Robots are finding new applications where physical interaction with a human is necessary, such as 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.
Interestingly, even in settings where pHRI does not occur, other works have used the human's actions to cause changes in the robot's desired trajectory. Mainprice and Berenson @cite_18 present one such scheme, where the robot explicitly tries to avoid collisions with the human. Based on a prediction of the human's workspace occupancy, the robot selects the desired trajectory which minimizes human-robot interference and task completion time. Indeed, as pointed out by Chao and Thomaz @cite_3 , if the human and robot are working together in close proximity---but wish to avoid physical contact---the workspace becomes a shared resource. To support these methods, human-subject studies have experimentally found that deforming the desired trajectory in response to human actions objectively and subjectively improves human-robot collaboration @cite_27 . However, it is not necessarily clear which trajectory deformation is optimal; as a result, there is interest in understanding how humans modify their own trajectories during similar situations. Pham and Nakamura @cite_21 develop a trajectory deformation algorithm which preserves the original trajectory's affine invariant features, with applications in transferring recorded human motions to humanoid robots.
@cite_27 @cite_18 @cite_21 @cite_3
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In this paper we present a framework that allows a human and a robot to perform simultaneous manipulation tasks safely in close proximity. The proposed framework is based on early prediction of the human's motion. The prediction system, which builds on previous work in the area of gesture recognition, generates a prediction of human workspace occupancy by computing the swept volume of learned human motion trajectories. The motion planner then plans robot trajectories that minimize a penetration cost in the human workspace occupancy while interleaving planning and execution. Multiple plans are computed in parallel, one for each robot task available at the current time, and the trajectory with the least cost is selected for execution. We test our framework in simulation using recorded human motions and a simulated PR2 robot. Our results show that our framework enables the robot to avoid the human while still accomplishing the robot's task, even in cases where the initial prediction of the human's motion is incorrect. We also show that taking into account the predicted human workspace occupancy in the robot's motion planner leads to safer and more efficient interactions between the user and the robot than only considering the human's current configuration. To enable safe and efficient human–robot collaboration in shared workspaces, it is important for the robot to predict how a human will move when performing a task. While predicting human motion for tasks not known a priori is very challenging, we argue that single-arm reaching motions for known tasks in collaborative settings (which are especially relevant for manufacturing) are indeed predictable. Two hypotheses underlie our approach for predicting such motions: First, that the trajectory the human performs is optimal with respect to an unknown cost function, and second, that human adaptation to their partner's motion can be captured well through iterative replanning with the above cost function. The key to our approach is thus to learn a cost function that “explains” the motion of the human. To do this, we gather example trajectories from pairs of participants performing a collaborative assembly task using motion capture. We then use inverse optimal control to learn a cost function from these trajectories. Finally, we predict reaching motions from the human's current configuration to a task-space goal region by iteratively replanning a trajectory using the learned cost function. Our planning algorithm is based on the trajectory optimizer: stochastic trajectory optimizer for motion planning [1] ; it plans for a 23-degree-of-freedom human kinematic model and accounts for the presence of a moving collaborator and obstacles in the environment. Our results suggest that in most cases, our method outperforms baseline methods when predicting motions. We also show that our method outperforms baselines for predicting human motion when a human and a robot share the workspace. Assuming that a robot trajectory is given from a high-level planning or learning mechanism, it needs to be adapted to react to dynamic environment changes. In this article we propose a novel approach to deform trajectories while keeping their local shape similar, which is based on the discrete Laplace---Beltrami operator. The approach can be readily extended and covers multiple deformation techniques including fixed waypoints that must be passed, positional constraints for collision avoidance or a cooperative manipulation scheme for the coordination of multiple robots. Due to its low computational complexity it allows for real-time trajectory deformation both on local and global scale and online adaptation to changed environmental constraints. Simulations illustrate the straightforward combination of the proposed approach with other established trajectory-related methods like artificial potential fields or prioritized inverse kinematics. Experiments with the HRP-4 humanoid successfully demonstrate the applicability in complex daily-life tasks. We propose a new approach to deform robot trajectories based on affine transformations. At the heart of our approach is the concept of affine invariance: Trajectories are deformed in order to avoid unexpected obstacles or to achieve new objectives but, at the same time, certain definite features of the original motions are preserved. Such features include, for instance, trajectory smoothness, periodicity, affine velocity, or more generally, all affine-invariant features, which are of particular importance in human-centered applications. Furthermore, this approach enables one to “convert” the constraints and optimization objectives regarding the deformed trajectory into constraints and optimization objectives regarding the matrix of the deformation in a natural way, making constraints satisfaction and optimization substantially easier and faster in many cases. As illustration, we present an application to the transfer of human movements to humanoid robots while preserving equiaffine velocity, a well-established invariant of human hand movements. Building on the presented affine deformation framework, we finally revisit the concept of trajectory redundancy from the viewpoint of group theory.