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KinDER: A Physical Reasoning Benchmark for Robot Learning and Planning

Yixuan Huang, Bowen Li, Vaibhav Saxena, Yichao Liang, Utkarsh Aashu Mishra, Liang Ji, Lihan Zha, Jimmy Wu, Nishanth Kumar, Sebastian Scherer, Danfei Xu, Tom Silver

arXiv:2604.25788v2cs.RO

TL;DR

Robots must reason about kinematic and dynamic constraints from their embodiment, environment, and tasks, but existing physical-reasoning methods lack systematic evaluation. KinDER introduces a benchmark with procedurally generated environments and standardized baselines, finding that the best baseline achieves only 0.57 average success across tasks.

  • Problem

    Robots must reason about kinematic and dynamic constraints imposed by their embodiment, environment, and task requirements.

  • Method

    KinDER provides 25 procedurally generated environments, a Gymnasium-compatible software package, and a standardized benchmark with 13 implemented baselines.

  • Results

    Across benchmark environments, BP achieves the highest average success rate at 0.57, followed by LLMCon and VLMCon at 0.43.

  • Takeaways & Limitations

    KinDER offers an open-source basis for systematic comparison across approaches to robot physical reasoning, including real-to-sim-to-real evaluation.

  • Takeaways & Limitations

    The benchmark does not fully capture real-world physics and excludes factors including stochasticity, partial observability, diverse robot embodiments, and multi-robot coordination.

Abstract

from arXiv · show

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/

I. INTRODUCTION

KinDER addresses the difficulty of evaluating physical reasoning in robotics, where embodied, environmental, and task constraints create challenges that existing benchmarks and fragmented perspectives do not adequately capture. It contributes procedurally generated environments, a Gymnasium-compatible library, a standardized benchmark, and real-to-sim-to-real validation.

  • Motivation: Physical reasoning requires robots to account for kinematic and dynamic limits arising from their morphology, environment, and task requirements.These constraints can make seemingly simple manipulation tasks difficult.
  • Motivation: Robots must reason about obstacles, regrasping, and constrained placement rather than merely executing a fixed move-grasp-place sequence.The introduction illustrates these issues through storing a book on a shelf.
  • Problem: Existing benchmarks and procedural task variations do not fully measure physical reasoning, leaving the field without a clear state of the art.The paper argues that no single task or limited set of variations captures physical reasoning in full generality.
  • Contributions: KinDER comprises 25 simulated environments with infinite procedurally generated variations, a Gymnasium-compatible Python package, and a standardized benchmark with 13 pre-implemented baselines.KinDERGym also includes parameterized skills and concepts, teleoperation interfaces, and demonstration datasets.
  • Validation: The open-source contributions are tested across multiple operating systems and evaluated through real-to-sim-to-real experiments.These experiments assess whether the simulated environments correspond to real physical reasoning challenges.

II. KINDER CORE CHALLENGES

KinDER prioritizes five core physical reasoning challenges selected from gaps between active research problems and existing benchmarks. The benchmark focuses on physical reasoning while acknowledging broader decision-making demands such as long horizons, sparse feedback, broad task distributions, and time pressure.

  • Challenge selection: KinDER’s challenges were selected by reviewing one-off physical reasoning environments and related benchmarks to identify underrepresented active-research themes.The selection targets frontier problems that existing benchmarks do not adequately represent.
  • Core challenges: The five core challenges include basic spatial relations and nonprehensile multi-object manipulation beyond pick-and-place.Basic spatial relations require passive and active understanding, while generalized manipulation includes actions such as pushing, pulling, sweeping, and scooping.
  • Scope and limitations: KinDER deliberately excludes broader decision-making challenges from its core list, including long task horizons, sparse feedback, broad task distributions, and time pressure.These challenges remain pervasive in KinDER but are omitted to keep the benchmark focused on physical reasoning.

III. RELATED WORK

KinDER distinguishes itself by isolating core physical reasoning challenges across 2D and 3D environments, rather than entangling them with application-specific complexity. It complements existing robot-learning, planning, application-driven, and nonrobotic physical-reasoning benchmarks.

