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Time-Optimal Path Tracking with ISO Safety Guarantees

Shohei Fujii, Quang-Cuong Pham

TL;DR

This work tackles time-optimal path tracking under ISO SSM safety requirements, ensuring the robot remains stationary at the collision instant. It introduces a TOPP-RA–based policy that uses a pre-computation phase to build stoppable sets and Time-to-Reach values and an execution phase to select the farthest safe stop along the path, achieving time-optimal trajectories under kinodynamic constraints. A GPU-accelerated parallel 1-D LP solver speeds up pre-computation by roughly 10x, enabling near real-time operation. Demonstrations on a 6-DoF industrial robot show reduced conservatism compared to state-of-the-art safe-control methods and real-time safe control in the presence of dynamic obstacles.

Abstract

One way of ensuring operator's safety during human-robot collaboration is through Speed and Separation Monitoring (SSM), as defined in ISO standard ISO/TS 15066. In general, it is impossible to avoid all human-robot collisions: consider for instance the case when the robot does not move at all, a human operator can still collide with it by hitting it of her own voluntary motion. In the SSM framework, it is possible however to minimize harm by requiring this: \emph{if} a collision ever occurs, then the robot must be in a \emph{stationary state} (all links have zero velocity) at the time instant of the collision. In this paper, we propose a time-optimal control policy based on Time-Optimal Path Parameterization (TOPP) to guarantee such a behavior. Specifically, we show that: for any robot motion that is strictly faster than the motion recommended by our policy, there exists a human motion that results in a collision with the robot in a non-stationary state. Correlatively, we show, in simulation, that our policy is strictly less conservative than state-of-the-art safe robot control methods. Additionally, we propose a parallelization method to reduce the computation time of our pre-computation phase (down to 0.5 sec, practically), which enables the whole pipeline (including the pre-computation) to be executed at runtime, nearly in real-time. Finally, we demonstrate the application of our method in a scenario: time-optimal, safe control of a 6-dof industrial robot.

Time-Optimal Path Tracking with ISO Safety Guarantees

TL;DR

This work tackles time-optimal path tracking under ISO SSM safety requirements, ensuring the robot remains stationary at the collision instant. It introduces a TOPP-RA–based policy that uses a pre-computation phase to build stoppable sets and Time-to-Reach values and an execution phase to select the farthest safe stop along the path, achieving time-optimal trajectories under kinodynamic constraints. A GPU-accelerated parallel 1-D LP solver speeds up pre-computation by roughly 10x, enabling near real-time operation. Demonstrations on a 6-DoF industrial robot show reduced conservatism compared to state-of-the-art safe-control methods and real-time safe control in the presence of dynamic obstacles.

Abstract

One way of ensuring operator's safety during human-robot collaboration is through Speed and Separation Monitoring (SSM), as defined in ISO standard ISO/TS 15066. In general, it is impossible to avoid all human-robot collisions: consider for instance the case when the robot does not move at all, a human operator can still collide with it by hitting it of her own voluntary motion. In the SSM framework, it is possible however to minimize harm by requiring this: \emph{if} a collision ever occurs, then the robot must be in a \emph{stationary state} (all links have zero velocity) at the time instant of the collision. In this paper, we propose a time-optimal control policy based on Time-Optimal Path Parameterization (TOPP) to guarantee such a behavior. Specifically, we show that: for any robot motion that is strictly faster than the motion recommended by our policy, there exists a human motion that results in a collision with the robot in a non-stationary state. Correlatively, we show, in simulation, that our policy is strictly less conservative than state-of-the-art safe robot control methods. Additionally, we propose a parallelization method to reduce the computation time of our pre-computation phase (down to 0.5 sec, practically), which enables the whole pipeline (including the pre-computation) to be executed at runtime, nearly in real-time. Finally, we demonstrate the application of our method in a scenario: time-optimal, safe control of a 6-dof industrial robot.
Paper Structure (14 sections, 14 equations, 13 figures, 1 algorithm)

This paper contains 14 sections, 14 equations, 13 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Time-Optimal Path Tracking with Safety Guarantees
  4. Terminologies and Definitions
  5. Problem Formulation
  6. Pre-computation Phase
  7. Execution Phase
  8. Parallel 1-D Linear Programming on GPU
  9. Experiments and Results
  10. Comparison with Existing Method
  11. Parallel 1-D Linear Programming on GPU
  12. Simulation on a 6-Dof Industrial Robot
  13. Conclusion
  14. Proof of Optimality

Figures (13)

  • Figure 1:
  • Figure 2:
  • Figure 4: 1-D car simulation setting for comparison
  • Figure 5: Comparison of Zanchettin's and Ours - Positions, Distance between cars and a wall, Velocities and Accelerations in a time series. See the video of this simulation at https://youtu.be/SHwyOOU3X2A.
  • Figure 6: Effect of the number of velocity discretization $M$
  • ...and 8 more figures