Matt Strong

Matt Strong

CS PhD at Stanford University

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Trajectory Deformations from Physical Human-Robot Interaction

Dylan P. Losey, Marcia K. O'Malley

Seminal October 2017

TL;DR Add an online deformation of the robot's future desired trajectory to impedance control, so a human's push changes where the robot plans to go and not just where it is. In a 10-subject study on a wrist exoskeleton, users applied about half the torque (2.25 vs 4.64 Nm) and moved more smoothly than with impedance control alone.

What they do

Under impedance control a human can push a robot off its path, but the robot’s desired trajectory stays fixed, so the human has to keep pushing to change its behavior. This paper lets forces applied during physical interaction also deform a future segment of the desired trajectory. The deformed segment rejoins the original trajectory after a fixed time, so the robot keeps doing the task on its own once the human lets go.

How it works

  • Endpoint constraints. Requiring the actuator force to stay continuous at the start and end of each deformation means the deformation must match the original trajectory’s position and velocity at both ends.
  • Optimal shape. Over N waypoints, the deformation minimizes an energy that trades the work done to the human (assuming future force equals the current force) against total jerk. Lagrange multipliers give a closed form: the deformation is the current force times a fixed, precomputed smooth shape, scaled by an admittance-like gain mu and the waypoint spacing so it does not depend on N or the update rate.
  • Arbitration. Large mu hands control to the human; mu near zero makes the trajectory hard to deform. The deformation duration tau sets how far ahead it reaches.
  • Multi-DoF. With diagonal stiffness and damping the update runs separately on each task-space coordinate, so cost grows linearly with task dimension.

Results

  • 1-DoF simulations: with 5001 waypoints the algorithm still ran ten times faster than real time on a laptop.
  • 10 subjects on a 2-DoF wrist exoskeleton followed a circle while steering around obstacles. With deformations, applied torque fell from 4.64 to 2.25 Nm and interaction percent from 57.9% to 20.8% (both p < 0.001); movement smoothness improved from -2.91 to -2.66 (p = 0.027).
  • Collision percent (0.71% vs 1.41%) and tracking error (0.016 vs 0.027 rad) rose slightly, but not significantly.

Limitations

The human cannot change the overall task timing. Unintended contacts also deform the trajectory, so forces must be filtered, and deformations that violate constraints are simply rejected. tau and mu were tuned by hand, and the authors note the results may not carry over to other tasks or users.

Figures

From Figure 1: The robot renders an impedance to the human, and the human's applied force also deforms the robot's fu...
From Figure 1: The robot renders an impedance to the human, and the human's applied force also deforms the robot's future desired trajectory.
From Figure 2: The segment of the desired trajectory between the start and end times of a deformation is shifted by a...
From Figure 2: The segment of the desired trajectory between the start and end times of a deformation is shifted by a variation field (red) in the direction of the human's force, giving the deformed segment (blue). Dashed lines are other members of the family of possible deformations.
From Figure 9: Participants grasp the handle of the OpenWrist haptic device (1) and move a cursor in the virtual task...
From Figure 9: Participants grasp the handle of the OpenWrist haptic device (1) and move a cursor in the virtual task on the monitor (2).
From Figure 11: Mean applied torque, interaction percent, collision percent, tracking error and movement smoothness a...
From Figure 11: Mean applied torque, interaction percent, collision percent, tracking error and movement smoothness across subjects for impedance control (IC, gray) and IC with trajectory deformations (IC-PITD, orange). Asterisks mark p < 0.05.
Abstract

Robots are finding new applications where physical interaction with a human is necessary: manufacturing, healthcare, and social tasks. Accordingly, the field of physical human-robot interaction (pHRI) has leveraged impedance control approaches, which support compliant interactions between human and robot. However, a limitation of traditional impedance control is that---despite provisions for the human to modify the robot's current trajectory---the human cannot affect the robot's future desired trajectory through pHRI. In this paper, we present an algorithm for physically interactive trajectory deformations which, when combined with impedance control, allows the human to modulate both the actual and desired trajectories of the robot. Unlike related works, our method explicitly deforms the future desired trajectory based on forces applied during pHRI, but does not require constant human guidance. We present our approach and verify that this method is compatible with traditional impedance control. Next, we use constrained optimization to derive the deformation shape. Finally, we describe an algorithm for real time implementation, and perform simulations to test the arbitration parameters. Experimental results demonstrate reduction in the human's effort and improvement in the movement quality when compared to pHRI with impedance control alone.

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