  • Benchmarks for Robot Learning and Planning: KinDER covers core physical reasoning challenges in both 2D and 3D environments, enabling study across multiple levels of abstraction.Its focus contrasts with application-driven benchmarks where physical reasoning is entangled with other factors.
  • Benchmarks for Robot Learning and Planning: Existing robot-learning benchmarks span imitation learning, reinforcement learning, foundation-model methods, and comparisons across technique families, commonly using tabletop manipulation.Mobile and bimanual manipulation are also represented.
  • Benchmarks for Robot Learning and Planning: Classical robot planning has fewer integrated benchmarks: motion and task planning are typically separate, while the only known combined TAMP benchmark is not actively used.KinDER facilitates direct comparisons between planning and learning approaches.
  • Application-Driven Benchmarks: KinDER is complementary to application-driven benchmarks because it isolates fundamental physical reasoning challenges and provides a clearer signal for studying them.Application-oriented examples include home-assistance benchmarks such as ALFRED, AI2-THOR, BEHAVIOR-1k, Habitat, and RoboCasa.
  • Physical Reasoning Benchmarks: KinDER draws inspiration from nonrobotic physical-reasoning benchmarks such as the Virtual Tools Game and PHYRE, while targeting advances in robotics rather than human reasoning.Connections to human-like physical reasoning are identified as future work.

IV. KINDERGARDEN: ENVIRONMENTS

KinDERGarden provides 25 procedurally generated environments across four kinematic and dynamic categories for studying robot physical reasoning. Its Gymnasium-compatible, object-centric design supports sparse-reward tasks spanning varied spatial, manipulation, tool-use, geometric, and dynamic challenges.

  • Environment Overview: KinDERGarden contains 25 environments grouped into Kinematic2D, Dynamic2D, Kinematic3D, and Dynamic3D categories.The categories organize environments by dimensionality and whether velocities and accelerations are modeled.
  • General Environment Structure: All environments follow the Gymnasium API, use procedurally generated task distributions, and provide sparse rewards of −1 per step until successful termination.Procedural generation occurs inside reset(), while success is recognized only when the goal is achieved.
  • General Environment Structure: KinDER distinguishes itself through object-centric states mapping named objects to real-valued feature vectors whose dimensions depend on object type.For example, a MobileManipulator state includes base position and velocity, arm configuration and velocity, and gripper joint value.
  • 2D Environments: Kinematic2D has six environments for abstract tool use and combinatorial geometric constraints, while Dynamic2D has four for nonprehensile manipulation and tool use with modeled velocities and accelerations.Kinematic2D uses 2D shapes without velocity or acceleration modeling; Dynamic2D uses the Pymunk physics backend.
  • 2D Environments: In Obstruction2D, obstacles must be picked and placed before the target, whereas DynObstruction2D can permit pushing obstacles aside while holding the target when space allows.The contrast illustrates qualitatively different reasoning between kinematic and dynamic environments.
  • 3D Environments: Kinematic3D includes five environments, while Dynamic3D includes 10 that collectively cover all five core physical reasoning challenges.Kinematic3D uses PyBullet-based kinematics and collision checking; Dynamic3D models velocities and accelerations with MuJoCo and dynamic grasping.

V. KINDERGYM: ACCESSIBLE SOFTWARE

KinDERGym is a pip-installable Python package providing KinDER environments, parameterized skills and concepts, teleoperation interfaces, and precollected demonstrations. Its relational concepts and accessible control interfaces support planning, demonstration collection, and evaluation across multiple environment dimensions.

  • Software package: KinDERGym packages KinDER environments with parameterized skills and concepts, teleoperation interfaces, and precollected demonstrations in a pip-installable Python library.The package follows software engineering standards including continuous integration, linting, and type checking.
  • Skills and concepts: KinDERGym supports stateful option policies, including policies that generate and follow motion plans.Parameterized skills can vary by arguments such as relative grasps θ ∈SE(3).
  • Skills and concepts: Concepts are relational predicates grounded in object-centric states, and they define skill preconditions and effects while forming a two-level scene graph.For example, On(object, surface) is true when an object is above and in contact with a surface.
  • Planning support: KinDERGym skills and concepts support bilevel, LLM, and VLM planning baselines, while designing or learning hierarchical skills remains future work.Hierarchical task decompositions are not always readily apparent or easy to engineer.
  • Teleoperation interfaces: Teleoperation spans mouse-and-keyboard or PS5 controller input for 2D environments and iPhone or Meta Quest 3S control for 3D environments.The iPhone interface uses gyroscope and accelerometer inputs, while arm control maps to task space and uses inverse kinematics.
  • Demonstrations: KinDERGym combines teleoperation and planning to provide ≥100 precollected demonstrations for 10 environments.Users are encouraged to collect and open-source additional demonstrations through the provided interfaces.

