The phrase "a given trajectory" is correct and usable in written English.
It can be used when discussing a specific path or course that has been established or defined in a particular context, such as physics, mathematics, or project planning.
Example: "In analyzing the satellite's movement, we must consider a given trajectory to predict its future position accurately."
Alternatives: "a specified path" or "a defined course".
We, then, apply the concept to the case of TBR with application-based accuracy constraints in obeying a given trajectory.
One of the most important manipulator operations is the control of the manipulator to track a given trajectory.
Distance-based performance criteria for a given trajectory are proposed to do a comparative analysis for the input undulatory waveforms.
The number of factors limits the maximum allowable loads, which can be achieved by a mobile manipulator during a given trajectory.
Furthermore, we study the dynamics of shadow boundaries on the surfaces of the obstacles when the vantage point moves along a given trajectory.
It is shown how to use the Lagrange multipliers associated with these constraints to compute the work associated with a given trajectory.
These unknown nonlinearities are approximated by the fuzzy system with~a set of fuzzy IF THEN rules whose parameters are adjusted on-line according to some adaptive laws for the purpose of controlling the output of the nonlinear system to track~a given trajectory.
The task is moving an object based on given trajectories which come across an obstacle, to examine the performance of the developed control law.
This paper extends the earlier work and allows for determination of the required ranges of the kinematically redundant active prismatic joint variables of a mechanism to allow given trajectories to be singularity-free.
Occasionally, two non-overlapping core trajectories are found for a given complete trajectory in which case, after the extension step, they abut in time.
It is evident that consecutive snapshots in a given MD trajectory are highly dependent (non-ergodic) and it is known that even long MD trajectories only yield a limited number of samples that can be considered to be i.i.d.i.d
