Trajectory Optimization Through Contacts and Automatic Gait Discovery for Quadrupeds (1607.04537v1)

Abstract: In this work we present a trajectory Optimization framework for whole-body motion planning through contacts. We demonstrate how the proposed approach can be applied to automatically discover different gaits and dynamic motions on a quadruped robot. In contrast to most previous methods, we do not pre-specify contact switches, timings, points or gait patterns, but they are a direct outcome of the optimization. Furthermore, we optimize over the entire dynamics of the robot, which enables the optimizer to fully leverage the capabilities of the robot. To illustrate the spectrum of achievable motions, here we show eight different tasks, which would require very different control structures when solved with state-of-the-art methods. Using our trajectory Optimization approach, we are solving each task with a simple, high level cost function and without any changes in the control structure. Furthermore, we fully integrated our approach with the robot's control and estimation framework such that optimization can be run online. By demonstrating a rough manipulation task with multiple dynamic contact switches, we exemplarily show how optimized trajectories and control inputs can be directly applied to hardware.

• The paper introduces a novel SLQ-based optimization framework that computes whole-body trajectories through continuous contact dynamics in quadruped robots.
• It demonstrates automatic gait discovery by optimizing trajectories without relying on pre-defined contact sequences.
• Experimental results confirm rapid convergence and versatile control, enabling both standard motion tasks and under-actuated, humanoid-like gait experiments.

Trajectory Optimization Through Contacts and Automatic Gait Discovery for Quadrupeds

The paper "Trajectory Optimization Through Contacts and Automatic Gait Discovery for Quadrupeds" presents a robust framework for whole-body motion planning applied to quadrupedal robots. The approach hinges on optimizing trajectory paths via contact, enabling the automatic discovery of various gaits and dynamic motions without relying on pre-specified patterns or timings. This methodology diverges from traditional systems that require defined contact points and sequences, instead allowing optimization to intuitively harness the entire dynamic potential of the quadruped robot.

The paper delineates the trajectory optimization problem as a general, time-varying, nonlinear optimal control problem, solved through Sequential Linear Quadratic (SLQ) control. SLQ is shown to be effective for complex legged systems, utilizing differential dynamic programming and a high-performance customized solver to keep optimization time manageable, typically under one minute.

Strong Points and Claims

The research asserts that discovering gaits and dynamic motions through contact optimization is pivotal, contrasting it with state-of-the-art methods that often limit the robot's adaptive capabilities by defining its movement parameters in advance. By leveraging complete dynamics, the framework reveals eight tasks requiring dissimilar control structures solved uniformly using high-level cost functions, necessitating no structural changes. This is significant, as traditional methods typically require numerous adjustments across disparate tasks.

SLQ's efficiency is highlighted through its rapid convergence for time-varying feedback and feedforward control generation, minimizing a quadratic cost function with rigorous waypoint guidance. This yields optimized motions where variables such as contact switching times emerge naturally from the solver's outcomes rather than as predefined constraints.

Theoretical and Practical Implications

From a theoretical perspective, the paper contributes to understanding the complexities of trajectory optimization in legged robotics not only by demonstrating SLQ's feasibility but also by integrating it with real-time robotic control frameworks. Practically, the robot hardware validation exemplifies the applicability of optimized trajectories even under real-world disturbances, showcasing the framework’s robust versatility and potential for expanding legged robotic applications.

The paper also ventures into under-actuated scenarios by having the quadruped robot walk on hind legs, experimenting with humanoid-like gaits not typically associated with quadrupeds. Such experiments push the boundaries of quadruped capabilities, unlocked through trajectory optimization techniques emphasized in this paper.

Future Outlook

Future developments could explore incorporating stochastic elements into SLQ to address dynamic environment challenges and improve trajectory robustness in noisy, unpredictable conditions. Furthermore, integration of SLQ into Model Predictive Control (MPC) as a re-planning method anticipates expanding trajectory optimization applications, accommodating complex navigational tasks in dynamic settings by maintaining real-time adaptability.

Ultimately, this paper posits trajectory optimization through contacts not just as a novel approach but as a significant expansion in the toolkit available for quadruped control systems. The capacity to discover gaits and manage dynamic motions seamlessly stands to offer substantial advancements across both theoretical robotics research and practical implementations.