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 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 model is designed by partitioning the environment into multiple belief regions and employed at the high-level navigation planner to estimate the dynamic obstacles' location. This additional location information of dynamic obstacles offered by belief abstraction enables less conservative long-horizon navigation actions beyond guaranteeing immediate collision avoidance. 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 nonperiodic 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 the 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.
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Reactive Locomotion Decision-Making and Robust Motion Planning for Real-Time Perturbation Recovery
In this paper, we examine the problem of push recovery for bipedal robot locomotion and present a reactive decision-making and robust planning framework for locomotion resilient to external perturbations. Rejecting perturbations is an essential capability of bipedal robots and has been widely studied in the locomotion literature. However, adversarial disturbances and aggressive turning can lead to negative lateral step width (i.e., crossed-leg scenarios) with unstable motions and self-collision risks. These motion planning problems are computationally difficult and have not been explored under a hierarchically integrated task and motion planning method. We explore a planning and decision-making framework that closely ties linear-temporal-logic-based reactive synthesis with trajectory optimization incorporating the robot’s full-body dynamics, kinematics, and leg collision avoidance constraints. Between the high-level discrete symbolic decision-making and the low-level continuous motion planning, behavior trees serve as a reactive interface to handle perturbations occurring at any time of the locomotion process. Our experimental results show the efficacy of our method in generating resilient recovery behaviors in response to diverse perturbations from any direction with bounded magnitudes.
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- Award ID(s):
- 1924978
- NSF-PAR ID:
- 10348405
- Date Published:
- Journal Name:
- International Conference on Robotics and Automation
- Page Range / eLocation ID:
- 1896 to 1902
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Contact-based decision and planning methods are becoming increasingly important to endow higher levels of autonomy for legged robots. Formal synthesis methods derived from symbolic systems have great potential for reasoning about high-level locomotion decisions and achieving complex maneuvering behaviors with correctness guarantees. This study takes a first step toward formally devising an architecture composed of task planning and control of whole-body dynamic locomotion behaviors in constrained and dynamically changing environments. At the high level, we formulate a two-player temporal logic game between the multi-limb locomotion planner and its dynamic environment to synthesize a winning strategy that delivers symbolic locomotion actions. These locomotion actions satisfy the desired high-level task specifications expressed in a fragment of temporal logic. Those actions are sent to a robust finite transition system that synthesizes a locomotion controller that fulfills state reachability constraints. This controller is further executed via a low-level motion planner that generates feasible locomotion trajectories. We construct a set of dynamic locomotion models for legged robots to serve as a template library for handling diverse environmental events. We devise a replanning strategy that takes into consideration sudden environmental changes or large state disturbances to increase the robustness of the resulting locomotion behaviors. We formally prove the correctness of the layered locomotion framework guaranteeing a robust implementation by the motion planning layer. Simulations of reactive locomotion behaviors in diverse environments indicate that our framework has the potential to serve as a theoretical foundation for intelligent locomotion behaviors.
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null (Ed.)Ultimately, feedback control is about making adjustments using current state information in order to meet an objective in the future. In the control of bipedal locomotion, linear velocity of the center of mass has been widely accepted as the primary variable around which feedback control objectives are formulated. In this paper, we argue that it is easier to predict the one-step ahead evolution of angular momentum about the contact point than it is to make a similar prediction for linear velocity, and hence it provides a superior quantity for feedback control. So as not to confuse the benefits of predicting angular momentum with any other control design decisions, we reformulate the standard LIP model in terms of angular momentum and show how to regulate swing foot touchdown position at the end of the current step so as to meet an angular momentum objective at the end of the next step. We implement the resulting feedback controller on the 20 degreeof- freedom bipedal robot, Cassie Blue, where each leg accounts for nearly one-third of the robot’s total mass of 32 Kg. Under this controller, the robot achieves fast walking, rapid turning while walking, large disturbance rejection, and locomotion on rough terrain.more » « less
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We propose a locomotion framework for bipedal robots consisting of a new motion planning method, dubbed trajectory optimization for walking robots plus (TOWR+), and a new whole-body control method, dubbed implicit hierarchical whole-body controller (IHWBC). For versatility, we consider the use of a composite rigid body (CRB) model to optimize the robot’s walking behavior. The proposed CRB model considers the floating base dynamics while accounting for the effects of the heavy distal mass of humanoids using a pre-trained centroidal inertia network. TOWR+ leverages the phase-based parameterization of its precursor, TOWR, and optimizes for base and end-effectors motions, feet contact wrenches, as well as contact timing and locations without the need to solve a complementary problem or integer program. The use of IHWBC enforces unilateral contact constraints (i.e., non-slip and non-penetration constraints) and a task hierarchy through the cost function, relaxing contact constraints and providing an implicit hierarchy between tasks. This controller provides additional flexibility and smooth task and contact transitions as applied to our 10 degree-of-freedom, line-feet biped robot DRACO. In addition, we introduce a new open-source and light-weight software architecture, dubbed planning and control (PnC), that implements and combines TOWR+ and IHWBC. PnC provides modularity, versatility, and scalability so that the provided modules can be interchanged with other motion planners and whole-body controllers and tested in an end-to-end manner. In the experimental section, we first analyze the performance of TOWR+ using various bipeds. We then demonstrate balancing behaviors on the DRACO hardware using the proposed IHWBC method. Finally, we integrate TOWR+ and IHWBC and demonstrate step-and-stop behaviors on the DRACO hardware.more » « less
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null (Ed.)Can we design motion primitives for complex legged systems uniformly for different terrain types without neglecting modeling details? This paper presents a method for rapidly generating quadrupedal locomotion on sloped terrains-from modeling to gait generation, to hardware demonstration. At the core of this approach is the observation that a quadrupedal robot can be exactly decomposed into coupled bipedal robots. Formally, this is represented through the framework of coupled control systems, wherein isolated subsystems interact through coupling constraints. We demonstrate this concept in the context of quadrupeds and use it to reduce the gait planning problem for uneven terrains to bipedal walking generation via hybrid zero dynamics. This reduction method allows for the formulation of a nonlinear optimization problem that leverages low-dimensional bipedal representations to generate dynamic walking gaits on slopes for the full-order quadrupedal robot dynamics. The result is the ability to rapidly generate quadrupedal walking gaits on a variety of slopes. We demonstrate these walking behaviors on the Vision 60 quadrupedal robot; in simulation, via walking on a range of sloped terrains of 13°, 15°, 20°, 25°, and, experimentally, through the successful locomotion of 13° and 20° ~ 25° sloped outdoor grasslands.more » « less
- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1109/ICRA46639.2022.9812068
