Fast yet predictable braking manoeuvers for real-time robot control

TL;DR

This work tackles safe, fast braking of robotic arms in shared workspaces by predicting stopping trajectories online. It introduces a modal-space braking framework that decouples the nonlinear dynamics at the braking state via an orthogonal transform $\mathbf{Q}$ so that $\mathbf{M}_Q\ddot{\vq}_Q = \tilde{\vtau}_Q$, and designs braking trajectories in modal space using quintic Bezier curves, with two scaling strategies: conservative (consv) and maximal (opt). A physically-admissible momentum-scaling method guarantees that modal inputs remain feasible in the original space, while preserving simultaneous stopping across joints; online trajectory prediction yields end-effector paths and stopping distances for collision avoidance. The approach is validated in simulation on a 7-DoF Franka Panda with three active joints, showing smooth, fast braking that respects actuator limits and provides accurate online stopping-distance predictions, and is benchmarked against a nonlinear time-optimal controller. The results demonstrate a real-time capable braking framework that enhances safety in cobot operations and enables actionable online decisions for safe velocity scaling and collision avoidance.

Abstract

This paper proposes a framework for generating fast, smooth and predictable braking manoeuvers for a controlled robot. The proposed framework integrates two approaches to obtain feasible modal limits for designing braking trajectories. The first approach is real-time capable but conservative considering the usage of the available feasible actuator control region, resulting in longer braking times. In contrast, the second approach maximizes the used braking control inputs at the cost of requiring more time to evaluate larger, feasible modal limits via optimization. Both approaches allow for predicting the robot's stopping trajectory online. In addition, we also formulated and solved a constrained, nonlinear final-time minimization problem to find optimal torque inputs. The optimal solutions were used as a benchmark to evaluate the performance of the proposed predictable braking framework. A comparative study was compiled in simulation versus a classical optimal controller on a 7-DoF robot arm with only three moving joints. The results verified the effectiveness of our proposed framework and its integrated approaches in achieving fast robot braking manoeuvers with accurate online predictions of the stopping trajectories and distances under various braking settings.

Figures (9)

• Figure 1: A conceptual pHRI scenario. A robot arm executes its task in a fenceless, shared workspace with human coworkers. Since undesired collisions may occur, the robot must be equipped with controlled stops to be triggered when its current braking distance $\hat{d}_b$ drops below dynamically evaluated distance thresholds. The scalar quantities $\hat{d}_h,\,\hat{d}_{obst.}$ denote the shortest distances to the closest human body parts and obstacles in the robot vicinity, respectively.
• Figure 2: Braking control and prediction architecture.
• Figure 3: Design of braking control in modal space. (a) Intuitive braking torque direction for a mass moving in the modal space (for $n=2$). (b) Feasible control torques in the original space ${\small \tilde{\Omega}}$ and modal space ${\small \tilde{\Omega}_{Q}}$. (c) Corresponding feasible acceleration regions (${\small {\Psi}^a}$ and ${\small {\Psi}^a_{Q}}$) obtained via scaling. The regions ${\small \tilde{\Omega}^{\prime}/{\Psi}^{a\prime}}$ and ${\small \tilde{\Omega}_{Q}^{\prime}/ {\Psi}_{Q}^{a\prime}}$ denote conservative regions, in which torque/acceleration control inputs stay admissible as specified by the physical actuator limits.
• Figure 4: A designed braking curve (left) using a quintic Bezier curve (right), whose anchor points are given by $P_0 \cdots P_5$ and the corner point is denoted $P_\mathrm{trans}$.
• Figure 5: Braking settings for robot joints moving with low (left) and high (right) velocities during different trapezoidal motions. The braking triggering instants $s_i^{\mathrm{X}}$, $i=1,2$ are indicated with purple vertical lines, where the superscript $\mathrm{X} \in \{\mathrm{acc},\mathrm{cruise},\mathrm{dec}\}$ indicates the braking scenario, i.e. ($\mathrm{acc}$) during acceleration, ($\mathrm{cruise}$) during cruise, and ($\mathrm{dec}$) during deceleration.