Trajectory Deformations From Physical Human–Robot Interaction

Abstract

Abstract-Robots are finding new applications where physical interaction with a human is necessary: manufacturing, healthcare, and social tasks. Accordingly, the field of physical humanrobot 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.

Learning from Extrapolated Corrections

“…It is this explicit estimation lens that exposes our choices for how to interpret and extrapolate from corrections, challenging or validating assumptions we've made in the past. From the perspective of work that uses non-Euclidean norms to deform trajectories [2], [16], we validate that these are also useful when learning cost functions based on the deformed trajectories. From the perspective of work that learns cost functions [1], [3], we challenge the notion that Euclidean norms are always best [3], and support the choice to sometimes use non-Euclidean deformation [1].…”

“…This has an intuitive interpretation: the robot uses the inverse of the norm to propagate the correction to the rest of the trajectory, while keeping the start and the goal fixed. This is analogous to using a norm to respond to changes in the goal, as in [2], and similar to work in responding to a force during haptic robot teleoperation [16] (there, the propagation happens not from the current point, but from a future time point, so that the human does not have to keep providing input).q…”

“…Building on work that has explored deforming trajectories based on changing waypoints in contexts outside of learning cost functions [2], [16], we cast the problem of estimating the full trajectory explicitly as a function approximation problem: we have a current estimate (the current trajectory), we receive one new data point (that the corrected timepoint maps to the corrected configuration), and we re-estimate our trajectory online based on this new data point. Different choices of the space of functions we use for approximation (different inner products) map to different assumptions about what the user intended in prior work, with a notable difference between Euclidean [3] and non-Euclidean [1] inner products.…”

Interactive Trajectory Adaptation through Force-guided Bayesian Optimization

“…A similar work on physically interactive trajectory deformations used an analytical smooth family of trajectories to find the local spatial deformations as a function of the applied force [16]. The analytical formulation allowed to use gradient-based optimization to find the parameters of the deformed trajectory.…”

Trajectory Advancement during Human-Robot Collaboration

“…The authors of [9] use affine transformations on parts of the motion trajectory which ensures preserving affine-invariant features of the original trajectory like line smoothness and velocity. More recently, the authors of [10] demonstrated optimal trajectory deformation through constrained optimization of an energy function ensuring the minimum-jerk profile. Although the resulting deformed trajectories are optimal, a main limitation in the above works is that the speed of the task is unchanged.…”