Trajectory planning of single and dual-arm robots for time-optimal handling of liquids and objects

This Thesis studies the optimal control problem of single-arm and dual-arm serial robots to achieve the time-optimal handling of liquids and objects. The first topic deals with the planning of time-optimal anti-sloshing trajectories of an industrial robot carrying a cylindrical container filled with a liquid, considering 1-dimensional and 2-dimensional planar motions. A technique for the estimation of the sloshing height is presented, together with its extension to 3-dimensional motions. An experimental validation campaign is provided and discussed to assess the thoroughness of such a technique. As far as anti-sloshing trajectories are concerned, 2-dimensional paths are considered and, for each one of them, three constrained optimizations with different values of the sloshing-height thresholds are solved. Experimental results are presented to compare optimized and non-optimized motions. The second part focuses on the time-optimal trajectory planning for dual-arm object handling, employing two collaborative robots (cobots) and adopting an admittance-control strategy. The chosen manipulation approach, known as cooperative grasping, is based on unilateral contact between the cobots and the object, and it may lead to slipping during motion if an internal prestress along the contact-normal direction is not prescribed. Thus, a virtual penetration is considered, aimed at generating the necessary internal prestress. The stability of cooperative grasping is ensured as long as the exerted forces on the object remain inside the static-friction cone. Constrained-optimization problems are solved for 3-dimensional paths: the virtual penetration is chosen among the control inputs of the problem and friction-cone conditions are treated as inequality constraints. Also in this case experiments are presented in order to prove evidence of the firm handling of the object, even for fast motions.

On the motion planning & control of nonlinear robotic systems

In the last decades, we saw a soaring interest in autonomous robots boosted not only by academia and industry, but also by the ever in- creasing demand from civil users. As a matter of fact, autonomous robots are fast spreading in all aspects of human life, we can see them clean houses, navigate through city traffic, or harvest fruits and vegetables. Almost all commercial drones already exhibit unprecedented and sophisticated skills which makes them suitable for these applications, such as obstacle avoidance, simultaneous localisation and mapping, path planning, visual-inertial odometry, and object tracking. The major limitations of such robotic platforms lie in the limited payload that can carry, in their costs, and in the limited autonomy due to finite battery capability. For this reason researchers start to develop new algorithms able to run even on resource constrained platforms both in terms of computation capabilities and limited types of endowed sensors, focusing especially on very cheap sensors and hardware. The possibility to use a limited number of sensors allowed to scale a lot the UAVs size, while the implementation of new efficient algorithms, performing the same task in lower time, allows for lower autonomy. However, the developed robots are not mature enough to completely operate autonomously without human supervision due to still too big dimensions (especially for aerial vehicles), which make these platforms unsafe for humans, and the high probability of numerical, and decision, errors that robots may make. In this perspective, this thesis aims to review and improve the current state-of-the-art solutions for autonomous navigation from a purely practical point of view. In particular, we deeply focused on the problems of robot control, trajectory planning, environments exploration, and obstacle avoidance.

Dynamics of undeactuated cable-driven parallel robots

This thesis focuses on the dynamics of underactuated cable-driven parallel robots (UACDPRs), including various aspects of robotic theory and practice, such as workspace computation, parameter identification, and trajectory planning. After a brief introduction to CDPRs, UACDPR kinematic and dynamic models are analyzed, under the relevant assumption of inextensible cables. The free oscillatory motion of the end-effector (EE), which is a unique feature of underactuated mechanisms, is studied in detail, from both a kinematic and a dynamic perspective. The free (small) oscillations of the EE around equilibria are proved to be harmonic and the corresponding natural oscillation frequencies are analytically computed. UACDPR workspace computation and analysis are then performed. A new performance index is proposed for the analysis of the influence of actuator errors on cable tensions around equilibrium configurations, and a new type of workspace, called tension-error-insensitive, is defined as the set of poses that a UACDPR EE can statically attain even in presence of actuation errors, while preserving tensions between assigned (positive) bounds. EE free oscillations are then employed to conceive a novel procedure aimed at identifying the EE inertial parameters. This approach does not require the use of force or torque measurements. Moreover, a self-calibration procedure for the experimental determination of UACDPR initial cable lengths is developed, which consequently enables the robot to automatically infer the EE initial pose at machine start-up. Lastly, trajectory planning of UACDPRs is investigated. Two alternative methods are proposed, which aim at (i) reducing EE oscillations even when model parameters are uncertain or (ii) eliminate EE oscillations in case model parameters are perfectly known. EE oscillations are reduced in real-time by dynamically scaling a nominal trajectory and filtering it with an input shaper, whereas they can be eliminated if an off-line trajectory is computed that accounts for the system internal dynamics.

Path planning for image based visual servoing

This thesis deals with Visual Servoing and its strictly connected disciplines like projective geometry, image processing, robotics and non-linear control. More specifically the work addresses the problem to control a robotic manipulator through one of the largely used Visual Servoing techniques: the Image Based Visual Servoing (IBVS). In Image Based Visual Servoing the robot is driven by on-line performing a feedback control loop that is closed directly in the 2D space of the camera sensor. The work considers the case of a monocular system with the only camera mounted on the robot end effector (eye in hand configuration). Through IBVS the system can be positioned with respect to a 3D fixed target by minimizing the differences between its initial view and its goal view, corresponding respectively to the initial and the goal system configurations: the robot Cartesian Motion is thus generated only by means of visual informations. However, the execution of a positioning control task by IBVS is not straightforward because singularity problems may occur and local minima may be reached where the reached image is very close to the target one but the 3D positioning task is far from being fulfilled: this happens in particular for large camera displacements, when the the initial and the goal target views are noticeably different. To overcame singularity and local minima drawbacks, maintaining the good properties of IBVS robustness with respect to modeling and camera calibration errors, an opportune image path planning can be exploited. This work deals with the problem of generating opportune image plane trajectories for tracked points of the servoing control scheme (a trajectory is made of a path plus a time law). The generated image plane paths must be feasible i.e. they must be compliant with rigid body motion of the camera with respect to the object so as to avoid image jacobian singularities and local minima problems. In addition, the image planned trajectories must generate camera velocity screws which are smooth and within the allowed bounds of the robot. We will show that a scaled 3D motion planning algorithm can be devised in order to generate feasible image plane trajectories. Since the paths in the image are off-line generated it is also possible to tune the planning parameters so as to maintain the target inside the camera field of view even if, in some unfortunate cases, the feature target points would leave the camera images due to 3D robot motions. To test the validity of the proposed approach some both experiments and simulations results have been reported taking also into account the influence of noise in the path planning strategy. The experiments have been realized with a 6DOF anthropomorphic manipulator with a fire-wire camera installed on its end effector: the results demonstrate the good performances and the feasibility of the proposed approach.