Complementarity-Free Multi-Contact Modeling and Optimization for Dexterous Manipulation (2408.07855v2)

Abstract: A significant barrier preventing model-based methods from matching the high performance of reinforcement learning in dexterous manipulation is the inherent complexity of multi-contact dynamics. Traditionally formulated using complementarity models, multi-contact dynamics introduces combinatorial complexity and non-smoothness, complicating contact-rich planning and control. In this paper, we circumvent these challenges by introducing a novel, simplified multi-contact model. Our new model, derived from the duality of optimization-based contact models, dispenses with the complementarity constructs entirely, providing computational advantages such as explicit time stepping, differentiability, automatic satisfaction of Coulomb friction law, and minimal hyperparameter tuning. We demonstrate the effectiveness and efficiency of the model for planning and control in a range of challenging dexterous manipulation tasks, including fingertip 3D in-air manipulation, TriFinger in-hand manipulation, and Allegro hand on-palm reorientation, all with diverse objects. Our method consistently achieves state-of-the-art results: (I) a 96.5% average success rate across tasks, (II) high manipulation accuracy with an average reorientation error of 11{\deg} and position error of 7.8 mm, and (III) model predictive control running at 50-100 Hz for all tested dexterous manipulation tasks. These results are achieved with minimal hyperparameter tuning.

• The paper introduces a novel complementarity-free formulation that simplifies multi-contact dynamics for dexterous robotic manipulation.
• It achieves explicit time-stepping, automatic friction compliance, and minimal hyperparameter tuning to enhance performance.
• The model demonstrates high precision and real-time capability with success rates around 96-97% in diverse manipulation tasks.

An Overview of Complementarity-Free Multi-Contact Modeling and Optimization for Dexterous Manipulation

The paper "Complementarity-Free Multi-Contact Modeling and Optimization for Dexterous Manipulation" introduces an innovative framework for addressing the complexities associated with the multi-contact dynamics inherent in dexterous robotic manipulation. Traditional model-based methods have struggled in these tasks due to the hybrid and non-smooth nature of multi-contact dynamics, typically represented using complementarity models which introduce significant computational challenges.

Key Contribution

This work circumvents these obstacles by proposing a novel, simplified multi-contact model that dispenses with complementarity constructs entirely. This approach leverages optimization-based contact models' duality to create a complementarity-free formulation. The primary advantages of this new model include:

• Explicit Time-Stepping and Differentiability: The model allows the next system state to be explicitly determined as a differentiable function of the current state and inputs.
• Automatic Satisfaction of Coulomb’s Friction Law: The model inherently respects the frictional constraints without requiring additional parameters or approximative models.
• Minimal Hyperparameter Tuning: The new model reduces dependency on hyperparameters, streamlining the configuration process for different tasks and environments.

Methodology

The authors derive the theoretical foundation of their model by addressing inherent issues in traditional rigid-body contact dynamics, generally formulated with nonconvex complementarity constraints. Instead, their approach involves transforming these constructs in the dual space of optimization-based models, resulting in an explicit form. The derived model bypasses the need to solve nonlinear complementarity problems (NCPs) or their relaxed versions, such as cone complementarity problems (CCPs), significantly improving computation efficiency.

Theoretical Basis

The crux of the paper lies in the transformation of contact dynamics:

• The dual formulation is relaxed using a diagonal positive definite matrix $\boldsymbol{K}(\boldsymbol{q})$, approximating the matrix formed from traditional contact constraints.
• This results in a closed-form solution for the dual problem, eliminating complementarity constructs and simplifying the contact force calculations into straightforward mathematical operations.

Applications and Results

The authors demonstrate their model's effectiveness across various challenging dexterous manipulation tasks—including fingertip 3D in-air manipulation, TriFinger in-hand manipulation, and Allegro hand on-palm reorientation—achieving a notably high performance:

• 96.5% Average Success Rate: For a range of dexterous manipulation tasks.
• Accuracy: High precision with an average reorientation error of $11^\circ$ and position error of $7.8 \text{mm}$.
• Real-Time Performance: Model predictive control (MPC) achieves speeds of 50-100 Hz.

Case Studies

Fingertip Manipulation

Testing on different objects (e.g., Stanford bunny, cube, foam brick, stick) revealed that the proposed model excels in both in-air manipulation and ground operations. The robustness across these diverse objects underscores the model's generalizability and efficiency.

TriFinger In-Hand Manipulation

The model maintained high accuracy and speed during TriFinger tasks, demonstrating superior success rates compared to complementarity-based methods. The flexibility in parameter $\boldsymbol{K}(\boldsymbol{q})$ settings further proved the model's robustness, showing acceptable performance across a range of parameter values.

Allegro Hand On-Palm Reorientation

The Allegro hand tests involved complex reorientation tasks, where the model continued to deliver high performance. The overall success rate was around 97.64%, showcasing the model's ability to handle intricate finger-object interactions and maintain stability in manipulation.

Implications and Future Work

The practical implications of this research are substantial. The model’s efficiency and real-time capability pave the way for more advanced robotic applications requiring dexterous manipulation. The theoretical implications also merit attention, as this complementarity-free approach opens new avenues for developing smoother, more computationally friendly multi-contact models.

Future developments may explore:

• Integration of Learning Frameworks: Further reduction in hyperparameters through learning-based tuning.
• Extension to Full Dynamic Models: Examining the model’s applicability in scenarios involving more dynamic motions.
• Real-World Deployment: Transitioning from simulation environments to real-world robotic manipulations.

This research signifies a meaningful advancement in facilitating more efficient and effective model-based methods for dexterous manipulation, promising significant improvements in both robot autonomy and control precision.