Collision-free Source Seeking Control Methods for Unicycle Robots

TL;DR

To tackle the mixed relative degree and avoid the undesired position offset for the nonholonomic unicycle model, this work proposes a novel construction of a CBF that can be integrated with the recent gradient-ascent source-seeking control law.

Abstract

In this work, we propose a collision-free source-seeking control framework for a unicycle robot traversing an unknown cluttered environment. In this framework, obstacle avoidance is guided by the control barrier functions (CBF) embedded in quadratic programming, and the source-seeking control relies solely on the use of onboard sensors that measure the signal strength of the source. To tackle the mixed relative degree and avoid the undesired position offset for the nonholonomic unicycle model, we propose a novel construction of a control barrier function (CBF) that can directly be integrated with our recent gradient-ascent source-seeking control law. We present a rigorous analysis of the approach. The efficacy of the proposed approach is evaluated via Monte-Carlo simulations, as well as, using a realistic dynamic environment with moving obstacles in Gazebo/ROS.

Figures (5)

• Figure 1: Simulation results based on the zeroing control barrier function $h(x,y,v,\dot{x},\dot{y}) = D(x,y) e^{-P(x,y,v,\dot{x},\dot{y})}$, where both the longitudinal and angular velocity are given by the optimal solution of ZCBF-QP \ref{['eq:QP-zcbf']}. The source is set at the origin $(0,0)$, surrounded by multiple circular-shape obstacles, and the signal strength is distributed in the field: $(a):J_1(x,y)=-x^2-y^2$; $(b):J_2(x,y)= -5x^2-8xy-5y^2$, respectively. The robot is set at initial position (given by $\circ$) to search the source while avoiding any potential collisions.
• Figure 2: (a). The distance of the robot to the closest obstacle $D_{\text{obs}}= \left\|\left[x_{\text{obs}}y_{\text{obs}}\right]-\left[xy\right]\right\|$ and to the source $D_s = \left\|\left[x^*y^*\right]-\left[xy\right]\right\|$; (b) The comparison of motion variables where $v_s, \omega_s$ are the nominal source-seeking signals and $v^*, \omega^*$ are the optimized safe control inputs for obstacle avoidance.
• Figure 3: Box plot of the Monte Carlo simulation of the three control barrier function-based methods using the same reference source seeking control parameters ($k_1= 0.3, k_2 = 30$). The robot is initialized at $50$ random initial positions for each group of simulations.
• Figure 4: Laser-embedded turtlebot3 robot in the constructed gazebo world, which contains fixed walls and walking people as potential collisions for robot navigation. The center point of the green circle area stands for the source location.
• Figure 5: Simulation of the zeroing control barrier function (ZCBF)-based collision-free source seeking in the unknown environment. Three pedestrians are walking around as dynamic obstacles. Robot is initialized with the state $(0, 0, \frac{1}{2}, \frac{\sqrt{2}}{4}, \frac{\sqrt{2}}{4} )$ in \ref{['fig:zcbf_left']}, and eventually arrived at the source $(-3,2)$ in \ref{['fig:zcbf_right']}. The source seeking control parameters in the field $J(x,y) = -(x+3)^2-(y-2)^2$ are set as $k_1=0.2, k_2=0.5$.

Theorems & Definitions (9)

• Remark 2.1
• Definition 2.2
• Definition 2.3
• Remark 2.4
• Definition 3.1
• Proposition 3.2
• proof
• Theorem 3.3
• proof