Desensitized motion planning for underactuated multibody systems

Abstract

Model-plant mismatches can severely limit the effectiveness of conventional model-based motion design methods. To solve this issue, a method for robust trajectory planning that can reduce the effects of parametric uncertainties is presented in this work. The method is based on an indirect variational formulation, which is translated into a Two-Point Boundary Value Problem (TPBVP) and then solved numerically. Robustness is obtained by incorporating into the problem the sensitivity functions of the plant, and imposing some additional constraints on the initial and final points of the trajectory. A formulation aimed at reducing both the residual and the transient oscillations, as well as keeping small the control effort, is also proposed. The work presents a numerical verification of the effectiveness of the method for an underactuated system, such as a double-pendulum crane, by showing its effectiveness and robustness when performing fast rest-to-rest motions.

On the Trajectory Planning for Energy Efficiency in Industrial Robotic Systems †

“…Following the approaches that are presented in [13,14,16], it is possible to derive a formulation for the energy consumption related to the parameters that describe the given trajectory. In this work, we consider the trapezoidal and cycloidal profiles [20], which are characterized by four parameters: acceleration time t 1 , constant velocity time t 2 , deceleration time t 3 , and total length of the path L.…”

“…The method only considers the acceleration time to improve energy efficiency of a gantry crane system. Furthermore, in [14], a point-to-point trajectory based on a S-curve is designed in order to reduce energy consumption of a robotic linear axis, yet, only numerical results have been presented. In [15], an analytical model for minimum-energy planning in rest-to-rest motion is presented.…”

Energetically Optimal Trajectory for a Redundant Planar Robot by Means of a Nested Loop Algorithm

“…Promising results have been obtained at the simulation level and in real implementations. This is the case of the technique of the subspace trust method [2], Euler/Runge Kutta with multiple method shooting [3], dynamic programming with Dubins routes [4], dynamic programming "Mixed Integer Nonlinear Programming" [5], Interior Point Optimizer (IP) [6], evolutionary model and swarm intelligence [7], differential evolution [8], gradientbased algorithm [9], dynamic programming [10], Kalman heuristic algorithm [11], Genetic Algorithm (GA) [12], metaheuristic algorithm type vector evaluated particle swarm optimization [13], sequential quadratic programming [14], Hessian and GA matrix [15], Pontryagin's minimum algorithm [16], and optimization of multiple immune targets of restrictions [17]. Finally, in [18], a trajectory planning method is developed based on a surrogate or substitute model for an unmanned electric excavator.…”

“…Similarly, to determine the energy used by the robotic manipulator, using an objective function, it is possible to consider different variables obtained from the RE operation Energetically Optimal Trajectory for a Redundant Planar Robot by Means of a Nested Loop Algorithm such as total work [13], some squared torque variants [3], [14], [19]; squared current [12], actuator motor power [5], [11], [15], [16]; squared acceleration [4], [17], [20]; potential and kinetic energy [8], mean square torque [9], [21] and mechanical power [9]. In addition, the authors consider the use of a weight vector that penalizes the influence of each joint in the optimization task, such as Zhao, Lin, and Tomizuka [22] and Wigstrom, Lennartson, Vergnano, and Breitholtz [5].…”

“…Regarding the functions used as a basis in the optimization process trajectory, a Spline function is often used in [6], [9], [14], [17], and [19]. In [13] and [15], a cycloidal path and an S-curve profile are used, respectively. In [12], a polynomial formulation of the 3 rd and 4 th degree is used.…”