Safe Feedback Motion Planning in Unknown Environments: An Instantaneous Local Control Barrier Function Approach

TL;DR

Numerical simulations are conducted to reveal the effectiveness of the proposed SFMP strategy that drives mobile robots to safely reach the destination incrementally in diverse prior-unknown environments.

Abstract

Mobile robots are desired with resilience to safely interact with prior-unknown environments and finally accomplish given tasks. This paper utilizes instantaneous local sensory data to stimulate the safe feedback motion planning (SFMP) strategy with adaptability to diverse prior-unknown environments without building a global map. This is achieved by the numerical optimization with the constraints, referred to as instantaneous local control barrier functions (IL-CBFs) and goal-driven control Lyapunov functions (GD-CLFs), learned from perceptional signals. In particular, the IL-CBFs reflecting potential collisions and GD-CLFs encoding incrementally discovered subgoals are first online learned from local perceptual data. Then, the learned IL-CBFs are united with GD-CLFs in the context of quadratic programming (QP) to generate the safe feedback motion planning strategy. Rather importantly, an optimization over the admissible control space of IL-CBFs is conducted to enhance the solution feasibility of QP. The SFMP strategy is developed with theoretically guaranteed collision avoidance and convergence to destinations. Numerical simulations are conducted to reveal the effectiveness of the proposed SFMP strategy that drives mobile robots to safely reach the destination incrementally in diverse prior-unknown environments.

Figures (12)

• Figure 1: Schematic of the SFMP strategy that maps raw sensory data to motion commands. The IL-CBFs learned from sensory data in Section \ref{['sec IL-CBF']} characterize the obstacle boundaries; The decomposed short-horizon subtasks are encoded by GD-CLFs clarified in Section \ref{['sec GD-CLF']}; The LP optimization is conducted to enlarge the ACSs in Section \ref{['sec enlarge ACS']} to improve the feasibility of the QP formulated in Section \ref{['sec QP problem']}.
• Figure 2: Graphical illustration of IL-CBFs and obstacles. The whole boundaries of obstacles $\mathcal{O}_l$ are described by explicit CBFs $h_l = (x - x_{o_{l}})^2 + (y - y_{o_{l}})^2 - r^2_l$, $c_l = \left(x_{o_{l}}, y_{o_{l}}\right)$, $l = 1, 2,3,4,5$. The mobile robot observes $\mathfrak{D} = \left\{\bar{p}_1, \bar{p}_2, \cdots, \bar{p}_{7} \right\}$ and classifies $\mathfrak{D}$ into subgroups $\mathfrak{D}_k$, $k = 1,2$. Thus, $K = 2$, and $I_1 = 4$, $I_2 = 3$ here. The mobile robot learns $\hat{h}_k$ based on the $k$-th data subgroup $\mathfrak{D}_k$.
• Figure 3: Graphical illustration of GD-CLFs and subgoals. The mobile robot uses the collision-free data group $\mathfrak{A} = \left\{\tilde{p}_1, \tilde{p}_2, \cdots, \tilde{p}_{9} \right\}$ and Algorithm \ref{['GLCLF learn algorithm']} to determine the position $\tilde{p}_4 \in \mathfrak{A}$ as its first subgoal $\tilde{p}_{d_{1}}$. Then, the constructed GD-CLF $V_1$ guides the robot toward $\tilde{p}_{d_{1}}$. The robot would determine its $j+1$-the subgoal when it arrives at $\delta$-neighboured around the $j$-th subgoal. Following the above-mentioned process, the mobile robot would travel along the successively discovered subgoals $\tilde{p}_{d_{2}}$, $\tilde{p}_{d_{3}}$, $\cdots$, and finally reaches the goal $p_d$.
• Figure 4: The geometric interpretation of the sets $\mathcal{A}_{1_{k}}$ (the blue shaded area) and $\mathcal{U}$ (the green shaded area)
• Figure 5: The performance comparison between the optimized $\alpha^*_1$ and the predetermined $\alpha_2$, $\alpha_3$ associated QP solutions.

Theorems & Definitions (8)

• Remark 1
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