KinDER: A Physical Reasoning Benchmark for Robot Learning and Planning

Abstract: Robotic systems that interact with the physical world must reason about kinematic and dynamic constraints imposed by their own embodiment, their environment, and the task at hand. We introduce KinDER, a benchmark for Kinematic and Dynamic Embodied Reasoning that targets physical reasoning challenges arising in robot learning and planning. KinDER comprises 25 procedurally generated environments, a Gymnasium-compatible Python library with parameterized skills and demonstrations, and a standardized evaluation suite with 13 implemented baselines spanning task and motion planning, imitation learning, reinforcement learning, and foundation-model-based approaches. The environments are designed to isolate five core physical reasoning challenges: basic spatial relations, nonprehensile multi-object manipulation, tool use, combinatorial geometric constraints, and dynamic constraints, disentangled from perception, language understanding, and application-specific complexity. Empirical evaluation shows that existing methods struggle to solve many of the environments, indicating substantial gaps in current approaches to physical reasoning. We additionally include real-to-sim-to-real experiments on a mobile manipulator to assess the correspondence between simulation and real-world physical interaction. KinDER is fully open-sourced and intended to enable systematic comparison across diverse paradigms for advancing physical reasoning in robotics. Website and code: https://prpl-group.com/kinder-site/

• The paper introduces KinDER, a systematic benchmark that isolates physical reasoning from perceptual dependencies using 25 procedurally generated environments.
• It details a standardized suite (KinDERGym) supporting teleoperation, multi-modal demonstrations, and diverse planning approaches from classical to learning-based methods.
• Benchmark evaluations reveal classical planning outperforms learning models on complex tasks, highlighting challenges in scaling and generalizing physical reasoning in robotics.

KinDER: A Physical Reasoning Benchmark for Robot Learning and Planning

Introduction and Motivation

KinDER introduces an extensible, systematic benchmark for evaluating physical reasoning in robotic learning and planning, addressing an existing gap where prior benchmarks fail to isolate and stress-test embodied physical reasoning skills divorced from complex perceptual or linguistic dependencies. KinDER consists of three main components: KinDERGarden (a suite of 25 procedurally generated 2D/3D environments), KinDERGym (a standardized, Gymnasium-compatible Python API with parameterized skills, teleoperation, and demonstration capabilities), and KinDERBench (a collection of diverse, well-implemented baselines spanning task and motion planning, reinforcement and imitation learning, and foundation-model-based approaches).

A primary objective of KinDER is to focus on five canonical physical reasoning challenges: basic spatial relations, nonprehensile multi-object manipulation, tool use, combinatorial geometric constraints, and dynamic constraints. Each challenge is disentangled from perception and language grounding to facilitate controlled study and direct comparison between algorithmic families.

Core Physical Reasoning Challenges in KinDER

KinDER prioritizes the following five physical reasoning challenges:

• Basic Spatial Relations: Locative reasoning about relative positions and placements.
• Nonprehensile Multi-Object Manipulation: Whole-arm, dynamic interactions beyond simple pick-and-place, including pushing, sweeping, and scooping.
• Tool Use: Manipulating objects indirectly via intermediate objects, requiring abstraction over tool affordances.
• Combinatorial Geometric Constraints: Reasoning about collision avoidance, packing, and spatial arrangement at scale.
• Dynamic Constraints: Accounting for inertial and force-related limits, stability, and safety during dynamic tasks.

Figure 1: KinDER core challenges illustrated across tasks such as object arrangement, sweeping, packing, transport, and tossing, each instantiating a distinct physical reasoning theme.

These challenges are operationalized across environments designed for kinematic/dynamic reasoning in both 2D and 3D, with procedurally generated task variations to defeat memorization and assess generalization.

Figure 2: KinDERGarden categorizes environments by which of the five core challenges are targeted, ensuring comprehensive coverage.

Benchmark Structure: Environments and Software

KinDERGarden

KinDERGarden offers 25 procedurally generated environments across four structure types: Kinematic2D, Dynamic2D, Kinematic3D, and Dynamic3D. Each environment exposes object-centric states, facilitating both symbolic and neural approaches. Rewards are uniformly sparse and goal-terminated, emphasizing reasoning and efficiency.

Procedural generation introduces combinatorial variation in objects, obstacles, goals, and spatial arrangements. For example, in $\mathrm{ConstrainedCupboard3D}$, the feasible shelving configuration is randomized at each reset, stressing planning under geometric uncertainty.

