From Compliant to Rigid Contact Simulation: a Unified and Efficient Approach

Abstract: Whether rigid or compliant, contact interactions are inherent to robot motions, enabling them to move or manipulate things. Contact interactions result from complex physical phenomena, that can be mathematically cast as Nonlinear Complementarity Problems (NCPs) in the context of rigid or compliant point contact interactions. Such a class of complementarity problems is, in general, difficult to solve both from an optimization and numerical perspective. Over the past decades, dedicated and specialized contact solvers, implemented in modern robotics simulators (e.g., Bullet, Drake, MuJoCo, DART, Raisim) have emerged. Yet, most of these solvers tend either to solve a relaxed formulation of the original contact problems (at the price of physical inconsistencies) or to scale poorly with the problem dimension or its numerical conditioning (e.g., a robotic hand manipulating a paper sheet). In this paper, we introduce a unified and efficient approach to solving NCPs in the context of contact simulation. It relies on a sound combination of the Alternating Direction Method of Multipliers (ADMM) and proximal algorithms to account for both compliant and rigid contact interfaces in a unified way. To handle ill-conditioned problems and accelerate the convergence rate, we also propose an efficient update strategy to adapt the ADMM hyperparameters automatically. By leveraging proximal methods, we also propose new algorithmic solutions to efficiently evaluate the inverse dynamics involving rigid and compliant contact interactions, extending the approach developed in MuJoCo. We validate the efficiency and robustness of our contact solver against several alternative contact methods of the literature and benchmark them on various robotics and granular mechanics scenarios. Our code is made open-source at https://github.com/Simple-Robotics/Simple.

• The paper proposes a novel unified approach leveraging ADMM with proximal methods and adaptive hyperparameters to efficiently and robustly solve Nonlinear Complementarity Problems for both compliant and rigid contacts in robotic simulations.
• Numerical experiments demonstrate substantial performance gains over existing solvers on challenging benchmarks, improving both efficiency and physical consistency in multi-contact scenarios.
• This work provides a robust, scalable framework for robotic simulators and is open-sourced, facilitating future research and application across diverse fields requiring precise dynamic modeling.

Unified and Efficient Approach to Contact Simulation in Robotics

The paper "From Compliant to Rigid Contact Simulation: A Unified and Efficient Approach" presents a novel methodology for addressing contact interaction complexities in robotics, specifically through Nonlinear Complementarity Problems (NCPs) related to both rigid and compliant point contacts. Traditional solvers used in prevalent simulation environments often compromise on either the physical consistency or scalability in tackling these problems. The authors propose a unified solution leveraging the Alternating Direction Method of Multipliers (ADMM) in conjunction with proximal algorithms to ameliorate such trade-offs.

Methodological Insights

The core innovation of this work lies in deploying ADMM-based frameworks for solving NCPs that arise in dynamic simulations involving contact. This approach strategically utilizes proximal methods to create a conciliatory model that integrates rigid and compliant interfaces within a singular methodological framework. One challenge in NCPs is the poor conditioning presented by real-world scenarios, like a robotic hand manipulating high-flexibility objects. To counter this, the authors introduce an adaptive strategy that dynamically updates ADMM hyperparameters, significantly enhancing robustness and convergence rates.

Numerical Performance

The numerical experiments conducted showcase the robust and efficient nature of the devised contact solver. The extensive experimentation covered a variety of challenging benchmark settings from both robotics and computational mechanics communities. The introduction of a proximal-based inverse dynamics evaluation further extends the capabilities of simulators similar to MuJoCo. Empirical results indicate substantial performance gains over existing solvers, particularly in high-complexity environments characterized by multiple simultaneous contacts and intricate physical interactions.

Implications and Future Work

This work offers impactful contributions to the domain of robotic simulations both from theoretical and practical perspectives. It not only provides a framework to improve computational efficiency in robotic simulations but also advances the fidelity of simulations by maintaining physical consistency without falling into computational limitations. The inherent adaptability of the proposed methods aligns well with the growing demands for scalable solutions in dynamic multi-contact robotics scenarios.

Future research directions could explore the enhancement of the collision detection routines, which remain computational bottlenecks. The robustness of this approach against potential algorithmic divergence suggests that developing theoretical convergence guarantees could further cement its reliability. Moreover, broadening the applicability of the inverse dynamics algorithm could accommodate scenarios involving underactuation and unattainable reference accelerations.

By open-sourcing the codebase, the authors facilitate further validation and evolution of their work in diverse applications, ranging from robotic manipulation to more complex simulations requiring precise dynamic modeling. This direction signifies a promising trajectory toward improved, physically consistent, and computationally efficient robotic simulators, potentially impacting various fields where simulation capabilities are critical.