Optimal Tube Following for Robotic Manipulators

Abstract

Optimal path following for robots considers the problem of moving along a predetermined Cartesian geometric end effector path (which is transformed into a predetermined geometric joint path), while some objective is minimized: e.g. motion time or energy loss. In practice it is often not required to follow a path exactly but only within a certain tolerance. By deviating from the path, within the allowable tolerance, one could gain in optimality. In this paper, we define the allowable deviation from the path as a tube around the given geometric path. We then search for the optimal motion inside the tube. This transforms the path following problem to a tube following problem. In contrast to the (time or energy) optimal path following problem, the tube following problem is not convex. However, we propose a problem formulation that can still be solved efficiently, as will be illustrated by some numerical examples.

Speed-Up of Nonlinear Model Predictive Control for Robot Manipulators Using Task and Data Parallelism

“…This is done without modifying the NLP solution algorithms themselves nor their convergence properties. We explore task parallelism, i.e., multi-core parallelization, and data parallelism, i.e., single-instruction-multiple-data (SIMD), to efficiently evaluate multiple instances of the robot dynamics and kinematics in a tunnel-following MPC [6], [7] for a robot manipulator, where the underlying OCP is solved by using (i) the firstorder method PANOC with augmented Lagrangian, and (ii) the second-order method SCQP. The effect of parallelization of function evaluations on both methods is also compared.…”

Time-optimal motion planning for n-DOF robot manipulators using a path-parametric system reformulation

“…where the velocity of the end-effector can be written aṡ p = J(q)q, with J(q) the robot Jacobian, andṡ is obtained from (8).…”

“…where we obtainṡ from (8). Note that both OCPs (13) and (14) are equivalent to (12), as the objective function and the constraints remain equivalent after transformation of variables.…”

“…The geometric path in the workspace of the robot may not be completely strict and, in fact, limited deviations may be perfectly acceptable, for instance in tasks with a certain machining tolerance, or in orientation invariant tasks. The work in [8] presents a time-optimal approach which allows deviation from the reference path, by projecting the robot dynamics on the reference path and introducing constraints on the forward position kinematics. As in [8], we propose a trajectory generation methodology closely related to the decoupled approach.…”

“…The work in [8] presents a time-optimal approach which allows deviation from the reference path, by projecting the robot dynamics on the reference path and introducing constraints on the forward position kinematics. As in [8], we propose a trajectory generation methodology closely related to the decoupled approach. The main difference is that we do not project the robot dynamics onto a predefined path.…”