Motion planning for highly-dynamic unconditioned reflexes based on chained Signed Distance Functions

TL;DR

This work addresses real-time, highly dynamic obstacle avoidance for articulated manipulators by introducing a chained local-SDF framework. offline, it precomputes three groups of local SDFs describing static geometry, link surfaces, and reachability; online, these SDFs are chained to yield global geometric information and a fast escape-velocity cue, which is mapped to joint-space actions via a modified geometric Jacobian and Jacobian-pseudo-inverse with null-space projection. The approach achieves millisecond-scale reflex-like responses to dynamic obstacles while pursuing targets, outperforming state-of-the-art planning methods in static scenarios and neural-distance baselines in dynamic scenarios. The framework reduces online computation to rapid table lookups, enabling drastically faster reaction times and robust obstacle avoidance in both simulated and real-world experiments, with practical implications for human-robot collaboration and safe daily-life manipulation.

Abstract

The unconditioned reflex (e.g., protective reflex), which is the innate reaction of the organism and usually performed through the spinal cord rather than the brain, can enable organisms to escape harms from environments. In this paper, we propose an online, highly-dynamic motion planning algorithm to endow manipulators the highly-dynamic unconditioned reflexes to humans and/or environments. Our method is based on a chained version of Signed Distance Functions (SDFs), which can be pre-computed and stored. Our proposed algorithm is divided into two stages. In the offline stage, we create 3 groups of local SDFs to store the geometric information of the manipulator and its working environment. In the online stage, the pre-computed local SDFs are chained together according the configuration of the manipulator, to provide global geometric information about the environment. While the point clouds of the dynamic objects serve as query points to look up these local SDFs for quickly generating escape velocity. Then we propose a modified geometric Jacobian matrix and use the Jacobian-pseudo-inverse method to generate real-time reflex behaviors to avoid the static and dynamic obstacles in the environment. The benefits of our method are validated in both static and dynamic scenarios. In the static scenario, our method identifies the path solutions with lower time consumption and shorter trajectory length compared to existing solutions. In the dynamic scenario, our method can reliably pursue the dynamic target point, avoid dynamic obstacles, and react to these obstacles within 1ms, which surpasses the unconditioned reflex reaction time of humans.

Figures (20)

• Figure 1: The unconditioned reflexes enable humans to react to stimulus (e.g., pain) quickly to avoid harm from environments. To guarantee real-time, the unconditioned reflexes are usually performed through the spinal cord rather than the brain. Accordingly, it is essential to endow robots the highly-dynamic unconditioned reflex to humans and/or environments, such that it can work collaboratively with humans or serve people in daily life.
• Figure 2: The difference between the explicit method and the SDF method is presented. The explicit method represents an object with multiple points and the expressions of functions between these points. In contrast, the SDF returns the signed distance from any point in space to the surface of the $\Omega$. The dashed lines on the right are contour lines that indicate the distance from the surface of the $\Omega$.
• Figure 3: Illustration of a generalist robot working in a household environment, featuring both static and dynamic obstacles. The manipulator must respond in real time to avoid these obstacles and reach the target pose.
• Figure 4: (a) depict the $SDF_{\mathcal{S}_0}\left({\boldsymbol{p}}\right)$ created for the permanent object, e.g., the wall. (b), (c) and (d) depict the schematic diagram of the $SDF_{\mathcal{S}_i}\left({\boldsymbol{p}}\right)$ created for each static obstacle. (d) shows the $SDF_{\mathcal{S}}\left({\boldsymbol{p}}\right)$, which is the fusion of all the local $SDF_{\mathcal{S}_i}\left({\boldsymbol{p}}\right)$. The colors indicate the signed distance (Unit: mm). The contour lines are also marked in each subfigure.
• Figure 5: (a) shows the schematic diagram of the $SDF_{\mathcal{L}_i}\left({\boldsymbol{p}}\right)$ and (b) shows the $Gradient_{\mathcal{L}_i}\left({\boldsymbol{p}}\right)$. These local SDFs returns the signed distance and gradient information to the surface of $\{\mathcal{L}_i\}$. In (a), the colors indicate the signed distance (Unit: mm) while the colored lines mark the contour lines. In (b), the direction and magnitude of the gradient are illustrated by the arrows' direction and color, respectively. The magnitude is normalized for visualization.