Trajectory optimization for autonomous mobile robots in ITER

Highlights

• Path planning for mobile robots in cluttered environments with high safety constrains as in nuclear facilities like ITER.

• Line guidance and free roaming path planning methodologies for vehicles with rhombic-like kinematics.

• Integration of multiple maneuvers in path planning.

• Methodology that maximizes the common parts of different trajectories.

Abstract

The Cask and Plug Remote Handling System (CPRHS) is one of the remote handling systems that will operate in the International Thermonuclear Experimental Reactor (ITER), transporting heavy and highly activated in-vessel components between the Tokamak Building and the Hot Cell Building, the two main buildings of the nuclear facility. The CPRHS has similar dimensions as an autobus, maximum weight of 100 tons, with kinematics of a rhombic-like vehicle (two drivable and steerable wheels) and has to move in cluttered environments. Two main approaches for trajectory optimization were developed and implemented aiming at providing smooth paths that maximize the clearance to obstacles taking into account the flexibility of rhombic-like vehicles: line guidance (same path for both wheels) and free roaming (different paths for each wheel). The line guidance approach includes maneuvers when necessary and the ability of maximizing the common parts of different paths used in the most of the nominal operations. Free roaming is mainly used when line guidance is not possible, namely in rescue operations. Both approaches were implemented in a standalone application that receives 2D CAD models of the buildings and returns the best trajectories, including a report of the most risky points of collision and the swept volume of the vehicle along the missions. This paper also presents the main results of these approaches applied in the models of the real scenarios, crucial to proceed with the construction of the Tokamak Building. Conclusions and future work are presented and discussed.

Introduction

There is a practical need for developing and exploring nuclear fusion as a source of energy for the humankind benefit. The shortage predictions on fossil fuels, especially with the inevitable oil extraction decline, require an urgent development and exploration of new sources of energy.

The current energy supply policy is mostly based on fossil fuels (oil, coal and natural gas) representing almost 80% of the total energy consumption  [1]. To worsen this scenario, the world population is expected to grow from 6 to 9 billion people until 2050  [2] resulting in an expressive raise of energy demand.

According to  [3], no single technology is likely to provide all of the world’s future energy needs and replace the actual oil-based energy infrastructure. It is important to achieve a more sustainable mix of fossil fuels but, more importantly, develop an energy consumption-frame based on new technologies and alternative energies such as solar, geothermal and nuclear, fission and fusion power.

The International Thermonuclear Experimental Reactor (ITER) project is a worldwide research experiment that aims to explore nuclear fusion as a viable source of energy for the coming years.

Besides the major scientific objective of exploring the nuclear fusion as a source of energy, future fusion power plants have to be safely and effectively maintained through Remote Handling (RH) techniques, due to restrictions on human being in activated areas.

Among the various RH systems that are expected to operate in ITER, as described in  [4], this paper focus on a large and complex transporter unit that was chosen for the transfer of heavy and contaminated loads between the two main buildings of ITER, the Tokamak Building (TB), lodging the tokamak reactor and with access by vacuum vessel port cells (from this point forward simply identified as “ports”) and the Hot Cell Building (HCB), that will work mainly as a support area. In Fig. 1 the two main buildings and their relative dimensions are depicted.

During ITER lifetime, the internal components of the vacuum vessel of the reactor, such as the blanket and divertor modules detached in Fig. 1, will become activated due to exposure to highly energetic neutrons released during the fusion reaction. Additionally, these in-vessel materials might get contaminated with small amounts of radioactive dust. Hence, the components that provide the base functions for the ITER machinery will need to be periodically inspected and upgraded. To manage such operations and provided that the human presence will not be authorized in activated areas, the ITER maintenance system will mostly rely on RH devices.

The foreseen RH equipment will have a large impact on the design and assembly of the remaining ITER components, for instance, on building structural aspects and interfaces. Therefore, motion planning studies for the CPRHS in all its missions are required for the sake of the feasibility of the ITER structure design and the space reservation for the RH missions and to avoid the handwork to generate hundred of trajectories and also to speed up the study of the mission feasibility with the CPRHS.