Figure 3: Sample from $\mathrm{ConstrainedCupboard3D}$ showing random shelf arrangements and consequent planning complexity.

Kinematic and dynamic environments are further distinguished by whether transitions model only configuration or also velocities and forces. The design supports scaling the number of objects (and thus geometric constraints), and exposes both low-dimensional and image-based interfaces.

Figure 4: Demonstration of how kinematic (collision-based) and dynamic (force-based) environments demand fundamentally different manipulation strategies even for similar high-level goals.

KinDERGym

KinDERGym standardizes environment access and supports:

• Parameterized Skills & Concepts: Encoded as options and symbolic predicates, enabling abstract task decomposition for hierarchical planners and data labelling for imitation learning.
• Multi-modal Teleoperation: Interfaces for game controllers, web/iOS/VR, supporting intuitive large-scale demonstration collection.
• Demonstrations at Scale: Both human and planner-generated datasets, already provided for a subset of environments, and extensible for continual contribution.

KinDERBench

KinDERBench implements and evaluates 13 baselines representing classical task/motion planning, LLM/VLM-based planning (zero- and few-shot), model predictive control, model-based RL, generative skill chaining with diffusion, and both on-policy/off-policy RL and imitation learning with advanced policies (e.g., Diffusion Policy, vision-language-action models). All approaches are evaluated under identical interface constraints and metrics.

Benchmark Evaluation and Results

Evaluations are run in environments spanning all reasoning challenges, measuring success rate, cumulative (sparse-reward) efficiency, and inference time.

Key findings:

• Classical bilevel planning (BP) outperforms all learning-based and FM-based planners in overall success, especially on geometrically complex or long-horizon tasks, but at significant engineering cost and lower scaling with object count.
• LLM- and VLM-based planners underperform on tasks requiring closed-loop control or long-horizon decomposition, with marginal gains from vision beyond state information, indicating little visual grounding in pre-trained FM planners in these physical domains.
• Imitation learning (Diffusion Policy, VLA) baselines demonstrate strong results, with VLA models surprisingly robust to visual domain shift and generalizing to out-of-distribution numbers of objects in dynamic environments.
• Reinforcement learning approaches only succeed in short-horizon, simple settings, with dense rewards providing limited improvement.
• Model-based RL (MBRL) underperforms ground-truth model-based MPC, emphasizing the practical limitations of learned simulation for robust reasoning.
• Scaling studies reveal rapid efficiency loss and feasibility decreases for planning methods as combinatorial complexity increases (e.g., packing or multi-button tasks).

Practical deployment is validated via real-to-sim-to-real transfer on $\mathrm{Shelf3D}$, with object-centric state estimation enabling closed-loop planning in simulation and reliable execution in the physical world.

Implications, Limitations, and Prospects

KinDER enables precise diagnosis of the specific challenges where current foundation models, imitation learning, and reinforcement learning fail to capture sufficient physical reasoning, especially for tasks combining tool use, combinatorial constraints, or dynamic interaction. The systematic, isolated evaluation setting further allows for rigorous ablation and compositional skill generalization studies.

The boldest claim supported by the results is that no existing learning or FM-based approach closes the gap to classical planners on physically complex robotic reasoning tasks, even when provided optimal state estimation and skill libraries.

However, several limitations remain:

• All experiments are simulation-based, with inevitable gaps in real-world fidelity, particularly for dynamics and contact-rich manipulation.
• The scope is constrained to single-robot, deterministic scenarios with full state observability.
• Baseline coverage, while broad, is not exhaustive; future work should evaluate state-of-the-art hybrid, hierarchical, and neuro-symbolic frameworks.

Future research directions include:

• Learning skill and concept representations directly from multi-modal demonstration at scale.
• Hybridizing classical planning with robust learned closed-loop policies for long-horizon, physically grounded decision making.
• Leveraging KinDER to design and validate next-generation foundation models and neuro-symbolic systems that internalize explicit physical reasoning.

Conclusion

KinDER inaugurates a targeted, systematic approach to benchmarking physical reasoning in robotic agents, providing the community with environments, baselines, and analytic tools for direct, fair, and extensible comparison. The results establish clear gaps and opportunities for algorithmic advancement, particularly in generalization, scaling, and physical abstraction, and underscore the need for continued development and rigorous evaluation of embodied reasoning paradigms in robotics.