An Integrated Programmable CPG with Bounded Output (2204.07766v1)

Abstract: Cyclic motions are fundamental patterns in robotic applications including industrial manipulation and legged robot locomotion. This paper proposes an approach for the online modulation of cyclic motions in robotic applications. For this purpose, we present an integrated programmable Central Pattern Generator (CPG) for the online generation of the reference joint trajectory of a robotic system out of a library of desired periodic motions. The reference trajectory is then followed by the lower-level controller of the robot. The proposed CPG generates a smooth reference joint trajectory convergence to the desired one while preserving the position and velocity joint limits of the robot. The integrated programmable CPG consists of one novel bounded output programmable oscillator. We design the programmable oscillator for encoding the desired multidimensional periodic trajectory as a stable limit cycle. We also use the state transformation method to ensure that the oscillator's output and its first-time derivative preserve the joint position and velocity limits of the robot. With the help of Lyapunov-based arguments, We prove that the proposed CPG provides the global stability and convergence of the desired trajectory. The effectiveness of the proposed integrated CPG for trajectory generation is shown in a passive rehabilitation scenario on the Kuka iiwa robot arm, and also in a walking simulation on a seven-link bipedal robot.

• The paper presents a programmable oscillator design that produces stable, bounded cyclic trajectories using Lyapunov-based state transformation methods.
• It achieves dual stability by providing asymptotic stability for trajectory tracking and asymptotic orbital stability for maintaining limit cycles.
• The approach adapts to abrupt motion transitions in applications like industrial manipulation and legged locomotion, as demonstrated on robotic platforms.

Overview of "An Integrated Programmable CPG with Bounded Output"

The paper introduces an innovative method for modulating cyclic motions within robotic systems by proposing an integrated programmable Central Pattern Generator (CPG) with bounded output. Cyclic motions are essential in various robotic applications, such as industrial manipulation and legged robot locomotion, making the paper of significant interest to the field. This research presents a method for the online generation of reference joint trajectories from a library of desired periodic motions, ensuring that the trajectories conform with the position and velocity joint limits of the robot.

Key Contributions

1. Programmable Oscillator Design: The authors describe the construction of a programmable oscillator that facilitates the global stability and convergence of the desired multidimensional periodic trajectory. This oscillator leverages Lyapunov-based techniques for stability analysis and employs a state transformation method to maintain joint limits.
2. Bounded Output: The CPG consists of a novel bounded output programmable oscillator that encodes desired trajectories as stable limit cycles. The innovations extend the oscillator to encode multidimensional trajectories, ensuring both its output and its derivative respect the robot's joint limits.
3. Adaptability and Stability: The proposed approach allows smooth modulation and abrupt transition between target trajectories, offering both asymptotic stability (AS) for trajectory tracking and asymptotic orbital stability (AOS) for limit cycle tracking. This dual capability facilitates implementation across both constant postures and cyclic movements within robotic systems.

Numerical Results and Claims

The effectiveness of the proposed integrated CPG was demonstrated through passive rehabilitation applications on the Kuka iiwa robot arm and walking simulations on a seven-link bipedal robot. The integrated CPG successfully managed transitions between different desired motions while maintaining position and velocity limits. Additionally, the authors indicate that the CPG facilitates optimal motion tracking and consistently responds to changes in desired motion.

Implications

From a theoretical perspective, this research enhances understanding by illustrating how programmable oscillators can be effectively employed to maintain desired trajectory performance while adhering to physical constraints. Practically, this approach offers a reliable method for robot trajectory generation that can be applied in various domains requiring cyclic motion and constant stability, such as human-robot interaction and legged locomotion.

Future Directions

The paper provides foundational work that suggests several avenues for future exploration in AI and robotics. Integrating environmental feedback could further enhance adaptability, potentially improving real-world interaction capabilities and robustness. Additionally, exploring machine learning techniques to adaptively tune the oscillator parameters could automate response optimization to unforeseen perturbations. These developments could substantially advance flexible and reliable automated systems.

In conclusion, the paper represents a significant contribution to the efficient generation of bounded trajectories in robotic systems using the integrated CPG. The introduced techniques and demonstrated results show promise for broader applications, encouraging future research and development.