A method is disclosed for estimating a trajectory of an object on a map given a sequence of traces for the moving object. Each trace of the object including information defining a position measured at a given time for the object, as well as information as to an area of accuracy around the measured position. The method processes pairs of successive traces, corresponding to two positions successive in time in the sequence of measured positions for the moving object. For each trace of a pair of successive traces, the method defines road segments on the map within the area of accuracy of the trace. For each road segment within the area of accuracy of a first trace of a pair of traces and each road segment within the area of accuracy of the second trace of the pair, the method determines at least one candidate path between the two road segments. A neural network and a neural graph model are used to compute the most probable sequence of candidate paths to estimate the trajectory of the object on the map.

An approach to positioning one or more robotic arms in an assembly system may be described herein. For example, a system for robotic assembly may include a first robot, a second robot, and a control unit. The control unit may be configured to receive a first target location proximal to a second target location. The locations may indicate where the robots are to position the features. The control unit may be configured to calculate a first calculated location of the first feature of the first subcomponent, measure a first measured location of the first feature of the first subcomponent, determine a first transformation matrix between the first calculated location and the first measured location, reposition the first feature of the first subcomponent to the first target location using the first robot, the repositioning based on the first transformation matrix.

A kinematics model-free trajectory tracking method for a robotic arm includes the following steps. Obtain an actual trajectory equation r.sub.a(t) of the robotic arm at time t according to a sensor, and combines the actual trajectory equation r.sub.a(t) with a predetermined target trajectory equation r.sub.d(t) to obtain a first error function e(t). Obtain a differential equation (I) of a state change rate of a driver of the robotic arm. Obtain a second error function ϵ(t). Pass the second error function c(t) through the applied gradient neural network to obtain equation (IV). Jointly solve equation (I) and equation (IV) to obtain an joint state vector θ(t) of the robotic arm. Drive a motion of the robotic arm by a controller according to the joint state vector θ(t) of the robotic arm to complete trajectory tracking.

A mobile robot configured to travel across a residential floor or other surface while cleaning the surface with a cleaning pad and cleaning solvent is disclosed. The robot includes a controller for managing the movement of the robot as well as the treatment of the surface with a cleaning solvent. The movement of the robot can be characterized by a class of trajectories that achieve effective cleaning. The trajectories include sequences of steps that are repeated, the sequences including forward and backward motion and optional left and right motion along arcuate paths.

A full-state control method for a master-slave robot system with flexible joints and time-varying delays is provided. In a teleoperation system formed by connecting a master robot and a slave robot through network, a proportional damping controller based on a position error and velocities, and a full-state feedback controller based on backstepping are designed for the master robot and the slave robot, respectively. High-dimension uniform accurate differentiators are designed to realize an exact difference to the virtual controllers. Delay-dependent stability criteria are established by constructing Lyapunov functions. Therefore, the criteria for selecting controller parameters are presented such that the global stability of the master-slave robot system with flexible joints and time-varying delays is realized. For the master-slave robot system with flexible joints, the global precise position tracking performance is realized by adopting a full-state feedback controller based on the backstepping method and the high-dimensional uniform accurate differentiators. Moreover, the global asymptotic convergence of the system is guaranteed and the robustness of the system is improved.

A control device is provided which is operable to change the position of a distal end side link hub by driving each of arms, which are proximal end side links of a plurality of link mechanisms by means of an actuator. When in a series of operations, the position change of the distal end side link hub is mad by an angle greater than a predetermined angle, a relay position setting unit is provided for setting a relay point between a starting point and a terminating point of each of the arms so that the interference of the three axis arms may be relieved. A position change control unit performs a position control so as to pass simultaneously through the relay point so set.

A mobile robot configured to travel across a residential floor or other surface while cleaning the surface with a cleaning pad and cleaning solvent is disclosed. The robot includes a controller for managing the movement of the robot as well as the treatment of the surface with a cleaning solvent. The movement of the robot can be characterized by a class of trajectories that achieve effective cleaning. The trajectories include sequences of steps that are repeated, the sequences including forward and backward motion and optional left and right motion along arcuate paths.

A solution to a system of simultaneous equations where an exact mathematical solution to a multivariate signal path or physical trajectory problem includes time and allows a control regulator to maintain high accuracy simultaneously over multiple variables such as but not limited to distance, velocity, and time. In a flight vehicle, for example, the regulator maintains with high accuracy the position of the vehicle in X, Y, and Z at exactly the time required over the entire trajectory making its position highly predictable at any time.

A computing system for generating optimal tracking control (TC) policies for controlling a machine to track a given time-varying reference (GTVR) trajectory. An updated augmented state of the machine is obtained. Stored in memory is the GTVR trajectory, a constraint-admissible invariant set (CAIS) of machine states satisfying machine state constraints and a corresponding TC policy mapping a machine state within the CAIS to a control input satisfying control input rate constraints. A processor jointly controls the computing system to control the operation to drive an augmented state of the machine to zero, and update the CAIS and TC policy. Joint control includes using a sequence of control inputs and a sequence of augmented machine states within CAIS corresponding to the sequence of tracking control inputs. Execute a constrained tracking approximate dynamic programming (TADP) using the received data to update the value function, update the CAIS and the corresponding TC policy.

A Full-Body Inverse Kinematic (FBIK) module for use in tracking a user in a virtual reality (VR) environment. The FBIK module has an enclosure containing a power source, a plurality of active tags with lights for use by a motion tracking system to track the user, and a controller that flashes the lights in distinct patters to identify the user of the FBIK module.