Provably Safe Trajectory Generation for Manipulators Under Motion and Environmental Uncertainties

• URL: http://arxiv.org/abs/2603.09083v1
• Date: Tue, 10 Mar 2026 01:48:48 GMT
• Title: Provably Safe Trajectory Generation for Manipulators Under Motion and Environmental Uncertainties
• Abstract summary: This article proposes a novel risk-bounded motion planning framework to address the unmet need for safe optimal motion planning.<n>Our approach integrates a rigid manipulator deep Koopman operator (RM-DeKO) model to predict the robot's state distribution under motion uncertainty.<n>We then introduce an efficient hierarchical verification method that combines parallel physics simulations with sum-of-squares (SOS) programming as a filter for fine-grained, formal certification of collision risk.
• Score: 26.41382315967256
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Robot manipulators operating in uncertain and non-convex environments present significant challenges for safe and optimal motion planning. Existing methods often struggle to provide efficient and formally certified collision risk guarantees, particularly when dealing with complex geometries and non-Gaussian uncertainties. This article proposes a novel risk-bounded motion planning framework to address this unmet need. Our approach integrates a rigid manipulator deep stochastic Koopman operator (RM-DeSKO) model to robustly predict the robot's state distribution under motion uncertainty. We then introduce an efficient, hierarchical verification method that combines parallelizable physics simulations with sum-of-squares (SOS) programming as a filter for fine-grained, formal certification of collision risk. This method is embedded within a Model Predictive Path Integral (MPPI) controller that uniquely utilizes binary collision information from SOS decomposition to improve its policy. The effectiveness of the proposed framework is validated on two typical robot manipulators through extensive simulations and real-world experiments, including a challenging human-robot collaboration scenario, demonstrating sim-to-real transfer of the learned model and its ability to generate safe and efficient trajectories in complex, uncertain settings.

