Global Sampling-Based Trajectory Optimization for Contact-Rich Manipulation via KernelSOS

THE PROBLEM

This paper focuses on motion planningControl & PlanningMotion planningFinding a path or motion that gets the robot from start to goal.. Global-MPPI unifies global explorationImitation & Reinforcement LearningExplorationTrying different actions to discover useful behavior. and local refinement for contact-rich manipulationManipulation & TasksManipulationUsing a robot arm or hand to move or interact with objects. by using kernel sum-of-squares optimization to identify promising regions, employing graduated non-convexity with log-sum-exp smoothing to handle non-smooth contactMovement, Mechanics & Robot BodyContactPhysical interaction between the robot and an object or surface. dynamicsMovement, Mechanics & Robot BodyDynamicsThe study of motion including forces, torques, mass, and inertia., and refining solutions via model-predictive path integral methods. Demonstrates improvements on PushT and dexterous manipulationManipulation & TasksDexterous manipulationHighly precise object handling, usually with fingers or complex contact. tasks. Read the paper by tracking the taskCore ConceptsTaskThe job the robot is supposed to complete, such as pick-and-place, navigation, or drawer opening. definition, the robotCore ConceptsRobotA physical system with sensors and actuators that can observe the world and take actions. or data assumptions, and the evidence that supports the claimed improvement.

HOW IT WORKS

1

Task framing

The paper frames the work as motion planningControl & PlanningMotion planningFinding a path or motion that gets the robot from start to goal.. Start here because it defines what success means and which assumptions the rest of the method inherits.

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Figure 3: Cost convergence comparison for PushT and dexterous in-hand manipulation task. The solid lines represent the median across six random seeds, and the shaded regions indicate the interquartile range. Our method achieves faster convergence, lower final costs, and reduced variance compared to other sampling-based methods.

Figure 4: Ablation study of Global-MPPI on the PushT and dexterous in-hand manipulation tasks. We evaluate Global-MPPI by removing key components, including GNC, local refinement, and automatic calibration. The solid lines represent the median across six random seeds, and the shaded regions indicate the interquartile range. For the PushT task, removing any of these components significantly degrades performance, leading to slower convergence, higher final costs, and increased variance. The dexterous manipulation task is less sensitive to removing the refinement or GNC, but auto calibration rema

Figure 5: Visualization of the PushT task with four different methods. The dashed red region denotes the target pose of the object. Under the same environment, Global-MPPI achieves the lowest cost and shortest trajectory path length. Predictive sampling can push the object into the target region, but it incurs large stage costs and inefficient trajectories due to random exploration. MPPI and DIAL-MPC, as local optimization methods, fail to push the object to the target region.

2

Core method

This paper solves a critical robotics problem: finding good trajectories for contact-heavy tasks (pushing, in-hand manipulationManipulation & TasksIn-hand manipulationManipulating an object within the robot hand without putting it down.) that would normally get stuck in bad local solutions. By combining global explorationImitation & Reinforcement LearningExplorationTrying different actions to discover useful behavior. via kernel optimization with local refinement, it enables robots to find high-quality manipulationManipulation & TasksManipulationUsing a robot arm or hand to move or interact with objects. strategies faster and more reliably than prior sampling-based methods. When reading the method section, identify the inputs, the learned or engineered representation, and the actionCore ConceptsActionA command the robot sends to its motors, controller, or low-level system. or prediction produced by the system.

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Figure 1: Overview of Global-MPPI. Our approach consists of three coupled components. First, we introduce a graduated non-convexity strategy via log-sum-exp (LSE) smoothing to transition the optimization landscape from a smoothed surrogate to the original non-smooth objective, enabling coarse-to-fine global exploration. Second, KernelSOS leverages samples to construct a global non-parametric surrogate and proposes a global solution candidate via semidefinite programming. Finally, the model-predictive path integral (MPPI) method performs efficient local refinement. Together, these components op

3

Data and supervision

For robotics work, the data story is part of the method: check whether the system depends on teleoperationImitation & Reinforcement LearningTeleoperation (teleop)A human remotely controlling the robot, often to collect demonstrations., simulationSimulation & Sim-to-RealSimulationA virtual environment where robots can be trained or tested., internet video, human labels, or robotCore ConceptsRobotA physical system with sensors and actuators that can observe the world and take actions. rollouts.

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4

Evaluation evidence

The paper should be judged through its evaluationSimulation & Sim-to-RealEvaluationMeasuring how well a robot system performs. protocol: what data is used, what robotCore ConceptsRobotA physical system with sensors and actuators that can observe the world and take actions. or simulator is tested, and which baselineEvaluation & ResearchBaselineA reference method used for comparison. comparisons support the claim. Look for the gap between the headline result and the deploymentSimulation & Sim-to-RealDeploymentPutting the trained system on a real robot. setting you would actually care about.

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Figure 2: Illustration of the advantages of Global-MPPI. For contact-rich problems, the original cost function (orange curve) often has sharp, asymmetric peaks. Graduated non-convexity via log-sum-exp smoothing transitions the optimization landscape from a smoothed surrogate (green curve) to the original non-smooth objective at each restart stage. This graduating smoothing facilitates global approximation by KernelSOS and enlarges the basin of attraction of low-cost solutions. MPPI then locally refines the solution from KernelSOS. As a result, the final solution gradually converges to the true

KEY RESULTS

WHY DEVELOPERS SHOULD CARE

LIMITATIONS

The main limitation to check is whether the claimed behavior holds outside the paper's reported setup. That means testing across different robotCore ConceptsRobotA physical system with sensors and actuators that can observe the world and take actions. embodiments, scenes, objects, and data distributions.

WHAT COMES NEXT

The practical next step is independent reproduction with clear baselines, ablations, and stress tests. For a developer, the useful follow-up is to map the paper's motion planningControl & PlanningMotion planningFinding a path or motion that gets the robot from start to goal. assumptions onto a concrete robotCore ConceptsRobotA physical system with sensors and actuators that can observe the world and take actions. stack, then test the smallest version of the method that could run end to end.

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