Safe Navigation in Unmapped Environments for Robotic Systems with Input Constraints

TL;DR

The paper tackles safe robotic navigation in unmapped environments under both state and input constraints. It proposes a unified framework that fuses online perception-derived local CBFs into a time-varying barrier via a soft-maximum, and incorporates actuator and speed limits through control dynamics and a soft-minimum composition to produce a single relaxed CBF guiding a closed-form optimal controller. The key contributions include (i) a time-varying perception barrier that tracks unknown obstacles, (ii) higher-order composite CBFs that merge state and input constraints, and (iii) a guaranteed forward-invariance controller with a closed-form surrogate control that stays near a desired input while satisfying all constraints. The approach enables real-time safe navigation in unknown environments, demonstrated on simulations of a LiDAR-equipped nonholonomic ground robot with multiple goals and obstacle avoidance.

Abstract

This paper presents an approach for navigation and control in unmapped environments under input and state constraints using a composite control barrier function (CBF). We consider the scenario where real-time perception feedback (e.g., LiDAR) is used online to construct a local CBF that models local state constraints (e.g., local safety constraints such as obstacles) in the a priori unmapped environment. The approach employs a soft-maximum function to synthesize a single time-varying CBF from the N most recently obtained local CBFs. Next, the input constraints are transformed into controller-state constraints through the use of control dynamics. Then, we use a soft-minimum function to compose the input constraints with the time-varying CBF that models the a priori unmapped environment. This composition yields a single relaxed CBF, which is used in a constrained optimization to obtain an optimal control that satisfies the state and input constraints. The approach is validated through simulations of a nonholonomic ground robot that is equipped with LiDAR and navigates an unmapped environment. The robot successfully navigates the environment while avoiding the a priori unmapped obstacles and satisfying both speed and input constraints.

Figures (4)

• Figure 1: $\eta$ given by Example \ref{['ex:g']} with $r=2$.
• Figure 2: Three closed-loop trajectories using the control \ref{['eq:softmax_h', 'eq:dynamics_control.a', 'eq:u_d_hat_def', 'eq:HOCBF.varphi', 'eq:softmin h', 'eq:uclose', 'eq:ulambda', 'eq:omegabar']} with the perception feedback $b_k$ generated from $360^{\circ}$ FOV perception in a static environment.
• Figure 3: $q_{\rm x}$, $q_{\rm y}$, $v$, $\theta$, $u$, $u_{\rm d}$, $v = [ \, v_1 \quad v_2 \,]^{\rm T}$, and $v_{\rm d} = [ \, v_{{\rm d}_1} \quad v_{{\rm d}_2} \,]^{\rm T}$ for $q_{{\rm g}}=[\,6 \quad 2.5\,]^{\rm T}$.
• Figure 4: $h$, $\psi_0$, $\min \xi_j$, and $\min \phi_j$ for $q_{\rm g} = [\,6\quad2.5\,]^{\rm T}$ m.

Theorems & Definitions (2)

• proof
• proof