- The paper introduces a smooth, closed-form Control Lyapunov Function integrated with omnidirectional RRT* to enable stable, real-time path planning.
- The system features a dual-layer architecture with a low-frequency planning thread and a high-frequency reactive thread that adapts to terrain variations.
- Experimental results on the Cassie Blue platform validate the approach, demonstrating efficient navigation across complex, unmapped terrains.
Reactive Planning System for Bipedal Locomotion in Undulating Terrains
This paper presents a reactive planning system tailored for bipedal robots navigating complex and unmapped terrains. Central to this research is the integration of a novel Control Lyapunov Function (CLF) within an omnidirectional Rapidly Exploring Random Tree (RRT*) to provide real-time path planning and adjustment capabilities, demonstrating the system's efficacy on the Cassie Blue bipedal robot.
System Architecture
The proposed system bridges a two-layered architectural design: a low-frequency planning thread and a high-frequency reactive thread. The planning thread operates at 5 Hz and incorporates several key components:
- Multi-Layer Local Map: This segment computes terrain traversability, allowing the robot to evaluate the feasibility of different paths based on elevation and slope.
- Anytime Omnidirectional CLF RRT*: The planning algorithm selects optimal sub-goals by leveraging an asymmetrically defined CLF that accounts for the biped's movement capabilities and limitations, particularly in lateral motion.
- Sub-goal Finding and Finite State Machine: These components enable the system to dynamically choose and update movement targets, accounting for situations where the final goal is beyond the current observable map segment.
The reactive thread functions at a significantly higher frequency of 300 Hz. Its role is to ensure the robot adapts to deviations from the planned path without inducing abrupt, non-smooth motions. This is achieved by utilizing a vector field that dynamically provides control commands based on the robot's instantaneous pose.
Key Contributions and Findings
One of the primary contributions is the development of a smooth CLF with a closed-form solution tailored for bipedal robots capable of omnidirectional movement. This function diverges from traditional wheeled robot models by emphasizing the robot's ability to approach a goal while managing orientation asymmetries. An accompanying distance metric within a pose-centric polar coordinate framework allows the planner to account for varying movement costs in different directions, particularly emphasizing the difficulty of lateral walking for bipeds like Cassie Blue.
The paper underscores the importance of integrating reactive planning into bipedal locomotion, particularly for environments that challenge the conventional planar assumptions of motion planning methods such as RRT. The performance metrics established in the simulations and real-world experiments suggest that the system provides stable, feasible paths across a variety of terrains, validating the theoretical constructs of the CLF.
Experimental Validation
The system was evaluated in simulated and experimental scenarios. Simulation tests used a simplified ALIP model to validate path planning across diverse terrains, yielding positive results. Further, Cassie Blue underwent a comprehensive set of experiments demonstrating the system's real-time adaptability on actual hardware. This included navigating the Wave Field with irregular terrain geometry and executing complex navigational strategies within indoor environments featuring dynamic obstacles.
Implications and Future Directions
The framework set forth in this paper carries significant implications for developing autonomous capabilities in bipedal robots. Beyond immediate applications, the concepts introduced, including the novel CLF and the memory-efficient local mapping techniques, present potential adaptations for application to a broader class of legged robots. Moreover, further exploration might involve refining control strategies to integrate Control Barrier Functions (CBF) to enhance obstacle avoidance, potentially extending system capabilities to include dynamic environments.
Looking forward, enhancing the CLF to support three-dimensional path planning and navigational tasks stands as a compelling avenue for exploration, providing a pathway to more robust autonomy in diverse operational contexts.