Contact-Implicit Trajectory Optimization for Dynamic Object Manipulation
Proposes a multi-stage multiple-shooting contact-implicit trajectory optimization (CIO) method with Newton impact law, achieving real-time dynamic object manipulation for 6-DOF robots.
Key Findings
Methodology
This paper introduces a contact-implicit trajectory optimization (CIO) framework based on a multi-stage multiple-shooting scheme. The core innovation lies in enforcing unilateral contact constraints via complementarity conditions at every discretized time point, coupled with Newton’s impact law to accurately model impact dynamics. The approach leverages the primal-dual interior point solver FORCES Pro to efficiently solve the resulting nonlinear program (NLP), which includes decision variables such as joint torques, states, and contact forces. The dynamics are discretized using an implicit Euler scheme to ensure numerical stability during high-speed impacts. The optimization problem is formulated as a mathematical program with complementarity constraints (MPCC), capturing the non-smooth contact phenomena directly. Extensive validation on a 6-DOF robotic manipulator demonstrates the method’s ability to generate dynamically feasible trajectories with realistic contact forces, significantly reducing computation time from minutes to milliseconds, enabling real-time control in dynamic manipulation tasks such as pushing and opening doors.
Key Results
- In pushing tasks, the optimized trajectories achieved positional accuracy within 2 centimeters of the target, with contact force peaks matching simulation predictions. The average computation time was approximately 350 milliseconds, enabling near real-time planning. The contact forces remained physically consistent, and impact responses adhered to Newton’s impact law, validating the physical correctness of the approach.
- In hardware experiments, the robot successfully executed push and door-opening tasks with a success rate exceeding 95%. The trajectories were repeatable across multiple trials, demonstrating robustness. The contact forces measured by force sensors closely matched the predicted forces, confirming the model’s fidelity.
- Ablation studies showed that incorporating Newton impact law improved impact response realism and prevented non-physical behaviors such as bouncing or penetration. The use of the high-performance solver FORCES Pro was critical in achieving the computational speed necessary for real-time applications.
Significance
This work addresses a long-standing challenge in robotic manipulation: achieving physically accurate, computationally efficient trajectory planning in contact-rich, dynamic environments. By integrating hard contact models with advanced optimization techniques, the proposed framework bridges the gap between high-fidelity physics simulation and real-time control. It opens new avenues for deploying autonomous robots in unstructured environments, where precise contact handling is crucial. The ability to generate feasible trajectories rapidly paves the way for more adaptive, robust, and intelligent robotic systems capable of complex manipulation tasks such as object pushing, door opening, and dynamic assembly, with broad implications for industrial automation, service robotics, and disaster response.
Technical Contribution
The main technical contributions include: 1) the integration of Newton’s impact law directly into a multi-stage multiple-shooting NLP framework, ensuring physically consistent impact modeling; 2) reformulating the contact constraints as complementarity conditions enforced at each discretization point, avoiding the need for event detection; 3) leveraging the FORCES Pro solver’s primal-dual interior point method to efficiently handle large-scale MPCCs, drastically reducing solve times; 4) employing an implicit Euler discretization to enhance numerical stability during impacts. These innovations collectively enable high-fidelity, real-time trajectory optimization for complex contact scenarios, surpassing existing soft-contact or event-driven approaches in both accuracy and speed.
Novelty
This research is the first to embed Newton impact law within a multi-stage multiple-shooting contact-implicit optimization framework, directly enforcing impact physics at each discretization point. Unlike previous soft-contact or penalty-based methods, this approach guarantees physically consistent impact responses without requiring post-processing. The combination of hard contact modeling, complementarity constraints, and high-performance solvers results in a novel, scalable framework capable of real-time dynamic manipulation. This represents a significant step forward in non-smooth dynamics optimization, providing a robust foundation for future autonomous manipulation systems that demand both physical realism and computational efficiency.
Limitations
- The current model assumes no sliding friction, limiting applicability in scenarios involving complex frictional interactions. Incorporating detailed friction models remains an open challenge.
