[Paper Review] Integrated Task and Motion Planning for Safe Legged Navigation in Partially Observable Environments

Abdulaziz Shamsah, Zhaoyuan Gu+3 more|arXiv (Cornell University)|Oct 23, 2021

Robotic Locomotion and Control54 references4 citations

TL;DR

This paper presents a hierarchically integrated task and motion planning (TAMP) framework for safe bipedal navigation in partially observable, dynamic environments with adversarial obstacles. It combines linear temporal logic (LTL) for high-level task planning with a reduced-order model (ROM)-based motion planner and a passivity-based foot placement controller, achieving formal safety guarantees and robustness against external perturbations on Cassie and Digit robots.

ABSTRACT

This study proposes a hierarchically integrated framework for safe task and motion planning (TAMP) of bipedal locomotion in a partially observable environment with dynamic obstacles and uneven terrain. The high-level task planner employs linear temporal logic (LTL) for a reactive game synthesis between the robot and its environment and provides a formal guarantee on navigation safety and task completion. To address environmental partial observability, a belief abstraction is employed at the high-level navigation planner to estimate the dynamic obstacles' location. Accordingly, a synthesized action planner sends a set of locomotion actions to the middle-level motion planner, while incorporating safe locomotion specifications extracted from safety theorems based on a reduced-order model (ROM) of the locomotion process. The motion planner employs the ROM to design safety criteria and a sampling algorithm to generate non-periodic motion plans that accurately track high-level actions. At the low level, a foot placement controller based on an angular-momentum linear inverted pendulum model is implemented and integrated with an ankle-actuated passivity-based controller for full-body trajectory tracking. To address external perturbations, this study also investigates safe sequential composition of the keyframe locomotion state and achieves robust transitions against external perturbations through reachability analysis. The overall TAMP framework is validated with extensive simulations and hardware experiments on bipedal walking robots Cassie and Digit designed by Agility Robotics.

Motivation & Objective

• Address the challenge of safe, formal navigation for bipedal robots in partially observable environments with dynamic and potentially adversarial obstacles.
• Provide multi-level formal safety guarantees across task, motion, and low-level control layers for underactuated legged systems.
• Integrate belief abstraction into high-level planning to handle sensor limitations and occlusions, ensuring collision avoidance despite partial observability.
• Ensure safe execution of high-level commands through ROM-based motion planning and reachability analysis for robust locomotion transitions.
• Validate the framework on both simulation and hardware (Cassie and Digit) to demonstrate real-world applicability and robustness under perturbations.

Proposed method

• Employ linear temporal logic (LTL) with reactive game synthesis to generate high-level navigation actions that formally guarantee safety and task completion.
• Introduce a belief abstraction in the high-level planner to estimate the set of possible locations of dynamic, non-visible obstacles, enabling safe navigation under partial observability.
• Use a reduced-order model (ROM) of the linear inverted pendulum to derive safety constraints and hyperparameters for non-periodic motion planning in the middle-level planner.
• Implement a phase-space planning (PSP) approach that integrates symbolically with the high-level LTL planner through hybrid planning, enabling safe, non-periodic gait generation.
• Design a foot placement controller based on the angular-momentum linear inverted pendulum model (ALIP), modified for phase-space plans, and integrate it with an ankle-actuated passivity-based controller for full-body trajectory tracking.
• Apply reachability analysis to ensure safe sequential composition of keyframe locomotion states, enabling robust transitions under external perturbations such as CoM velocity jumps.

Experimental results

Research questions

• RQ1 How can formal safety guarantees be achieved for both task completion and locomotion in a partially observable environment with dynamic, possibly adversarial obstacles?
• RQ2 What role does belief abstraction play in enabling safe navigation when the robot cannot observe all obstacles due to occlusions or limited sensor range?
• RQ3 How can a reduced-order model (ROM) of bipedal locomotion be used to generate safe, non-periodic motion plans that are compatible with high-level symbolic task plans?
• RQ4 What control architecture ensures robust full-body trajectory tracking and resilience to external disturbances while maintaining safety constraints?
• RQ5 How can safe sequential composition of keyframe states be achieved to ensure robust locomotion transitions under perturbations?

Key findings

• The proposed TAMP framework successfully enables safe navigation of bipedal robots in partially observable, dynamic environments with formal guarantees on safety and task completion.
• Belief abstraction in the high-level planner effectively handles uncertainty from occluded dynamic obstacles, ensuring collision avoidance across a broader set of environments.
• The integration of ROM-based motion planning with LTL task planning enables the generation of non-periodic, safe gait sequences that accurately track high-level commands.
• Hardware experiments on the 28-DoF Digit robot demonstrate successful full-body trajectory tracking with minimized foot placement and CoM velocity errors using the modified ALIP and passivity-based controller.
• Reachability analysis-based safe sequential composition of keyframe states enables robust locomotion transitions even under external perturbations such as sudden CoM velocity changes.
• The framework was validated through extensive simulations and real-world experiments on both Cassie and Digit, confirming its effectiveness and robustness in complex, real-world scenarios.