Reaching with multi-referential dynamical systems

We study a reaching movement controller for a redundant serial arm manipulator, based on two principles believed to be central to biological motion control: multi-referential control and dynamical system control. The resulting controller is based on two concurrent dynamical systems acting on different, yet redundant variables. The first dynamical system acts on the end-effector location variables and the second one acts on the joint angle variables. Coherence constraints are enforced between those two redundant representations of the movement and can be used to modulate the relative influence of each dynamical system. We illustrate the advantages of such a redundant representation of the movement regarding singularities and joint angle avoidanc

Adaptive sensorimotor peripersonal space representation and motor learning for a humanoid robot

This thesis presents possible computational mechanisms by which a humanoid robot can develop a coherent representation of the space within its reach (its peripersonal space), and use it to control its movements. Those mechanisms are inspired by current theories of peripersonal space representation and motor control in humans, targeting a cross-fertilization between robotics on one side, and cognitive science on the other side. This research addresses the issue of adaptivity the sensorimotor level, at the control level and at the level of simple task learning. First, this work considers the concept of body schema and suggests a computational translation of this concept, appropriate for controlling a humanoid robot. This model of the body schema is adaptive and evolves as a result of the robot sensory experience. It suggests new avenues for understanding various psychophysical and neuropsychological phenomenons of human peripersonal space representation such as adaptation to distorted vision and tool use, fake limbs experiments, body-part centered receptive fields, and multimodal neurons. Second, it is shown how the motor modality can be added to the body schema. The suggested controller is inspired by the dynamical system theory of motor control and allows the robot to simultaneously and robustly control its limbs in joint angles space and in end-effector location space. This amounts to controlling the robot in both proprioceptive and visual modalities. This multimodal control can benefit from the advantages offered by each modality and is better than traditional robotic controllers in several respects. It offers a simple and elegant solution to the singularity and joint limit avoidance problems and can be seen as a generalization of the Damped Least Square approach to robot control. The controller exhibits several properties of human reaching movements, such as quasi-straight hand paths and bell-shaped velocity profiles and non-equifinality. In a third step, the motor modalities is endowed with a statistical learning mechanism, based on Gaussian Mixture Models, that enables the humanoid to learn motor primitives from demonstrations. The robot is thus able to learn simple manipulation tasks and generalize them to various context, in a way that is robust to perturbations occurring during task execution. In addition to simulation results, the whole model has been implemented and validated on two humanoid robots, the Hoap3 and the iCub, enabling them to learn their arm and head geometries, perform reaching movements, adapt to unknown tools, and visual distortions, and learn simple manipulation tasks in a smooth, robust and adaptive way. Finally, this work hints at possible computational interpretations of the concepts of body schema, motor perception and motor primitives

Iterative Estimation of Rigid-Body Transformations: Application to Robust Object Tracking and Iterative Closest Point

Closed-form solutions are traditionally used in computer vision for estimating rigid body transformations. Here we suggest an iterative solution for estimating rigid body transformations and prove its global convergence. We show that for a number of applications involving repeated estimations of rigid body transformations, an iterative scheme is preferable to a closed-form solution. We illustrate this experimentally on two applications, 3D object tracking and image registration with Iterative Closest Point. Our results show that for those problems using an iterative and continuous estimation process is more robust than using many independent closed-form estimation

Pom1 gradient buffering through intermolecular auto-phosphorylation.

Concentration gradients provide spatial information for tissue patterning and cell organization, and their robustness under natural fluctuations is an evolutionary advantage. In rod-shaped Schizosaccharomyces pombe cells, the DYRK-family kinase Pom1 gradients control cell division timing and placement. Upon dephosphorylation by a Tea4-phosphatase complex, Pom1 associates with the plasma membrane at cell poles, where it diffuses and detaches upon auto-phosphorylation. Here, we demonstrate that Pom1 auto-phosphorylates intermolecularly, both in vitro and in vivo, which confers robustness to the gradient. Quantitative imaging reveals this robustness through two system's properties: The Pom1 gradient amplitude is inversely correlated with its decay length and is buffered against fluctuations in Tea4 levels. A theoretical model of Pom1 gradient formation through intermolecular auto-phosphorylation predicts both properties qualitatively and quantitatively. This provides a telling example where gradient robustness through super-linear decay, a principle hypothesized a decade ago, is achieved through autocatalysis. Concentration-dependent autocatalysis may be a widely used simple feedback to buffer biological activities