in this study, the problem of determining an optimal trajectory of a nonlinear injection into orbit problem with minimum time was investigated. the method was based on orthogonal polynomial approximation. this method consists of reducing the optimal control problem to a system of algebraic equations by expanding the state and control vector as chebyshev or legendre polynomials with undetermined...

The cooperativecontrol ofmultiplemanipulatorsattached to the samebase as they reposition a commonpayload is discussed. The theory is easily applied to inertiallybased problems, as well as space-based free- oatingplatforms. The system equations of motion are developed, as well as a Lyapunov-based controller that ensures stability. The closed chain aspect of the problem reduces the system’s degr...

Trajectories of moving objects are collected in many applications. Raw trajectory data is typically very large, and has to be simplified before use. In this paper, we introduce the notion of directionpreserving trajectory simplification, and show both analytically and empirically that it can support a broader range of applications than traditional position-preserving trajectory simplification. ...

We study optimal approximation of stochastic processes by polynomial splines with free knots. The number of free knots is either a priori fixed or may depend on the particular trajectory. For the s-fold integrated Wiener process as well as for scalar diffusion processes we determine the asymptotic behavior of the average Lp-distance to the splines spaces, as the (expected) number k of free knot...

Mobile manipulator systems comprising of a mobile platform with one or more manipulators are of great interest in a number of applications. This paper presents a modeling of the system without violating the nonholonomic constraints of the platform. Trajectory planning by soft motion and seventh order polynomial to control jerk acceleration, and velocity, is also presented. The hub torque requir...

Control and trajectory generation algorithms for a quadrotor helicopter with variable-pitch propellers are presented. The control law is not based on near-hover assumptions, allowing for large attitude deviations from hover. The trajectory generation algorithm fits a time-parametrized polynomial through any number of waypoints in R, with a closed-form solution if the corresponding waypoint arri...

The Implicit function theorem due to Lagrange is generalized to enable high order implicit rate calculations of general implicit functions about a nominal solution of interest. The sensitivities thus calculated are subsequently used in determining neighboring solutions about a nominal point, or in the case of a dynamical system, a trajectory. The generalization to dynamical systems, as a specia...

A new method of smooth trajectory generation which can replace typical polynomial type trajectory is suggested. A simple, practical, discrete polynomiallike trajectory generation method which is based on zero final state constraints was suggested and named ZSPOT. There is a progress about it by allowing nonzero final constraints and named ASPOT. Without watching control issues behind these meth...

This paper presents planning of smooth trajectories using the asymmetric profiles displacement, velocity, acceleration and jerk described higher degree polynomials. The presented way determination polynomial asymmetry coefficients as well motion time includes procedure at both constraints single kinematic quantities, i.e., acceleration, introducing a few simultaneously. Moreover, method with in...