KCFRC: Kinematic Collision-Aware Foothold Reachability Criteria for Legged Locomotion

Lei Ye1, Haibo Gao1, Huaiguang Yang1, Peng Xu1,*, Haoyu Wang1, Tie Liu1, Junqi Shan1,
Zongquan Deng1 and Liang Ding1,*

* Denotes corresponding author
1Harbin institute of Technology


Abstract

Legged robots face significant challenges in navigating complex environments, as they require precise real-time decisions for foothold selection and contact planning. While existing research has explored methods to select footholds based on terrain geometry or kinematics, a critical gap remains: no existing method can explicitly validate the existence of a non-collision swing trajectory.

This paper addresses this gap by introducing KCFRC, a novel approach for efficient foothold reachability analysis. We first formally define the foothold reachability problem and establish a sufficient condition for foothold reachability. Based on this condition, we develop the KCFRC algorithm, which enables robots to validate foothold reachability in real time. Our experimental results demonstrate that KCFRC achieves remarkable time efficiency, completing foothold reachability checks for a leg in an average of 2 ms (900 footholds). Furthermore, we show that KCFRC can accelerate trajectory optimization and is particularly beneficial for contact planning in confined spaces, enhancing the adaptability and robustness of legged robots in challenging environments.

Video

Method

KCFRC is a novel approach for efficient foothold reachability analysis. The major procedure of KCFRC algorithm is shown below.

Interpolation end reference image.

Experiments

Time Performance & Scalability

We test our algorithm in generated scenarios to assess the time performance and scalability of KCFRC. The 60×60 grid map is generated by fractal noise and the feasible corridor with length 2 is randomly generated using the QuickHull algorithm. We record the border length and consumed time of reachability check for 1000 reachable cases and plot it below. Linear fitting is applied to the collected data.

Random corridor generation

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Comparisons

Foothold Reachability Check Comparison


Applications

Trajectory Initialization

Trajectory can be initialization from Visibility Graph used in KCFRC. The green trajectory in this video is the initialized trajectory.

Optimization Acceleration

Optimize trajectories initialized from KCFRC's visibility graph not only alleviate local minima problem but also speed up the optimization process.


KCFRC Accelerated Optimization Comparisons

Comparing to other methods like MINCO-LBFGS, RRT-Connect and STOMP, the proposed method (KCFRC+MINCO) outperforms not only in terms of time consumption but also in terms of trajectory quality.


Experiments on Hardware

Crossing Barrier

We have conducted an experiment asking Elspider4 Air to climb across a 19cm × 12cm barrier (about 60% leg length) to illustrate FLTPlanner's ability of obstacle conquering and collision avoidance. Robot states are planned by MCTS planner with human instructions, and the swing trajectories are generated by FLTPlanner with PITD (Pose Interpolation Task Domain). The video is accelerated by 2x.


Crossing U-shaped Clamped Barrier

FLTPlanner is also able to handle more complex scenarios like crossing a U-shaped clamped barrier. The video below shows the process of the robot crossing the U-shaped clamped barrier. The video is accelerated by 2x.


Climbing Timber Piles

The video below shows Elspider4 Air climbing across timber piles with timber size of 20cm × 20cm × 10/20/30/40cm. The gridmap is predefined because of real-time elevation mapping inaccuracy. The video is accelerated by 2x.


Climbing Stairs

Elspider4 Air is also able to climb up and down stairs, as is shown in the video below. The video is accelerated by 4x.