Navigation functions learning from experiments: Application to anthropomorphic grasping

Abstract

Abstract-This paper proposes a method to construct Navigation Functions (NF) from experimental trajectories in an unknown environment. We want to approximate an unknown obstacle function and then use it within an NF. When navigating the same destinations with the experiments, this NF should produce the same trajectories as the experiments. This requirement is equivalent to a partial differential equation (PDE). Solving the PDE yields the unknown obstacle function, expressed with spline basis functions. We apply this new method to anthropomorphic grasping, producing automatic trajectories similar to the observed ones. The grasping experiments were performed for a set of different objects, Principal Component Analysis (PCA) allows reduction of the configuration space dimension, where the learning NF method is then applied.

Hand synergies: Integration of robotics and neuroscience for understanding the control of biological and artificial hands

“…To achieve these goals, research has focused on mapping human motion to anthropomorphic robot motion through non-linear, constrained optimization methods [86–89]. The anthropomorphic robot trajectories are then projected into low-dimensional manifolds of upper limb “principal components”, where appropriate Navigation Function models can be trained [90]. …”

Humanlike, task-specific reaching and grasping with redundant arms and low-complexity hands

“…These functions apply repulsive effects on the robot arm hand system, so as to reach anthropomorphic configurations. In order to learn the structure of the NF obstacle functions, we use B-Splines as described in [25]. The control law is constructed as follows:…”

“…where q, q d are the current the desired configurations respectively, γ d (q) = q − q d 2 is the paraboloid attractive effect, β = ∏ i∈I 0 β i is the aggregated obstacle repulsive effects and k ∈ N \ {0, 1} is a tuning parameter. More details regarding the NF, can be found in [25].…”

“…Regarding humanlike grasp planning, in [25] authors proposed Navigation Function models trained in a low-d manifold of human motion. These NF models used fictitious obstacle functions learned using B-Splines that: 1) embedded anthropomorphism and 2) applied repulsive effects on the robot artifact so as to attain new humanlike configurations.…”

Relating postural synergies to low-D muscular activations: Towards bio-inspired control of robotic hands

“…In [9], the concept of synergies, called principal motion directions for the particular case, is used in order to reduce the dimension of the search space in which a probabilistic roadmap planner is defined. Finally, in [10], Filippidis et al proposed a method for constructing Navigation Function (NF) controllers from experimental trajectories projected on the synergy space. Several other researchers have attempted to model human inter-joint coordination based on probabilistic techniques, [11], [12].…”