Related papers

• Distributed Motion Planning with Safety Guarantees for Self-Reconfiguring Robotic Boats [76.98547580312116]
  This paper proposes a hybrid framework that combines distributed Model Predictive Control (MPC) with Control Barrier Functions (CBFs)<n>To ensure safety in real time, distributed CBF-based filters are applied to enforce inter-agent avoidance.
  arXiv  Detail & Related papers  (2026-07-22T16:37:05Z)
• Simulation-Informed Diffusion for Decentralized Multi-robot Motion Planning [56.240199425429445]
  Multi-robot motion planning requires each robot to generate collision-free trajectories from local observations.<n>Most existing planners generate trajectories from a static snapshot of the local observation.<n>This paper introduces Simulation-Informed Diffusion (SID), a decentralized framework built on constraint-aware diffusion models.
  arXiv  Detail & Related papers  (2026-05-26T21:17:53Z)
• ToMPC: Task-oriented Model Predictive Control via ADMM for Safe Robotic Manipulation [20.83011691536596]
  The framework unifies collision-free motion and robot-environment interaction to address diverse scenarios.<n>It also introduces task-oriented obstacle avoidance that leverages kinematic redundancy to enhance manipulation efficiency in obstructed environments.<n>Results demonstrate that the framework can plan motion and/or force trajectories in real time, maximize the manipulation range while avoiding obstacles, and strictly adhere to safety-related hard constraints.
  arXiv  Detail & Related papers  (2026-03-14T13:35:24Z)
• Designing Control Barrier Function via Probabilistic Enumeration for Safe Reinforcement Learning Navigation [55.02966123945644]
  We propose a hierarchical control framework leveraging neural network verification techniques to design control barrier functions (CBFs) and policy correction mechanisms.<n>Our approach relies on probabilistic enumeration to identify unsafe regions of operation, which are then used to construct a safe CBF-based control layer.<n>These experiments demonstrate the ability of the proposed solution to correct unsafe actions while preserving efficient navigation behavior.
  arXiv  Detail & Related papers  (2025-04-30T13:47:25Z)
• Robotic World Model: A Neural Network Simulator for Robust Policy Optimization in Robotics [50.191655141020505]
  This work advances model-based reinforcement learning by addressing the challenges of long-horizon prediction, error accumulation, and sim-to-real transfer.<n>By providing a scalable and robust framework, the introduced methods pave the way for adaptive and efficient robotic systems in real-world applications.
  arXiv  Detail & Related papers  (2025-01-17T10:39:09Z)
• Integrating DeepRL with Robust Low-Level Control in Robotic Manipulators for Non-Repetitive Reaching Tasks [0.24578723416255746]
  In robotics, contemporary strategies are learning-based, characterized by a complex black-box nature and a lack of interpretability. We propose integrating a collision-free trajectory planner based on deep reinforcement learning (DRL) with a novel auto-tuning low-level control strategy.
  arXiv  Detail & Related papers  (2024-02-04T15:54:03Z)
• SAFE-SIM: Safety-Critical Closed-Loop Traffic Simulation with Diffusion-Controllable Adversaries [94.84458417662407]
  We introduce SAFE-SIM, a controllable closed-loop safety-critical simulation framework. Our approach yields two distinct advantages: 1) generating realistic long-tail safety-critical scenarios that closely reflect real-world conditions, and 2) providing controllable adversarial behavior for more comprehensive and interactive evaluations. We validate our framework empirically using the nuScenes and nuPlan datasets across multiple planners, demonstrating improvements in both realism and controllability.
  arXiv  Detail & Related papers  (2023-12-31T04:14:43Z)
• Tuning Legged Locomotion Controllers via Safe Bayesian Optimization [47.87675010450171]
  This paper presents a data-driven strategy to streamline the deployment of model-based controllers in legged robotic hardware platforms. We leverage a model-free safe learning algorithm to automate the tuning of control gains, addressing the mismatch between the simplified model used in the control formulation and the real system.
  arXiv  Detail & Related papers  (2023-06-12T13:10:14Z)
• Safe Machine-Learning-supported Model Predictive Force and Motion Control in Robotics [0.0]
  Many robotic tasks, such as human-robot interactions or the handling of fragile objects, require tight control and limitation of appearing forces and moments alongside motion control to achieve safe yet high-performance operation. We propose a learning-supported model predictive force and motion control scheme that provides safety guarantees while adapting to changing situations.
  arXiv  Detail & Related papers  (2023-03-08T13:30:02Z)
• Active Uncertainty Reduction for Safe and Efficient Interaction Planning: A Shielding-Aware Dual Control Approach [9.07774184840379]
  We present a novel algorithmic approach to enable active uncertainty reduction for interactive motion planning based on the implicit dual control paradigm. Our approach relies on sampling-based approximation of dynamic programming, leading to a model predictive control problem that can be readily solved by real-time gradient-based optimization methods.
  arXiv  Detail & Related papers  (2023-02-01T01:34:48Z)
• Nonprehensile Riemannian Motion Predictive Control [57.295751294224765]
  We introduce a novel Real-to-Sim reward analysis technique to reliably imagine and predict the outcome of taking possible actions for a real robotic platform. We produce a closed-loop controller to reactively push objects in a continuous action space. We observe that RMPC is robust in cluttered as well as occluded environments and outperforms the baselines.
  arXiv  Detail & Related papers  (2021-11-15T18:50:04Z)
• Risk-Sensitive Sequential Action Control with Multi-Modal Human Trajectory Forecasting for Safe Crowd-Robot Interaction [55.569050872780224]
  We present an online framework for safe crowd-robot interaction based on risk-sensitive optimal control, wherein the risk is modeled by the entropic risk measure. Our modular approach decouples the crowd-robot interaction into learning-based prediction and model-based control. A simulation study and a real-world experiment show that the proposed framework can accomplish safe and efficient navigation while avoiding collisions with more than 50 humans in the scene.
  arXiv  Detail & Related papers  (2020-09-12T02:02:52Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.