Layered Safety: Enhancing Autonomous Collision Avoidance via Multistage CBF Safety Filters

Abstract

This paper presents a general end-to-end framework for constructing robust and reliable layered safety filters that can be leveraged to perform dynamic collision avoidance over a broad range of applications using only local perception data. Given a robot-centric point cloud, we begin by constructing an occupancy map which is used to synthesize a Poisson safety function (PSF). The resultant PSF is employed as a control barrier function (CBF) within two distinct safety filtering stages. In the first stage, we propose a predictive safety filter to compute optimal safe trajectories based on nominal potentially-unsafe commands. The resultant short-term plans are constrained to satisfy the CBF condition along a finite prediction horizon. In the second stage, instantaneous velocity commands are further refined by a real-time CBF-based safety filter and tracked by the full-order low-level robot controller. Assuming accurate tracking of velocity commands, we obtain formal guarantees of safety for the full-order system. We validate the optimality and robustness of our multistage architecture, in comparison to traditional single-stage safety filters, via a detailed Pareto analysis. We further demonstrate the effectiveness and generality of our collision avoidance methodology on multiple legged robot platforms across a variety of real-world dynamic scenarios.

Figures (6)

• Figure 1: Layered Safety Filter. The PSF is computed using an occupancy map safe set representation. The solution enables the construction of safety constraints for use in a multistage safety filter: a predictive layer in series with a real-time layer. This framework generates safe autonomous actions, leading to collision-free behavior around dynamic obstacles. Experimental footage provided at https://youtu.be/s6v4QUUaNlY
• Figure 2: Occupancy Mapping. Left First, we process each point cloud and project it onto a 2D grid $M_0$. Middle Left Second, we convolve $M_0$ with a Gaussian kernel $K$, adding weight to occupied clusters and producing the map $\bar{M}$. Middle Right Third, we use $\bar{M}$ to dynamically update the confidence map $\Gamma$. Right Last, we threshold $\Gamma$ with hysteresis to generate a binary occupancy map $\hat{M}$.
• Figure 3: Pareto Front. Individually, the safety filters achieve the extreme ends of the Pareto front. By combining them into a multistage safety filter, we reach an intermediate operating point that yields a desirable tradeoff between optimality and robustness.
• Figure 4: Dynamic Collision Avoidance on Hardware. Top left Composite image showing the quadruped avoiding a rolling ball from right to left at three time instances. Top right PSF surfaces, $h$, from the robot view at each time instance. Middle The safety function values, $h$, throughout the avoidance, used to compute $J_{\text{robustness}}$. Bottom Left Measured position and yaw angle of the quadruped. Bottom Right Filtered velocity commands used to compute $J_{\text{optimality}}$. Footage of experiment trials is presented in the supporting video at https://youtu.be/s6v4QUUaNlY.
• Figure 5: Analysis of Avoidance Experiment. Left Evaluated optimality and robustness metrics for all 10 trials of collision avoidance with ball speeds of 1.0 m/s, with a confidence ellipse of the population mean. The results show tradeoffs in the metrics, forming an approximation of a Pareto front. Right Success/failure of experiment with ball speeds of 1.25 m/s. Our multistage architecture is more successful than the individual single-stage safety filters.

Theorems & Definitions (5)

• Definition 1
• Definition 2
• Theorem 1
• proof
• Remark 1: Verification