 2025).

5. CoopPush as pull/push coexistence in IoT wireless access

In “Coexistence of Pull and Push Communication in Wireless Access for IoT Devices” (Cavallero et al., 2024), “CoopPush” denotes a cooperative coexistence framework for two uplink communication modes in the same slotted frame: pull-based communication, in which a base station retrieves data through queries and wake-up signaling, and push-based communication, in which devices autonomously contend for uplink access. The setting is a 5G-enabled base station controlling wireless access over a shared narrow-band wireless channel. Pull-based devices are WuDs equipped with a wake-up receiver, and the base station addresses them individually through an identity-based wake-up mechanism.

The frame has fixed duration $\mathbb{R}^2 \times \mathbb{R}^2.$3 and is partitioned into a pull segment and a push segment,

$\mathbb{R}^2 \times \mathbb{R}^2.$4

With $\mathbb{R}^2 \times \mathbb{R}^2.$5 equal slots of duration $\mathbb{R}^2 \times \mathbb{R}^2.$6,

$\mathbb{R}^2 \times \mathbb{R}^2.$7

If serving one pull query requires $\mathbb{R}^2 \times \mathbb{R}^2.$8 slots for the wake-up signal and $\mathbb{R}^2 \times \mathbb{R}^2.$9 slots for data transmission, then serving $$0 \le f_n^{n} \le f_{n,\max}, \qquad 0 \le |f_n^{t}| \le \mu_c f_n^{n},$$0 queries consumes

$$0 \le f_n^{n} \le f_{n,\max}, \qquad 0 \le |f_n^{t}| \le \mu_c f_n^{n},$$1

The push segment contains $$0 \le f_n^{n} \le f_{n,\max}, \qquad 0 \le |f_n^{t}| \le \mu_c f_n^{n},$$2 control slots and $$0 \le f_n^{n} \le f_{n,\max}, \qquad 0 \le |f_n^{t}| \le \mu_c f_n^{n},$$3 access slots, so

$$0 \le f_n^{n} \le f_{n,\max}, \qquad 0 \le |f_n^{t}| \le \mu_c f_n^{n},$$4

This makes $$0 \le f_n^{n} \le f_{n,\max}, \qquad 0 \le |f_n^{t}| \le \mu_c f_n^{n},$$5 the primary design variable controlling the coexistence trade-off (Cavallero et al., 2024).

Pull queries arrive according to a Poisson process with rate $$0 \le f_n^{n} \le f_{n,\max}, \qquad 0 \le |f_n^{t}| \le \mu_c f_n^{n},$$6, giving per-frame mean

$$0 \le f_n^{n} \le f_{n,\max}, \qquad 0 \le |f_n^{t}| \le \mu_c f_n^{n},$$7

and push packets arrive with rate $$0 \le f_n^{n} \le f_{n,\max}, \qquad 0 \le |f_n^{t}| \le \mu_c f_n^{n},$$8, giving

$$0 \le f_n^{n} \le f_{n,\max}, \qquad 0 \le |f_n^{t}| \le \mu_c f_n^{n},$$9

The pull part is modeled as an $(\delta_x, \delta_y) \in [-1,1]^2,$00 system, and the pull success probability is approximated via Erlang-B by

$(\delta_x, \delta_y) \in [-1,1]^2,$01

The average number of successfully served queries is

$(\delta_x, \delta_y) \in [-1,1]^2,$02

For push access, framed ALOHA over $(\delta_x, \delta_y) \in [-1,1]^2,$03 access slots yields

$(\delta_x, \delta_y) \in [-1,1]^2,$04

and the paper defines the average push throughput as

$(\delta_x, \delta_y) \in [-1,1]^2,$05

A weighted coexistence objective is then

$(\delta_x, \delta_y) \in [-1,1]^2,$06

with the paper using

$(\delta_x, \delta_y) \in [-1,1]^2,$07

The design problem is to choose $(\delta_x, \delta_y) \in [-1,1]^2,$08 to maximize $(\delta_x, \delta_y) \in [-1,1]^2,$09 (Cavallero et al., 2024).

The reported interpretation is direct: increasing $(\delta_x, \delta_y) \in [-1,1]^2,$10 improves pull performance but leaves fewer access opportunities for push traffic, thereby increasing collisions and reducing push throughput. The default simulation settings are $(\delta_x, \delta_y) \in [-1,1]^2,$11 ms, $(\delta_x, \delta_y) \in [-1,1]^2,$12, $(\delta_x, \delta_y) \in [-1,1]^2,$13 ms, $(\delta_x, \delta_y) \in [-1,1]^2,$14, $(\delta_x, \delta_y) \in [-1,1]^2,$15, and $(\delta_x, \delta_y) \in [-1,1]^2,$16. Each simulation lasts $(\delta_x, \delta_y) \in [-1,1]^2,$17. The paper reports that analytical and simulation results match very well for push traffic, while the Erlang-B-based approximation for pull traffic remains a tight lower bound despite slight differences at low $(\delta_x, \delta_y) \in [-1,1]^2,$18 (Cavallero et al., 2024).

6. Conceptual commonalities and distinctions

Across these usages, CoopPush consistently denotes a coordination problem in which performance depends on aligning multiple action components under shared constraints. In the benchmark environment, those components are factored action heads controlling particles that must avoid obstructing one another while pushing boulders (Flavin et al., 25 Jun 2026). In collaborative planar pushing, they are robot contacts, feasible wrenches, and mode switches along an object trajectory (Tang et al., 2024). In ConPoSe, they are candidate contact points whose aggregate direction and torque must support a preplanned path (Steinkrüger et al., 9 Oct 2025). In the IoT coexistence setting, they are pull and push traffic classes sharing a finite frame budget (Cavallero et al., 2024).

A common misconception is to treat these usages as belonging to one homogeneous technical lineage. The papers indicate otherwise. The RL benchmark is explicitly formulated as a single-agent MDP with a factored multi-head action space, even though it is conceptually cooperative. The robotics papers address physical multi-robot transport under contact and geometry constraints. The IoT paper uses “push” in the communication-theoretic sense of autonomous uplink transmission rather than mechanical interaction. This suggests that the unifying feature is not domain or formalism, but the requirement that local decisions be coordinated to satisfy a collective objective under coupling constraints.

A second cross-cutting distinction concerns where the complexity resides. In the RL benchmark, the central issue is state-dependent inter-action dependence and credit assignment. In the hybrid pushing framework, it is hybrid mode generation, feasibility, and online tracking under under-actuation. In ConPoSe, it is the combinatorial growth of contact-point selection with object size and team size. In the IoT model, it is the frame-level trade-off between query satisfaction and push access success. The literature therefore uses “CoopPush” to mark different coordination bottlenecks rather than a single standardized algorithmic template.

Within current arXiv usage, the most technically salient senses of CoopPush are thus twofold: as a benchmark for action-factorization research and as a family of cooperative pushing problems in multi-robot manipulation. The term’s extension to wireless coexistence shows that it can also function as a broader label for systems that must jointly manage “cooperative” and “push” behaviors in a shared resource space (Flavin et al., 25 Jun 2026, Tang et al., 2024, Steinkrüger et al., 9 Oct 2025, Cavallero et al., 2024).