Nonlinear control of multiple mobile manipulator robots transporting a rigid object in coordination

Robotics as it is known today is an interdisciplinary science encompassing vast fields of research: vision, planning, motion / control, locomotion, design, and so on. The objective of the creation of robots in the early sixties was to relieve man of some tedious work such as: handling, repetitive tasks that are often tiring or even sometimes infeasible manually. Following this situation, several kinds of manipulators were created (Siciliano and Khatib (2016)).

Historically, the first more manufactured robots were the manipulator arms, which are widely used in industry. These robotic systems have the ability to act on the environment through the realization of manipulation tasks such as the grasping of objects, the assembly of pieces, etc. They are nevertheless very limited in their operational workspace and in the type of work that can be done. This is why mobile platforms, characterized by their ability to evolve in larger size environments, have appeared. These mobile platforms were first developed for navigation, maintenance or surveillance operations, in particular in hostile environments, by equipping them with various sensors (cameras, gas detectors, radioactivity detectors, etc.). For missions in a hostile, spatial environment, or simply those requiring combined locomotion and manipulation capabilities, these platforms had to be equipped with a manipulator arm to become mobile manipulators. The well known examples of mobile manipulators, more or less automated, are the truck-mounted cranes, satellite arms, submarines exploring the seabed or extra-planetary exploration vehicles. Basically, the exploitation of such systems relies on the implementation of a series of sequences:

a. A transport phase, where only the degrees of mobility of the platform are used, in order to bring the manipulator arm to the manipulation site;

b. A manipulation phase during which the base remains fixed, and where only the degrees of mobility of the arm are used;

c. A phase of coordination or transporting an object where both the degrees of mobility of the platforms and the degrees of mobility of the arm are used.

Some tasks requiring the handling of a heavy object are difficult to achieve by only one mobile manipulator. Multiple mobile manipulators can complete tasks in coordination which are difficult or impossible for a single robot. However, one of the most important problems remains the cooperation, planning and coordination of movements within a control / command architecture in a multi-robot context. The study of multi-robot systems has become a major concern in the field of robotic research, because whatever the capabilities of a single robot, it remains spatially limited. However, this significantly complicates the robotic system as its control design complexity increases greatly. The problem of controlling the mechanical system forming a closed kinematic chain mechanism lies in the fact that it imposes a set of kinematic constraints on the coordination of the position and velocity of the mobile manipulator. Therefore, there is a reduction in the degrees of freedom for the entire system. Further, the internal forces of the object produced by all mobile manipulators must be controlled. Few research works have been proposed to solve the control problem of these robotic systems, which have high degrees of freedom and are tightly interconnected because all their manipulators are in contact with the object.

In order to control and coordinate a multi-agent systems, various architectures and approaches have been developed (Wen et al. (2014), Wen et al. (2016), Aranda et al. (2015)). Many contributed works on multi-agent formation control have been performed using mobile robots (Panagou et al. (2016), Yu and Liu (2016a), Khan et al. (2016)), helicopter (Shaw et al. (2007)), underwater vehicles (Yin et al. (2016), Li et al. (2016)) and quadcopters (VargasJacob et al. (2016), Kang and Ahn (2016)). The multiple mobile manipulators are one of the most important categories of these robotic systems. The coordinated control of multiple mobile manipulators has attracted the attention of many researchers (Tanner et al. (2003), Chinelato and de Siqueira Martins-Filho (2013), Khatib et al. (1996b) and Sugar and Kumar (2002)). Interest in these systems is due to the greater capability of mobile manipulators in performing more complex tasks requiring skills that cannot be accomplished by a single mobile manipulator, which significantly complicates the robotic system, and greatly increases its control design complexity. The problem with controlling a mechanical system forming a closed kinematic chain mechanism is that it imposes a set of kinematic constraints on the coordination of the position and velocity of the mobile manipulator, thus leading to a reduction in the degrees of freedom of the entire system. Although the object internal forces produced by all mobile manipulators must be controlled, few works have been proposed to solve this control problem for this category of robotic systems, which have high degrees of freedom and are tightly interconnected because all manipulators are in contact with the object. The aim of the proposed nonlinear approaches is to be able to control multiple mobile manipulator robots transporting a rigid object in coordination under parameters uncertainties and disturbances.

Motion planning
Motion planning is one of the fundamental problems in robotics, this approach has been covered in some studies from the perspective of a group of MMRs (which is another fundamental problem in robotics, especially in multi-robot systems), where several robots perform the task of transporting an object in cooperation, in a known or unknown environment.

These studies include those presented in (LaValle (2006), Latombe (2012), Khatib (1985)). Morn Benewitz in (Bennewitz et al. (2001)) proposed a planning technique based on a « hillclimb » coast algorithm to optimize the robot trajectory. Another structure for planning optimal trajectories was introduced in (Desai and Kumar (1997)) for two mobile manipulators pushing a common object to a desired location. The authors in (Yamamoto and Fukuda (2002), Guozheng et al. (2002)) proposed a control method for multiple mobile manipulators holding a common object. The measures of kinematic and dynamic manipulability are given, taking into account collision avoidance. However, the dynamics of the object are ignored. In Guozheng et al. (2002) the authors have proposed a real-time trajectory planning approach for multiple mobile robots. In this approach, the robot considers only the problem of collision with the robot that has a higher priority

In Furuno et al. (2003), a trajectory planning method for a group of mobile manipulator robots in cooperation, which takes into consideration the dynamic characteristics of mobile manipulators and the object to be grasped, was proposed. The dynamics are composed of equations of the motion of mobile manipulators, the movements of the object, the non-holonomic constraints of mobile platforms and the geometric constraints between the end-effectors and the object. In Sun and Gong (2004b), Zhu and Yang (2003), a planning approach based on genetic algorithms was proposed. A navigation approach of non-holonomic mobile robots in a dynamic environment was proposed in Gakuhari et al. (2004). In this study, the information about the environment and the robots are fed back into the system in real time. The global motion planning is executed cyclically .