Global Planning for Contact-Rich Manipulation via Local Smoothing of Quasi-dynamic Contact Models (2206.10787v2)

Abstract: The empirical success of Reinforcement Learning (RL) in the setting of contact-rich manipulation leaves much to be understood from a model-based perspective, where the key difficulties are often attributed to (i) the explosion of contact modes, (ii) stiff, non-smooth contact dynamics and the resulting exploding / discontinuous gradients, and (iii) the non-convexity of the planning problem. The stochastic nature of RL addresses (i) and (ii) by effectively sampling and averaging the contact modes. On the other hand, model-based methods have tackled the same challenges by smoothing contact dynamics analytically. Our first contribution is to establish the theoretical equivalence of the two methods for simple systems, and provide qualitative and empirical equivalence on a number of complex examples. In order to further alleviate (ii), our second contribution is a convex, differentiable and quasi-dynamic formulation of contact dynamics, which is amenable to both smoothing schemes, and has proven through experiments to be highly effective for contact-rich planning. Our final contribution resolves (iii), where we show that classical sampling-based motion planning algorithms can be effective in global planning when contact modes are abstracted via smoothing. Applying our method on a collection of challenging contact-rich manipulation tasks, we demonstrate that efficient model-based motion planning can achieve results comparable to RL with dramatically less computation. Video: https://youtu.be/12Ew4xC-VwA

• The paper’s main contribution is the CQDC model that integrates local smoothing to mitigate numerical instabilities in contact-rich manipulation planning.
• It employs both randomized and analytic (log-barrier) smoothing techniques to balance computational efficiency with accurate quasi-dynamic simulation.
• Experimental results demonstrate that the approach outperforms traditional planners in tasks like dexterous in-hand manipulation and extrinsic dexterity.

Global Planning for Contact-Rich Manipulation: Local Smoothing of Dynamics

In the field of robotic manipulation, the complexity of contact-rich interactions presents significant challenges. The paper, "Global Planning for Contact-Rich Manipulation via Local Smoothing of Quasi-dynamic Contact Models," addresses these challenges by innovating on traditional model-based planning techniques through the integration of local smoothing approaches. The authors propose a novel contact dynamics model that effectively balances computational efficiency with the ability to capture the nuances of contact interactions, offering a significant advancement in contact-rich manipulation planning.

The key contribution of this paper lies in the development and analysis of a Convex, Quasi-dynamic, Differentiable Contact (CQDC) model. This model extends conventional quasi-dynamic systems by incorporating a convex formulation that manages rigid body contact through Anitescu's relaxation of friction constraints, mitigating the numerical instability often associated with traditional linear complementarity formulations. The CQDC model assumes a high-damping environment, a typical characteristic in robotic manipulation, allowing for robust predictions of long-term behavior without the complexities involved in simulating transient dynamics.

To further enhance the practical utility of their model, the authors bridge theoretical concepts with effective computational techniques. They introduce both randomized and analytic smoothing techniques to handle the inherent stiffness and non-smooth nature of contact dynamics. Randomized smoothing aligns with techniques often seen in reinforcement learning, offering an empirical balance between accuracy and computational cost, while analytic smoothing employs a log-barrier approach, akin to methods used in optimization, to achieve similar smoothing of contact dynamics.

The equivalence of these smoothing schemes is demonstrated for simple systems, with qualitative and empirical evidence provided for more complex scenarios. This theoretical framework allows the authors to substantiate their choice of a novel distance metric that is informed by local dynamic models. The proposed Local Mahalanobis Metric leverages the smooth surrogate dynamics to guide sampling-based motion planners (SBMPs), particularly Rapidly-Exploring Random Trees (RRTs), in exploring state spaces efficiently under the contact dynamic constraints.

The integration of smoothing techniques with a robust contact dynamics model culminates in a planner capable of addressing the global search problem inherent in contact-rich manipulation tasks. By employing a Mahalanobis metric derived from smoothed dynamic characteristics, the planner is shown to outperform those that do not incorporate reachability information or that rely on explicit contact mode enumeration. Notably, this planner is efficient enough to operate within the computational constraints typically encountered in practical applications.

Experimental results illustrate that the proposed model and planning approach can handle a diverse range of manipulation tasks, including dexterous in-hand object manipulation and tasks requiring extrinsic dexterity. The CQDC model coupled with local smoothing is shown to achieve results comparable to reinforcement learning-based approaches but with significantly reduced computational overhead.

In conclusion, the innovations presented in this paper have significant implications for the development of robotic systems capable of real-time, online planning in environments with complex contact interactions. The theoretical and computational advancements outlined suggest promising directions for future work, including real-time implementation and integration with machine learning frameworks to enhance adaptive behavior in robotics. With the CQDC model and its smoothing strategies, this research sets a foundation for advancing intelligent robotic manipulation capabilities in both structured and unstructured environments.