VI. KINDERBENCH: BASELINES AND METRICS

KinDERBench standardizes evaluation of robot physical reasoning with 13 baselines across eight environments and multiple effectiveness and efficiency metrics. Across benchmark and additional experiments, planning, imitation, model-predictive, and reinforcement-learning methods show distinct strengths and limitations.

  • Benchmark setup: KinDERBench evaluates 13 representative planning and learning baselines in 8 environments.The benchmark reports results for these baselines and releases their implementations.
  • Metrics: The benchmark measures Success Rate, Cumulative Rewards, and per-episode wall-clock Inference Time, while also noting engineering cost as an important qualitative metric.Cumulative Rewards are considered only for successful episodes because rewards are −1 until success.
  • Benchmark results: 0.57 average success rate: BP ranks highest, followed by LLMCon and VLMCon at 0.43, while SAC ranks lowest at 0.02.All baselines use 5 random seeds and 50 evaluation episodes per seed; the reported values are means.
  • Baseline analysis: In-context examples improve LLMPlan/VLMPlan performance, while BP outperforms them despite using the same parameterized skills, especially in challenging environments.The comparison indicates remaining room to improve the LLM- and VLM-based planning approaches.
  • Baseline analysis: 0.43 success rate: VLA is the only baseline with non-trivial performance on DynPushPullHook2D with 5 obstacles, requiring tool use and nonprehensile multi-object manipulation.DP also reaches 0.14 and DPES 0.04 on the long-horizon SweepIntoDrawer3D task, while DPES performs comparably to DP despite access to object-centric states.
  • Baseline analysis: MPC outperforms MBRL, suggesting predictive sampling helps while the learned transition model remains unreliable; PPO and SAC perform well only on short-horizon tasks.RL success rates remain low overall, although dense rewards can improve performance.
  • Additional results: As object count increases in StickButton2D, bilevel-planning success rate decreases while planning time increases, motivating learning-based improvements for physical reasoning at scale.The benchmark also finds that DP and VLA generalize surprisingly well to unseen obstacle counts after training with 1 obstacle.

VII. REAL WORLD VALIDATION

The authors validate KinDERGarden through a real-to-sim-to-real demonstration using TidyBot++ and the Shelf3D environment, showing correspondence with real-world physical reasoning challenges. They localize the robot and objects from overhead-camera observations, initialize object-centric states, plan in simulation, and execute the resulting plan on the real robot.

  • Plan transfer: The system generates motion plans in the twin simulation and executes them in the real world.The pipeline constructs the simulation from real-world observations before transferring the plan back to the physical robot.
  • Real-to-sim-to-real validation: The real-to-sim-to-real demonstration uses TidyBot++ as the physical robot and Shelf3D in KinDERGarden as the simulator.The experiment tests whether KinDERGarden corresponds to real-world physical reasoning challenges.
  • State initialization: An overhead camera localizes the robot and estimates object bounding boxes and poses before initializing corresponding robot and object-centric states.These estimated states provide the simulator initialization for the real-world scene.

VIII. LIMITATIONS AND DISCUSSION · APPENDIX

The paper acknowledges that its simulation-based benchmark does not fully capture real-world physics and interaction. It also notes that its mid-level reasoning focus and scope-limiting design choices exclude other dimensions relevant to robotics and physical reasoning, while the appendix reports test-time generalization for a bilevel planning baseline.

