Safe Start Regions for Medical Steerable Needle Automation

TL;DR

This work tackles the critical handoff problem in steerable-needle deployment by introducing a start-pose robustness metric that accounts for deviations in both position and orientation at the handoff. It builds a backward-range propagation framework anchored in Dubins path concepts to compute orientation ranges and a safe start region $\mathbf{Q}_1$ on the insertion surface, with a tunable trade-off parameter $y$ between positional $\rho$ and orientational $\alpha$ robustness. The method is model- and planner-agnostic and is demonstrated across abstract, liver, and lung planning scenarios, showing it can efficiently produce larger safe start regions than Monte Carlo baselines and that results depend strongly on curvature constraints $r_{\min}$ and surface angle $\theta$. This approach provides a practical tool for clinicians and robotic systems to ensure reliable handoffs and target reachability under realistic tissue-deformation and constraint conditions. The work lays groundwork for integrating start-pose robustness into planning pipelines and for validating the concept in physical experiments.

Abstract

Steerable needles are minimally invasive devices that enable novel medical procedures by following curved paths to avoid critical anatomical obstacles. Planning algorithms can be used to find a steerable needle motion plan to a target. Deployment typically consists of a physician manually inserting the steerable needle into tissue at the motion plan's start pose and handing off control to a robot, which then autonomously steers it to the target along the plan. The handoff between human and robot is critical for procedure success, as even small deviations from the start pose change the steerable needle's workspace and there is no guarantee that the target will still be reachable. We introduce a metric that evaluates the robustness to such start pose deviations. When measuring this robustness to deviations, we consider the tradeoff between being robust to changes in position versus changes in orientation. We evaluate our metric through simulation in an abstract, a liver, and a lung planning scenario. Our evaluation shows that our metric can be combined with different motion planners and that it efficiently determines large, safe start regions.

Figures (10)

• Figure 1: (a) We demonstrate our method in a liver biopsy scenario where a steerable needle is inserted from the skin (tan) into liver tissue (grey) and is steered towards a target (pink) representing a suspicious nodule while avoiding large blood vessels (red) and the ribs (brown). A physician first manually inserts the steerable needle into the insertion surface, then the physician hands off control to an automated robot which steers the steerable needle through tissue and to the target. Our method determines a safe start region around the start pose of a nominal motion plan (dark blue) on an insertion surface (tan). Poses in this safe start region can be both reached by the physician, and a collision-free motion plan to the target can be found. We determine the size of the safe start region in both position (yellow) and orientation (cyan). (b) There is a tradeoff between maximizing robustness in position and in orientation, and our method allows the user to choose this tradeoff according to their preferences and the specific insertion scenario.
• Figure 2: (a) The steerable needle (green) is deployed from the start region $\Sigma$ at configuration $\mathbf{q}_1 \in \Sigma$ and aims to reach $\mathbf{p}_\text{target}$. A needle plan (black) consists of constant curvature arcs characterized by an insertion length $l_i$, a radius of curvature $r_i$, and a rotation angle $\gamma_i$ that connect 3D poses $\mathbf{q}_i$. (b) Start pose robustness metric $R(\Pi, \Sigma,y)$ computes maximum allowable deviations depending on tradeoff parameter $y$, balancing robustness in position ($\rho$) and orientation ($\alpha$).
• Figure 3: (a) The backward reachable workspace (blue) of $\mathbf{q}_{i+1}$ consists of all positions from which $\mathbf{q}_{i+1}$ can be reached. It is limited by arcs of radius $r_\text{min}$, resulting in a trumpet-like shape. (b) We construct an $LSR$ Dubins path connecting $\mathbf{p}_i$ and $\mathbf{q}_{i+1}$ consisting of a left curve $L$ along circle $C_1$ centered at $\mathbf{c}_1$, a straight section $S$ along inner tangent $t$ and a right curve $R$ along circle $C_2$ centered at $\mathbf{c}_2$. (c) We achieve the rightmost orientation at $\mathbf{p}_i$ if $C_1$ (solid outline) is tangent to $C_2$ (light green path). Moving $C_1$ further away reduces the orientation to the right (dark green path). Rotating the orientation further to the right results in the shortest path (pink), violating the total curvature constraint. (d) We construct a triangle $\mathbf{c}_1$, $\mathbf{c}_2$, $\mathbf{p}_i$ to find the position of $\mathbf{c}_1$ and calculate the orientation vector $\mathbf{o}_r$. (e) We repeat this process for the leftmost orientation vector $\mathbf{o}_l$ by constructing an RSL path, which results in orientation range $\phi_i$ spanning orientations between $\mathbf{o}_l$ and $\mathbf{o}_r$.
• Figure 4: (a) We construct two constant curvature arcs $\mathbf{a}_l$ and $\mathbf{a}_r$ with radius of curvature $r_\text{min}$ connecting $\mathbf{p}_i$ and $\mathbf{p}_{i+1}$, resulting in orientations $\mathbf{o}_l$ and $\mathbf{o}_r$. This is the maximum orientation range that could be propagated from $\mathbf{p}_{i+1}$ without taking orientation range $\phi_{i+1}$ into account. (b) Orientation range $\phi_{i+1}$ (dark blue) can be reached from positions $\mathbf{p}_i$ within its backward reachable workspace (light blue) limited by arcs of radius $r_\text{min}$. We connect position $\mathbf{p}_i$ to $\mathbf{p}_{i+1}$ with a pair of constant curvature arcs (light green) to propagate the orientation range $\phi_{i+1}$ to $\mathbf{p}_i$. As arc $\mathbf{a}_l$ (dashed lines) lies partially outside the backward reachable workspace, we replace them with an RSL Dubins path (dark green). Some orientations in $\phi_{i+1}$ (pink) cannot be reached from $\mathbf{p}_i$.
• Figure 5: (a) Propagating orientation ranges backward along the plan starting at $\mathbf{q}_\text{target}$. We propagate orientation ranges $\Phi_{i+1}$ to create orientation ranges $\Phi_{i}$. (b) We try to find orientation ranges as wide as possible. To determine the left boundary $\mathbf{o}_l$ at $\mathbf{p}_i$, we find the leftmost $\phi_{i+1}$ to which an RSL connection (dotted lines) within their respective backward reachable workspaces (solid lines) exists. Here, $\phi_{i+1,0}$ is out of range, $\phi_{i+1,1}$ results in the leftmost $\mathbf{o}_l$, a connection less to the left exists to $\phi_{i+1,2}$, and $\phi_{i+1,3}$ is again unreachable. c) Orientation ranges in 3D (dark blue) are defined by their distance $d_{i,j}$ to the nominal position $\mathbf{p}_i$ (cyan), by the angle $\gamma_{i,j}$ between their center orientation and the deployment direction $\mathbf{R}_i^z$, and by the spread of the angular deviation $\beta_{i,j}$. After determining the initial boundaries of orientation ranges in 2D (light blue), we shrink the ranges to achieve symmetry around $\mathbf{R}_i^z$.