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.
Finally, from a motion planning perspective, optimization methods can be used to find human-like and collision-free desired trajectories by iteratively deforming the initial desired trajectory. For example, in work on redundant manipulators by Brock and Khatib @cite_42 , an initial desired trajectory from start to goal is given, and then potential fields are used to deform this trajectory in response to moving obstacles. More recently, Zucker . developed CHOMP @cite_35 , an optimization approach which uses covariant gradient descent to find the minimum cost desired trajectory; each step down the gradient deforms the previous desired trajectory. STOMP, from @cite_14 , generates a set of noisy deformations around the current desired trajectory, and then combines the beneficial aspects of those deformations to update the desired trajectory. TrajOpt, from @cite_45 , uses sequentially convex optimization to deform the initial desired trajectory---the resulting deformation satisfies both equality and inequality constraints. We observe that the discussed trajectory optimization schemes, @cite_42 @cite_25 @cite_16 @cite_8 @cite_13 , are not intended for pHRI, but have been successfully utilized to share control during teleoperation @cite_43 .
@cite_35 @cite_14 @cite_8 @cite_42 @cite_43 @cite_45 @cite_16 @cite_13 @cite_25
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We present a new optimization-based approach for robotic motion planning among obstacles. Like CHOMP (Covariant Hamiltonian Optimization for Motion Planning), our algorithm can be used to find collision-free trajectories from naA¯ve, straight-line initializations that might be in collision. At the core of our approach are (a) a sequential convex optimization procedure, which penalizes collisions with a hinge loss and increases the penalty coefficients in an outer loop as necessary, and (b) an efficient formulation of the no-collisions constraint that directly considers continuous-time safety Our algorithm is implemented in a software package called TrajOpt. We report results from a series of experiments comparing TrajOpt with CHOMP and randomized planners from OMPL, with regard to planning time and path quality. We consider motion planning for 7 DOF robot arms, 18 DOF full-body robots, statically stable walking motion for the 34 DOF Atlas humanoid robot, and physical experiments with the 18 DOF PR2. We also apply TrajOpt to plan curvature-constrained steerable needle trajectories in the SE(3) configuration space and multiple non-intersecting curved channels within 3D-printed implants for intracavitary brachytherapy. Details, videos, and source code are freely available at: http: rll.berkeley.edu trajopt ijrr. Existing high-dimensional motion planning algorithms are simultaneously overpowered and underpowered. In domains sparsely populated by obstacles, the heuristics used by sampling-based planners to navigate “narrow passages” can be needlessly complex; furthermore, additional post-processing is required to remove the jerky or extraneous motions from the paths that such planners generate. In this paper, we present CHOMP, a novel method for continuous path refinement that uses covariant gradient techniques to improve the quality of sampled trajectories. Our optimization technique both optimizes higher-order dynamics and is able to converge over a wider range of input paths relative to previous path optimization strategies. In particular, we relax the collision-free feasibility prerequisite on input paths required by those strategies. As a result, CHOMP can be used as a standalone motion planner in many real-world planning queries. We demonstrate the effectiveness of our proposed method in manipulation planning for a 6-DOF robotic arm as well as in trajectory generation for a walking quadruped robot. There is extensive literature on using convex optimization to derive piece-wise polynomial trajectories for controlling differential flat systems with applications to three-dimensional flight for Micro Aerial Vehicles. In this work, we propose a method to formulate trajectory generation as a quadratic program (QP) using the concept of a Safe Flight Corridor (SFC). The SFC is a collection of convex overlapping polyhedra that models free space and provides a connected path from the robot to the goal position. We derive an efficient convex decomposition method that builds the SFC from a piece-wise linear skeleton obtained using a fast graph search technique. The SFC provides a set of linear inequality constraints in the QP allowing real-time motion planning. Because the range and field of view of the robot's sensors are limited, we develop a framework of Receding Horizon Planning , which plans trajectories within a finite footprint in the local map, continuously updating the trajectory through a re-planning process. The re-planning process takes between 50 to 300 ms for a large and cluttered map. We show the feasibility of our approach, its completeness and performance, with applications to high-speed flight in both simulated and physical experiments using quadrotors. 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.