Structured contact force optimization for kino-dynamic motion generation (1605.08571v2)

Abstract: Optimal control approaches in combination with trajectory optimization have recently proven to be a promising control strategy for legged robots. Computationally efficient and robust algorithms were derived using simplified models of the contact interaction between robot and environment such as the linear inverted pendulum model (LIPM). However, as humanoid robots enter more complex environments, less restrictive models become increasingly important. As we leave the regime of linear models, we need to build dedicated solvers that can compute interaction forces together with consistent kinematic plans for the whole-body. In this paper, we address the problem of planning robot motion and interaction forces for legged robots given predefined contact surfaces. The motion generation process is decomposed into two alternating parts computing force and motion plans in coherence. We focus on the properties of the momentum computation leading to sparse optimal control formulations to be exploited by a dedicated solver. In our experiments, we demonstrate that our motion generation algorithm computes consistent contact forces and joint trajectories for our humanoid robot. We also demonstrate the favorable time complexity due to our formulation and composition of the momentum equations.

• The paper introduces an iterative algorithm that alternates between kinematic and momentum computations to optimize contact forces in legged robots.
• It leverages sparse optimal control formulations with integrated force variables to achieve significant computational efficiency improvements.
• Experimental results on simulated humanoids demonstrate consistent joint trajectories and effective force management across varied terrains.

Structured Contact Force Optimization for Kinodynamic Motion Generation: An Essay

This paper focuses on refining motion generation for legged robots by optimizing structured contact forces. It challenges the limitations of linear dynamic models, like the linear inverted pendulum model (LIPM), which traditionally facilitate locomotion tasks but falter in more complex environments. The research explores computationally efficient methodologies that integrate contact force optimization with whole-body kinematic planning, presenting a kinodynamic motion generation strategy that manages interaction forces for legged robots given predefined contact surfaces.

Core Contributions

The paper introduces an iterative motion generation algorithm that alternates between kinematic and momentum computations. Central to this approach is the decomposition of the motion planning problem into sub-problems that solve for force distributions and kinematic trajectories. This iterative strategy ensures that solutions are dynamically consistent, addressing the integration of external forces with kinematic models.

The authors employ optimal control formulations to establish momentum computations as sparse mathematical problems. This sparseness is exploited during optimization, enabling efficient problem-solving processes. A significant aspect discussed is the representation of contact forces and the influence of this representation on constraint formulations. By selectively representing forces acting at specific points, either at the center of pressure or the center of mass, they demonstrate how this influences algebraic properties and constraint structures.

The introduction of integrated variables for forces and torques optimizes the problem structure further, allowing rotational motion constraints to be resolved more effectively. The sequential approach, characterized by twice-integrated force variables, reveals how sparse representations can enhance computational efficiency and reduce problem size compared to simultaneous formulations.

Numerical and Experimental Insights

The paper presents results from experiments performed on a simulated humanoid stepping on varied terrains. Initial results highlight the coherence of joint trajectories and contact forces generated by the algorithm. The iterative optimization demonstrates convergence within reasonable computational limits and is reinforced by favorable numerical complexity scaling with time discretization.

Computational analyses reveal that both simultaneous and sequential optimal formulations maintain sparse structures conducive to efficient computation, especially when utilizing interior-point methods in optimization. The sequential formulation reduces the number of state variables significantly, indicating substantial efficiency improvements over simultaneous methods.

Implications for Robotics and AI

This paper's approach, particularly in the construction of sparse optimal control problems, has significant implications for robotics systems managing complex interactions with environments. The integration of contact force optimizations in motion generation holds promise for humanoid robots navigating uneven terrains or performing sophisticated maneuvers. Additionally, the findings propose efficiency improvements that can be applied more broadly across robotics and potentially in AI-driven control systems requiring dynamic problem-solving.

Future Directions

Further research could explore the extension of these methods to incorporate variable real-world environments and adapt dynamically to changing conditions. Addressing collision detection and avoidance in the motion generation phase could expand the algorithm's application scope to cluttered environments. The integration with more advanced contact planners that dynamically update contact points during motion could also present a logical progression of this work, ensuring adaptability and robustness in real-world applications.

In conclusion, this paper marks a significant advancement in the domain of structured contact force optimization for humanoid robotics. The innovative approach towards optimizing kinodynamic motion through sparse optimal formulations provides a promising pathway for enhancing robotic capabilities in complex environments.