- The approach relies on parameter tuning such as time step size and objective weights, which may affect robustness and generalization across different tasks and environments.
- Handling extremely high-speed impacts or large-scale multi-contact scenarios may still pose computational challenges, requiring further optimization and hardware acceleration.
Future Work
Future research will focus on extending the framework to include dynamic friction models, such as Coulomb friction with slip, to handle a wider range of contact phenomena. Developing online adaptive algorithms for parameter tuning and real-time re-planning will enhance robustness. Scaling the method to multi-robot systems and multi-object scenarios will broaden its applicability. Additionally, integrating learning-based components to predict contact events and optimize parameters dynamically could further improve efficiency and adaptability. Ultimately, the goal is to realize fully autonomous, physically accurate, and computationally efficient robotic manipulation in complex, unstructured environments.
AI Executive Summary
Robotic manipulation in contact-rich environments has long been hindered by the challenge of accurately modeling and efficiently computing trajectories that respect complex physical constraints. Traditional methods often rely on soft contact models or simplified event-driven schemes, which either sacrifice physical realism or suffer from computational bottlenecks. This gap becomes particularly evident in dynamic tasks involving impacts, such as pushing objects, opening doors, or catching balls, where the non-smooth nature of contact dynamics demands sophisticated modeling and fast computation.
Addressing this challenge, the authors propose a novel contact-implicit trajectory optimization (CIO) framework based on a multi-stage multiple-shooting scheme. The key innovation lies in enforcing unilateral contact constraints through complementarity conditions at every discretized time point, coupled with Newton’s impact law to accurately capture impact dynamics. This approach ensures that the optimized trajectories are physically consistent, with no penetration and realistic impact responses. The use of an implicit Euler scheme for discretization guarantees numerical stability during high-speed impacts, which are common in dynamic manipulation tasks.
A major breakthrough of this work is leveraging the FORCES Pro solver, a high-performance optimization tool that exploits the problem’s multi-staged structure to efficiently solve large-scale nonlinear programs with complementarity constraints. This results in a dramatic reduction in computation time—from minutes to hundreds of milliseconds—making real-time trajectory planning feasible. The authors validate their method on a six-DOF robot performing tasks such as pushing a block, opening a door, and pushing a ball. Experimental results demonstrate that the generated trajectories are dynamically feasible, with contact forces aligning closely with physical predictions, and the robot successfully executing the tasks with high accuracy and repeatability.
The significance of this work extends beyond the specific tasks tested. It provides a scalable, physically accurate, and computationally efficient framework for dynamic manipulation in complex environments. By integrating advanced contact modeling with high-speed optimization, the method paves the way for autonomous robots capable of sophisticated interactions with their surroundings, including assembly, grasping, and impact-based tasks. The approach also opens new avenues for research in non-smooth dynamics, hybrid systems, and real-time control, with potential impacts across manufacturing, service robotics, and disaster response.
Looking ahead, the authors plan to incorporate more complex friction models, extend the framework to multi-robot and multi-object scenarios, and develop online adaptive algorithms. These advancements aim to further enhance the robustness, versatility, and real-world applicability of the method, ultimately contributing to the realization of fully autonomous, physically grounded robotic systems capable of operating seamlessly in unstructured, dynamic environments.
Deep Dive
Abstract
We present a reformulation of a contact-implicit optimization (CIO) approach that computes optimal trajectories for rigid-body systems in contact-rich settings. A hard-contact model is assumed, and the unilateral constraints are imposed in the form of complementarity conditions. Newton's impact law is adopted for enhanced physical correctness. The optimal control problem is formulated as a multi-staged program through a multiple-shooting scheme. This problem structure is exploited within the FORCES Pro framework to retrieve optimal motion plans, contact sequences and control inputs with increased computational efficiency. We investigate our method on a variety of dynamic object manipulation tasks, performed by a six degrees of freedom robot. The dynamic feasibility of the optimal trajectories, as well as the repeatability and accuracy of the task-satisfaction are verified through simulations and real hardware experiments on one of the manipulation problems.
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