Dynamical systems theoryDynamical systems theory is an area of mathematics used to describe the behavior of complex dynamical systems, usually by employing differential equations or difference equations. When differential equations are employed, the theory is called continuous dynamical systems. From a physical point of view, continuous dynamical systems is a generalization of classical mechanics, a generalization where the equations of motion are postulated directly and are not constrained to be Euler–Lagrange equations of a least action principle.
Atlas (robot)Atlas is a bipedal humanoid robot primarily developed by the American robotics company Boston Dynamics with funding and oversight from the U.S. Defense Advanced Research Projects Agency (DARPA). The robot was initially designed for a variety of search and rescue tasks, and was unveiled to the public on July 11, 2013. The design and production of Atlas were overseen by DARPA, an agency of the United States Department of Defense, in cooperation with Boston Dynamics.
KinematicsKinematics is a subfield of physics, developed in classical mechanics, that describes the motion of points, bodies (objects), and systems of bodies (groups of objects) without considering the forces that cause them to move. Kinematics, as a field of study, is often referred to as the "geometry of motion" and is occasionally seen as a branch of mathematics. A kinematics problem begins by describing the geometry of the system and declaring the initial conditions of any known values of position, velocity and/or acceleration of points within the system.
RobotA robot is a machine—especially one programmable by a computer—capable of carrying out a complex series of actions automatically. A robot can be guided by an external control device, or the control may be embedded within. Robots may be constructed to evoke human form, but most robots are task-performing machines, designed with an emphasis on stark functionality, rather than expressive aesthetics.
Nao (robot)Nao (pronounced now) is an autonomous, programmable humanoid robot formerly developed by Aldebaran Robotics, a French robotics company headquartered in Paris, which was acquired by SoftBank Group in 2015 and rebranded as SoftBank Robotics. The robot's development began with the launch of Project Nao in 2004. On 15 August 2007, Nao replaced Sony's robot dog Aibo as the robot used in the RoboCup Standard Platform League (SPL), an international robot soccer competition.
Swarm roboticsSwarm robotics is an approach to the coordination of multiple robots as a system which consist of large numbers of mostly simple physical robots. ′′In a robot swarm, the collective behavior of the robots results from local interactions between the robots and between the robots and the environment in which they act.′′ It is supposed that a desired collective behavior emerges from the interactions between the robots and interactions of robots with the environment.
TrajectoryA trajectory or flight path is the path that an object with mass in motion follows through space as a function of time. In classical mechanics, a trajectory is defined by Hamiltonian mechanics via canonical coordinates; hence, a complete trajectory is defined by position and momentum, simultaneously. The mass might be a projectile or a satellite. For example, it can be an orbit — the path of a planet, asteroid, or comet as it travels around a central mass. In control theory, a trajectory is a time-ordered set of states of a dynamical system (see e.
Orbital state vectorsIn astrodynamics and celestial dynamics, the orbital state vectors (sometimes state vectors) of an orbit are Cartesian vectors of position () and velocity () that together with their time (epoch) () uniquely determine the trajectory of the orbiting body in space. State vectors are defined with respect to some frame of reference, usually but not always an inertial reference frame.
Constrained optimizationIn mathematical optimization, constrained optimization (in some contexts called constraint optimization) is the process of optimizing an objective function with respect to some variables in the presence of constraints on those variables. The objective function is either a cost function or energy function, which is to be minimized, or a reward function or utility function, which is to be maximized.
MicroboticsMicrobotics (or microrobotics) is the field of miniature robotics, in particular mobile robots with characteristic dimensions less than 1 mm. The term can also be used for robots capable of handling micrometer size components. Microbots were born thanks to the appearance of the microcontroller in the last decade of the 20th century, and the appearance of microelectromechanical systems (MEMS) on silicon, although many microbots do not use silicon for mechanical components other than sensors.
