Faster Motion on Cartesian Paths Exploiting Robot Redundancy at the Acceleration Level

The problem of minimizing the transfer time along a given Cartesian path for redundant robots can be approached in two steps, by separating the generation of a joint path associated to the Cartesian path from the exact minimization of motion time under kinematic/dynamic bounds along the obtained parameterized joint path. In this framework, multiple suboptimal solutions can be found, depending on how redundancy is locally resolved in the joint space within the first step. We propose a solution method that works at the acceleration level, by using weighted pseudoinversion, optimizing an inertia-related criterion, and including null-space damping. Several numerical results obtained on different robot systems demonstrate consistently good behaviors and definitely faster motion times in comparison with related methods proposed in the literature. The motion time obtained with our method is reasonably close to the global time-optimal solution along same Cartesian path. Experimental results on a KUKA LWR IV are also reported, showing the tracking control performance on the executed motions

Motion Planning of Uncertain Ordinary Differential Equation Systems

This work presents a novel motion planning framework, rooted in nonlinear programming theory, that treats uncertain fully and under-actuated dynamical systems described by ordinary differential equations. Uncertainty in multibody dynamical systems comes from various sources, such as: system parameters, initial conditions, sensor and actuator noise, and external forcing. Treatment of uncertainty in design is of paramount practical importance because all real-life systems are affected by it, and poor robustness and suboptimal performance result if it’s not accounted for in a given design. In this work uncertainties are modeled using Generalized Polynomial Chaos and are solved quantitatively using a least-square collocation method. The computational efficiency of this approach enables the inclusion of uncertainty statistics in the nonlinear programming optimization process. As such, the proposed framework allows the user to pose, and answer, new design questions related to uncertain dynamical systems. Specifically, the new framework is explained in the context of forward, inverse, and hybrid dynamics formulations. The forward dynamics formulation, applicable to both fully and under-actuated systems, prescribes deterministic actuator inputs which yield uncertain state trajectories. The inverse dynamics formulation is the dual to the forward dynamic, and is only applicable to fully-actuated systems; deterministic state trajectories are prescribed and yield uncertain actuator inputs. The inverse dynamics formulation is more computationally efficient as it requires only algebraic evaluations and completely avoids numerical integration. Finally, the hybrid dynamics formulation is applicable to under-actuated systems where it leverages the benefits of inverse dynamics for actuated joints and forward dynamics for unactuated joints; it prescribes actuated state and unactuated input trajectories which yield uncertain unactuated states and actuated inputs. The benefits of the ability to quantify uncertainty when planning the motion of multibody dynamic systems are illustrated through several case-studies. The resulting designs determine optimal motion plans—subject to deterministic and statistical constraints—for all possible systems within the probability space

Robot Excitation Trajectories for Dynamic Parameter Estimation using Optimized B-Splines

In this paper we adressed the problem of finding exciting trajectories for the identification of manipulator link inertia parameters. This can be formulated as a constraint nonlinear optimization problem. The new approach in the presented method is the parameterization of the trajectories with optimized B-splines. Experiments are carried out on a 7 joint Light-Weight robot with torque sensoring in each joint. Thus, unmodeled joint friction and noisy motor current measurements must not be taken into account. The estimated dynamic model is verified on a different validation trajectory. The results show a clear improvement of the estimated dynamic model compared to a CAD-valued model

An inverse kinematics algorithm for a highly redundant variable-geometry-truss manipulator

A new class of robotic arm consists of a periodic sequence of truss substructures, each of which has several variable-length members. Such variable-geometry-truss manipulator (VGTMs) are inherently highly redundant and promise a significant increase in dexterity over conventional anthropomorphic manipulators. This dexterity may be exploited for both obstacle avoidance and controlled deployment in complex workspaces. The inverse kinematics problem for such unorthodox manipulators, however, becomes complex because of the large number of degrees of freedom, and conventional solutions to the inverse kinematics problem become inefficient because of the high degree of redundancy. A solution is presented to this problem based on a spline-like reference curve for the manipulator's shape. Such an approach has a number of advantages: (1) direct, intuitive manipulation of shape; (2) reduced calculation time; and (3) direct control over the effective degree of redundancy of the manipulator. Furthermore, although the algorithm was developed primarily for variable-geometry-truss manipulators, it is general enough for application to a number of manipulator designs

Design and analysis of a wire-driven flexible manipulator for bronchoscopic interventions

Bronchoscopic interventions are widely performed for the diagnosis and treatment of lung diseases. However, for most endobronchial devices, the lack of a bendable tip restricts their access ability to get into distal bronchi with complex bifurcations. This paper presents the design of a new wire-driven continuum manipulator to help guide these devices. The proposed manipulator is built by assembling miniaturized blocks that are featured with interlocking circular joints. It has the capability of maintaining its integrity when the lengths of actuation wires change due to the shaft flex. It allows the existence of a relatively large central cavity to pass through other instruments and enables two rotational degrees of freedom. All these features make it suitable for procedures where tubular anatomies are involved and the flexible shafts have to be considerably bent in usage, just like bronchoscopic interventions. A kinematic model is built to estimate the relationship between the translations of actuation wires and the manipulator tip position. A scale-up model is produced for evaluation experiments and the results validate the performance of the proposed mechanism

Numerical approach of collision avoidance and optimal control on robotic manipulators

Collision-free optimal motion and trajectory planning for robotic manipulators are solved by a method of sequential gradient restoration algorithm. Numerical examples of a two degree-of-freedom (DOF) robotic manipulator are demonstrated to show the excellence of the optimization technique and obstacle avoidance scheme. The obstacle is put on the midway, or even further inward on purpose, of the previous no-obstacle optimal trajectory. For the minimum-time purpose, the trajectory grazes by the obstacle and the minimum-time motion successfully avoids the obstacle. The minimum-time is longer for the obstacle avoidance cases than the one without obstacle. The obstacle avoidance scheme can deal with multiple obstacles in any ellipsoid forms by using artificial potential fields as penalty functions via distance functions. The method is promising in solving collision-free optimal control problems for robotics and can be applied to any DOF robotic manipulators with any performance indices and mobile robots as well. Since this method generates optimum solution based on Pontryagin Extremum Principle, rather than based on assumptions, the results provide a benchmark against which any optimization techniques can be measured

A Novel Approach for Simplification of Industrial Robot Dynamic Model Using Interval Method

This paper proposes a new approach to simplify the dynamic model of industrial robot by means of interval method. Due to strong nonlinearities, some components of robot dynamic model such as the inertia matrix and the vector of centrifugal, Coriolis and gravitational torques, are very complicated for real-time control of industrial robots. Thus, a simplification algorithm is presented in this study in order to reduce the computation time and memory occupation. More importantly, this simplification is suitable for arbitrary trajectories in whole robot workspace. Furthermore, the method devotes to finding negligible inertia parameters, which is useful for robot model identification. A simulation has been carried out on a test trajectory using a 6-DOF industrial robot model, and the results have shown good performance and effectiveness of this method.ANR COROUSS