  • VIII. LIMITATIONS AND DISCUSSION: The limitations arise in part because the work is a simulation-based benchmark.
  • APPENDIX: Appendix Table V addresses test-time generalization for a bilevel planning baseline in the StickButton2D environment.
  • VIII. LIMITATIONS AND DISCUSSION: The simulation-based benchmark does not fully capture certain aspects of real-world physics and interaction.
  • VIII. LIMITATIONS AND DISCUSSION: The benchmark primarily targets mid-level reasoning, where fine-grained physical details may be less critical.
  • VIII. LIMITATIONS AND DISCUSSION: Real-world fidelity remains more important for other dimensions of physical reasoning.
  • VIII. LIMITATIONS AND DISCUSSION: The authors made scope-limiting design choices that exclude factors relevant to robotics and physical reasoning.

A. KinDERGarden Environment Details

KinDERGarden’s environments are detailed in Tables IX–XII, with state spaces varying across variants according to the number of objects. The corresponding tables report each variant’s state and action spaces.

  • Environment specifications: Tables IX–XII describe KinDERGarden environments and report state and action spaces for each variant.Variants within the same environment may differ in state spaces based on the number of objects (N).

B. KinDERGym Additional Details

KinDERGym collects demonstrations through teleoperation using device-specific controls for 2D and 3D environments. In 3D, operators separately control the base, arm, and gripper, with arm commands converted to joint values through inverse kinematics.

  • Teleoperation: 2D demonstrations use either a PS5 controller or keyboard to directly control the action space.
  • Teleoperation: 3D teleoperation separates control of the base, arm, and gripper into distinct modes.
  • Teleoperation: Base and gripper commands directly specify joint values, while arm commands specify end-effector pose and use inverse kinematics to compute joint values.

C. KinDERBench Additional Details · D. Additional Real-to-Sim-to-Real Details

KinDERBench supplements its baselines with specified planning, diffusion, reinforcement-learning, and evaluation procedures. Real-to-sim-to-real experiments detect object-centric states, reconstruct simulation, plan with bilevel search, and execute waypoints on a real robot.

  • C. KinDERBench Additional Details: Candidate trajectories use 10 control points to smooth motion and reduce effective search dimensionality.
  • C. KinDERBench Additional Details: Diffusion-policy models encode visual observations with group-normalized image encoders and robot states with MLPs, inject 128-dimensional timestep embeddings, and use 16 inference denoising steps.Training uses 100 diffusion timesteps, a squared-cosine noise schedule, epsilon prediction, and AdamW with learning rate 10^-4.
  • C. KinDERBench Additional Details: DPES extends Diffusion Policy with additional low-level environment states encoded using MLPs, while Finetuned VLA fine-tunes π0.5 on the diffusion-policy demonstrations.
  • C. KinDERBench Additional Details: Dense reward experiments add distance-based shaping for SAC and PPO in BaseMotion3D, measuring Euclidean-goal-distance changes projected onto the XOY plane.The comparison uses five random seeds.
  • C. KinDERBench Additional Details: Without engineered dense rewards, PPO performance degrades substantially in long-horizon sparse-reward settings, whereas the same reward decreases SAC performance.These findings highlight PPO’s sensitivity to reward design and SAC’s lower reliance on carefully engineered dense rewards.
  • D. Additional Real-to-Sim-to-Real Details: Real-to-sim reconstruction detects robot and environment object-centric states, combining camera-estimated base poses, proprioceptive arm and gripper states, and 2D object bounding boxes.Object positions are estimated from bounding-box centers.
  • D. Additional Real-to-Sim-to-Real Details: Bilevel planning generates task and motion plans for the reconstructed simulation, which are executed on the real robot by sequentially achieving each planned waypoint.The experiments are presented as initial steps toward real-to-sim-to-real systems for more complex tasks.

E. Noisy Observations and Actions

This section evaluates bilevel planning under simulated perception and dynamics noise. Observation and action wrappers introduce simple stochasticity into KinDER to model noisy real-world interactions.

  • Observation and action wrappers add noise to KinDER observations and actions to simulate stochasticity in perception and dynamics.The wrappers are intended to capture perception noise in real-world scenarios.
  • The evaluation varies noise levels when testing bilevel planning.These experiments are reported in Table VIII.
  • The noisy-observation and action setup targets challenges arising from stochastic perception and dynamics.The perturbations are applied to both what the system observes and how it acts.
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