Nonlinear constrained optimal trajectory control is an important and fundamental area of research that continues to advance in numerous fields. Many attempts have been made to present new methods that can solve for optimal trajectories more efficiently or to improve the overall performance of existing techniques. This research presents a recently developed bio-inspired method called the Virtual Motion Camouflage (VMC) method that offers a means of quickly finding, within a defined but varying search space, the optimal trajectory that is equal or close to the optimal solution. The research starts with the polynomial-based VMC method, which works within a search space that is defined by a selected and fixed polynomial type virtual prey motion. Next will be presented a means of improving the solution’s optimality by using a sequential based form of VMC, where the search space is adjusted by adjusting the polynomial prey trajectory after a solution is obtained. After the search space is adjusted, an optimization is performed in the new search space to find a solution closer to the global space optimal solution, and further adjustments are made as desired. Finally, a B-spline augmented VMC method is presented, in which a B-spline curve represents the prey motion and will allow the search space to be optimized together with the solution trajectory. It is shown that (1) the polynomial based VMC method will significantly reduce the overall problem dimension, which in practice will significantly reduce the computational cost associated with solving nonlinear constrained optimal trajectory problems; (2) the sequential VMC method will improve the solution optimality by sequentially refining certain parameters, such as the prey motion; and (3) the B-spline augmented VMC method will improve the solution iv optimality without sacrificing the CPU time much as compared with the polynomial based approach. Several simulation scenarios, including the Breakwell problem, the phantom track problem, the minimum-time mobile robot obstacle avoidance problem, and the Snell’s river problem are simulated to demonstrate the capabilities of the various forms of the VMC algorithm. The capabilities of the B-spline augmented VMC method are also shown in a hardware demonstration using a mobile robot obstacle avoidance testbed.

Les robots intégrés aux chaînes de production sont généralement isolés des ouvriers et ne prévoient pas d'interaction physique avec les humains. Dans le futur, le robot humanoïde deviendra un partenaire pour vivre ou travailler avec les êtres humains. Cette coexistence prévoit l'interaction physique et sociale entre le robot et l'être humain. En robotique humanoïde les futurs progrès dépendront donc des connaissances dans les mécanismes cognitifs présents dans les interactions interpersonnelles afin que les robots interagissent avec les humains physiquement et socialement. Un bon exemple d'interaction interpersonnelle est l'acte de la poignée de la main qui possède un rôle social très important. La particularité de cette interaction est aussi qu'elle est basée sur un couplage physique et social qui induit une synchronisation des mouvements et des efforts. L'intérêt d'étudier la poignée de main pour les robots consiste donc à élargir leurs propriétés comportementales pour qu'ils interagissent avec les humains de manière plus habituelle.Cette thèse présente dans un premier chapitre un état de l'art sur les travaux dans les domaines des sciences humaines, de la médecine et de la robotique humanoïde qui sont liés au phénomène de la poignée de main. Le second chapitre, est consacré à la nature physique du phénomène de poignée de main chez l'être humain par des mesures quantitatives des mouvements. Pour cela un système de mesures a été construit à l'Université Nationale Technique de Donetsk (Ukraine). Il est composé d'un gant instrumenté par un réseau de capteurs portés qui permet l'enregistrement des vitesses et accélérations du poignet et les forces aux points de contact des paumes, lors de l'interaction. Des campagnes de mesures ont permis de montrer la présence d'un phénomène de synchronie mutuelle précédé d'une phase de contact physique qui initie cette synchronie. En tenant compte de cette nature rythmique, un contrôleur à base de neurones rythmiques de Rowat-Selverston, intégrant un mécanisme d'apprentissage de la fréquence d'interaction, est proposé et etudié dans le troisième chapitre pour commander un bras robotique. Le chapitre quatre est consacré aux expériences d'interaction physique homme/robot. Des expériences avec un bras robotique Katana montrent qu'il est possible d'apprendre à synchroniser la rythmicité du robot avec celle imposée par une per-sonne lors d'une poignée de main grâce à ce modèle de contrôleur bio-inspiré. Une conclusion générale dresse le bilan des travaux menés et propose des perspectives. / Automated production lines integrate robots which are isolated from workers, so there is no physical interaction between a human and robot. In the near future, a humanoid robot will become a part of the human environment as a companion to help or work with humans. The aspects of coexistence always presuppose physical and social interaction between a robot and a human. In humanoid robotics, further progress depends on knowledge of cognitive mechanisms of interpersonal interaction as robots physically and socially interact with humans. An illustrative example of interpersonal interaction is an act of a handshake that plays a substantial social role. The particularity of this form of interpersonal interaction is that it is based on physical and social couplings which lead to synchronization of motion and efforts. Studying a handshake for robots is interesting as it can expand their behavioral properties for interaction with a human being in more natural way. The first chapter of this thesis presents the state of the art in the fields of social sciences, medicine and humanoid robotics that study the phenomenon of a handshake. The second chapter is dedicated to the physical nature of the phenomenon between humans via quantitative measurements. A new wearable system to measure a handshake was built in Donetsk National Technical University (Ukraine). It consists of a set of several sensors attached to the glove for recording angular velocities and gravitational acceleration of the hand and forces in certain points of hand contact during interaction. The measurement campaigns have shown that there is a phenomenon of mutual synchrony that is preceded by the phase of physical contact which initiates this synchrony. Considering the rhythmic nature of this phenomenon, the controller based on the models of rhythmic neuron of Rowat-Selverston, with learning the frequency during interaction was proposed and studied in the third chapter. Chapter four deals with the experiences of physical human-robot interaction. The experimentations with robot arm Katana show that it is possible for a robot to learn to synchronize its rhythm with rhythms imposed by a human during handshake with the proposed model of a bio-inspired controller. A general conclusion and perspectives summarize and finish this work.