skip to main content


The NSF Public Access Repository (NSF-PAR) system and access will be unavailable from 5:00 PM ET until 11:00 PM ET on Friday, June 21 due to maintenance. We apologize for the inconvenience.

This content will become publicly available on October 1, 2024

Title: Informed Sampling-Based Planning to Enable Legged Robots to Safely Negotiate Permeable Obstacles
Abstract Legged robots have a unique capability of traversing rough terrains and negotiating cluttered environments. Recent control development of legged robots has enabled robust locomotion on rough terrains. However, such approaches mainly focus on maintaining balance for the robot body. In this work, we are interested in leveraging the whole body of the robot to pass through a permeable obstacle (e.g., a small confined opening) with height, width, and terrain constraints. This paper presents a planning framework for legged robots manipulating their body and legs to perform collision-free locomotion through a permeable obstacle. The planner incorporates quadrupedal gait constraint, biasing scheme, and safety margin for the simultaneous body and foothold motion planning. We perform informed sampling for the body poses and swing foot position based on the gait constraint while ensuring stability and collision avoidance. The footholds are planned based on the terrain and the contact constraint. We also integrate the planner with robot control to execute the planned trajectory successfully. We validated our approach in high-fidelity simulation and hardware experiments on the Unitree A1 robot navigating through different representative permeable obstacles.  more » « less
Award ID(s):
Author(s) / Creator(s):
; ; ; ;
Date Published:
Journal Name:
Journal of Mechanisms and Robotics
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. Legged robots have the advantage of being able to maneuver rough, unstructured terrains unlike their wheeled counterparts. However, many legged robots require multiple sensors and online computations to specify the gait, trajectory or contact forces in real-time for a given terrain, and these methods can break down when sensory information is unreliable or not available. Over the years, underactuated mechanisms have demonstrated great success in object grasping and manipulation tasks due to their ability to passively adapt to the geometry of the objects without sensors. In this paper, we present an application of underactuation in the design of a legged robot with prismatic legs that maneuvers unstructured terrains under open-loop control using only four actuators – one for stance for each half of the robot, one for forward translation, and one for steering. Through experimental results, we show that prismatic legs can support a statically stable stance and can facilitate locomotion over unstructured terrain while maintaining its body posture. 
    more » « less
  2. Natural environments are often filled with obstacles and disturbances. Traditional navigation and planning approaches normally depend on finding a traversable “free space” for robots to avoid unexpected contact or collision. We hypothesize that with a better understanding of the robot–obstacle interactions, these collisions and disturbances can be exploited as opportunities to improve robot locomotion in complex environments. In this article, we propose a novel obstacle disturbance selection (ODS) framework with the aim of allowing robots to actively select disturbances to achieve environment-aided locomotion. Using an empirically characterized relationship between leg–obstacle contact position and robot trajectory deviation, we simplify the representation of the obstacle-filled physical environment to a horizontal-plane disturbance force field. We then treat each robot leg as a “disturbance force selector” for prediction of obstacle-modulated robot dynamics. Combining the two representations provides analytical insights into the effects of gaits on legged traversal in cluttered environments. We illustrate the predictive power of the ODS framework by studying the horizontal-plane dynamics of a quadrupedal robot traversing an array of evenly-spaced cylindrical obstacles with both bounding and trotting gaits. Experiments corroborate numerical simulations that reveal the emergence of a stable equilibrium orientation in the face of repeated obstacle disturbances. The ODS reduction yields closed-form analytical predictions of the equilibrium position for different robot body aspect ratios, gait patterns, and obstacle spacings. We conclude with speculative remarks bearing on the prospects for novel ODS-based gait control schemes for shaping robot navigation in perturbation-rich environments. 
    more » « less
  3. 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
  4. : Inspired by the locomotor nervous system of vertebrates, central pattern generator (CPG) models can be used to design gaits for articulated robots, such as crawling, swimming or legged robots. Incorporating sensory feedback for gait adaptation in these models can improve the locomotive performance of such robots in challenging terrain. However, many CPG models to date have been developed exclusively for open-loop gait generation for traversing level terrain. In this paper, we present a novel approach for incorporating inertial feedback into the CPG framework for the control of body posture during legged locomotion on steep, unstructured terrain. That is, we adapt the limit cycle of each leg of the robot with time to simultaneously produce locomotion and body posture control. We experimentally validate our approach on a hexapod robot, locomoting in a variety of steep, challenging terrains (grass, rocky slide, stairs). We show how our approach can be used to level the robot's body, allowing it to locomote at a relatively constant speed, even as terrain steepness and complexity prevents the use of an open-loop control strategy. 
    more » « less
  5. 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. 
    more » « less