Crocoddyl: An Efficient and Versatile Framework for Multi-Contact Optimal Control (1909.04947v2)

Abstract: We introduce Crocoddyl (Contact RObot COntrol by Differential DYnamic Library), an open-source framework tailored for efficient multi-contact optimal control. Crocoddyl efficiently computes the state trajectory and the control policy for a given predefined sequence of contacts. Its efficiency is due to the use of sparse analytical derivatives, exploitation of the problem structure, and data sharing. It employs differential geometry to properly describe the state of any geometrical system, e.g. floating-base systems. Additionally, we propose a novel optimal control algorithm called Feasibility-driven Differential Dynamic Programming (FDDP). Our method does not add extra decision variables which often increases the computation time per iteration due to factorization. FDDP shows a greater globalization strategy compared to classical Differential Dynamic Programming (DDP) algorithms. Concretely, we propose two modifications to the classical DDP algorithm. First, the backward pass accepts infeasible state-control trajectories. Second, the rollout keeps the gaps open during the early "exploratory" iterations (as expected in multiple-shooting methods with only equality constraints). We showcase the performance of our framework using different tasks. With our method, we can compute highly-dynamic maneuvers (e.g. jumping, front-flip) within few milliseconds.

• The paper introduces the FDDP algorithm that extends traditional DDP by handling infeasible state-control trajectories to improve multi-contact optimization.
• The paper demonstrates computation efficiency by solving high-dynamic maneuvers like jumping and flipping within milliseconds using sparse analytical derivatives.
• The paper leverages a feasibility-driven multiple-shooting approach that paves the way for real-time control applications in complex robotic tasks.

An Efficient and Versatile Framework for Multi-Contact Optimal Control

The paper presents "Crocoddyl," a new open-source framework designed for efficient multi-contact optimal control (OC) in legged robotics. This framework significantly contributes to computational efficiency and versatility by leveraging sparse analytical derivatives, exploiting problem structures, and employing techniques such as differential geometric handling of the state space. It introduces the Feasibility-driven Differential Dynamic Programming (FDDP) algorithm, enhancing the classical Differential Dynamic Programming (DDP) by allowing infeasible state-control trajectories and a novel approach to dynamic rollout.

Key Contributions

The contributions of the paper are notable in several areas:

1. Optimization Framework: Crocoddyl provides a robust platform for solving multi-contact OC problems, efficiently handling the computational demands associated with legged robotic applications. The efficient calculation of state trajectories and control policies, alongside the novel FDDP algorithm, makes the framework not just effective but versatile across various robotic tasks.
2. FDDP Algorithm: The introduced algorithm extends DDP by maintaining open gaps during the early iterations of the optimization process, capitalizing on multiple-shooting methods that use only equality constraints. This approach allows the handling of infeasible guesses that occur due to the discontinuities in trajectory optimization, particularly beneficial in highly dynamic maneuvers.
3. Dynamic Maneuvers: The paper reports achieving high-dynamic maneuvers such as jumping and flipping with computational efficiency, solving these complex tasks within milliseconds. These results underscore the framework's capability to adapt to diverse robotic control scenarios seamlessly.
4. Computation Efficiency: The framework's design focuses on computation efficiency by integrating routines for Lie groups and leveraging sparse derivatives for contact and impulse dynamics. This efficiency is demonstrated through benchmarking across various CPUs with different levels of parallelization.

Theoretical and Practical Implications

Crocoddyl's framework has the potential to influence both theoretical and practical spheres in robotic control:

• From a theoretical perspective, the introduction of the FDDP offers new insights into OC methodologies, particularly the role of infeasible trajectory handling and gap contraction strategies. The algorithm's equivalency with Newton's method for multiple-shooting formulations with equality constraints may pave the way for further exploration into OC problem-solving paradigms.
• Practically, Crocoddyl holds significant potential for real-time control applications in legged robotics. Its ability to perform under constraints involving contact dynamics suggests broad applicability in environments where robots need to exhibit dynamic and complex motion patterns.

Future Research Directions

The research outlines several avenues for future exploration:

• Integration of Inequality Constraints: The extension of the feasibility concept to encompass inequality constraints, such as joint torque limits and friction cones, remains a critical development point. Techniques like Augmented Lagrangian or interior-point methods could be important in this context.
• Broader Applicability and Robustness: Further evaluation of Crocoddyl's framework with different robots and under varying real-world conditions could help fine-tune its applicability and robustness. Additionally, adaptation for tasks involving non-legged robots might enhance its utility across more diverse robotic domains.

In conclusion, this paper offers a considerable advancement in the field of multi-contact OC for legged robotics. The innovative elements of the Crocoddyl framework, particularly the FDDP algorithm, underscore the burgeoning potential for improved computational efficiency and adaptability in robotic control applications. As the framework continues to evolve, it is poised to contribute significantly to the practical deployment of agile and responsive robotic systems in variable operational contexts.