Conformalized Reachable Sets for Obstacle Avoidance With Spheres

TL;DR

CROWS is a novel real-time, receding-horizon trajectory planner that generates probablistically-safe motion plans and outperforms a variety of state-of-the-art methods in solving challenging motion planning tasks in cluttered environments while remaining collision-free.

Abstract

Safe motion planning algorithms are necessary for deploying autonomous robots in unstructured environments. Motion plans must be safe to ensure that the robot does not harm humans or damage any nearby objects. Generating these motion plans in real-time is also important to ensure that the robot can adapt to sudden changes in its environment. Many trajectory optimization methods introduce heuristics that balance safety and real-time performance, potentially increasing the risk of the robot colliding with its environment. This paper addresses this challenge by proposing Conformalized Reachable Sets for Obstacle Avoidance With Spheres (CROWS). CROWS is a novel real-time, receding-horizon trajectory planner that generates probalistically-safe motion plans. Offline, CROWS learns a novel neural network-based representation of a spherebased reachable set that overapproximates the swept volume of the robot's motion. CROWS then uses conformal prediction to compute a confidence bound that provides a probabilistic safety guarantee on the learned reachable set. At runtime, CROWS performs trajectory optimization to select a trajectory that is probabilstically-guaranteed to be collision-free. We demonstrate that CROWS outperforms a variety of state-of-the-art methods in solving challenging motion planning tasks in cluttered environments while remaining collision-free. Code, data, and video demonstrations can be found at https://roahmlab.github.io/crows/

Figures (5)

• Figure 1: This paper presents CROWS, a method that generates probabilistically-safe motion plans in cluttered environments. Prior to planning, CROWS learns neural safety representation with confidence bounds computed by conformal prediction. CROWS also constructs an exact signed distance function of the obstacles in the scene (Assum. \ref{['assum:obstacles']}). At runtime, CROWS combines the signed distance function with the conformalized safety representation (pink) to generate probabilistically-safe trajectories between the start (blue) and goal (green) in a receding horizon manner. Each trajectory is selected by solving a nonlinear optimization problem with the learned safety representation (pink) guaranteeing with high probability that the robot remains collision-free.
• Figure 2: Overview of CROWS, a probabilistically-safe receding-horizon trajectory planner. Offline, CROWS constructs a dataset to train a network that predicts spherical overapproximations of parameterized swept volumes of a robot arm. After training, conformal prediction is used to quantify the uncertainty of the network's predictions. Online, the output of the network is buffered by a nonconformity score and used as a safety constraint during trajectory optimization. Finally, CROWS executes the trajectory while generating a plan for the next iteration.
• Figure 3: A visualization of the robot arm (grey), the obstacles (red), and a subset of the Spherical Forward Occupancy (purple) over a single time step $T_i$. The volume of each joint (solid purple) and link (transparent purple) is overapproximated by a collection of spheres (Thm. \ref{['thm:sparrows']}).
• Figure 4: A visual illustration of the construction of CROWS's conformalized reachable sets. Panel (A) compares the ground truth (left, purple), predicted (middle, orange), and conformalized (right, pink) reachable sets. To construct the conformalized reachable set, CROWS first defines the nonconformity score in \ref{['eq:buffer']}, which is the minimum buffer (blue) to ensure that the predicted sphere (orange) encloses the ground truth sphere (purple) (Panel C). The distribution of the nonconformity scores for joint $4$ over the interval $T_i$ with the values defining the quantiles indicated in blue (Panel B). Next, conformal prediction computes a confidence bound that upper bounds the nonconformity scores with a probability of $1-\epsilon$. The predicted joint sphere (A, middle) is then expanded by the size of this confidence bound to give the conformalized joint sphere (A, right). Finally, applying this procedure for all of the joint spheres gives the conformalized neural (A, right) reachable set that is guaranteed to cover the ground truth reachable set with probability greater than $(1-\epsilon)^{n_q +1}$ (Thm. \ref{['thm:crows']}).
• Figure 5: A subset of Realistic Scenarios where CROWS succeeds. The start, goal, and intermediate poses are shown in blue, green, and grey (transparent), respectively. Obstacles are shown in red (transparent).

Theorems & Definitions (3)

• Theorem 3
• Theorem 5
• proof