The CPRHS, represented in Fig. 2, is a large and complex transport unit to transport heavy and contaminated components between the TB and the HCB. The geometry of the CPRHS and its payload vary according to the cask and the components to be transported and hence, different CPRHS typologies will operate. As a reference, the largest CPRHS dimensions are 8.5 m × 2.62 m × 3.62 m (length × width × height) and the total weight with the maximum load can reach up to 100 tons.

A CPRHS is composed of three sub-systems: the cask envelope (container that enclosures the in-vessel components and the RH tools to be transported), the Cask Transfer System (CTS), which acts as a mobile robot and the pallet (interface between the cask and the CTS equipped with a handling platform to support the cask load and help on docking procedures). When underneath the pallet the CTS transports the entire CPRHS, but it can also move independently of the pallet and cask. The CTS has a rhombic-like configuration provided by two drivable and steerable wheels, identified as “F”ront and “R”ear wheels, as illustrated in Fig. 2. Given this configuration, the CTS has a higher maneuverability in confined spaces than the traditional cars with Ackerman or tricycle configurations  [5].

The CTS when operating individually or the CPRHS when carried out by the CTS are, hence, rhombic-like vehicles. For a question of simplicity and from this point forward the CPRHS and the CTS when moving alone are identified as “vehicle”.

As illustrated in Fig. 2, consider the state vector $q=\left[x_c{y}_c\theta \right]$ as a representation of the vehicle pose in the frame {I}, with $(x_c,y_c)$ the coordinates of the center of the vehicle and $\theta$ the orientation of the vehicle. Also, consider $v$ as the longitudinal speed and $\beta$ the controllable sideslip angle of the vehicle, both defined in {I}. A kinematic model for a rhombic-like vehicle in {I}, that allows the simulation of the vehicle motion directly through the desired longitudinal speed $v$, instead of imposing an individual linear speed for each wheel, was introduced in  [6] as:

$$\left[\begin{array}{c}\hfill {\dot{x}}_c\hfill \\ \hfill {\dot{y}}_c\hfill \\ \hfill \dot{{\theta }_m}\hfill \end{array}\right]=\left[\begin{array}{c}\hfill cos(\theta +\beta )\hfill \\ \hfill sin(\theta +\beta )\hfill \\ \hfill \frac{cos\beta \cdot [tan{\theta }_F-tan{\theta }_R]}{M}\hfill \end{array}\right]\cdot v\text{,}$$

where

$$\beta =arctan\left(\frac{v_F\cdot sin{\theta }_F+v_R\cdot sin{\theta }_R}{2\cdot v_R\cdot cos{\theta }_R}\right)$$

and

$$v=\frac{v_F\cdot cos{\theta }_F+v_R\cdot cos{\theta }_R}{2\cdot cos\beta }\text{.}$$

This modeling entails that the wheels of the vehicle roll without slipping, a constraint inherent to the nonholonomy of rhombic-like vehicles, and also considers a rigid body constraint, common to this type of vehicles, as follows:

$$v_{F}cos{\theta }_F=v_{R}cos{\theta }_R\text{.}$$

For the implementation, the $\dot{x}$ is considered as $(x(k+1)-x\left(k\right))/T$, where $T$ is the sampling time and “$k$” the iteration. The (1), (2), (3) become:

$$\left[\begin{array}{c}\hfill x_c(k+1)\hfill \\ \hfill y_c(k+1)\hfill \\ \hfill {\theta }_m(k+1)\hfill \end{array}\right]=\left[\begin{array}{c}\hfill cos(\theta \left(k\right)+\beta \left(k\right))\hfill \\ \hfill sin(\theta \left(k\right)+\beta \left(k\right))\hfill \\ \hfill \frac{cos\beta \left(k\right)\cdot [tan{\theta }_F\left(k\right)-tan{\theta }_R\left(k\right)]}{M}\hfill \end{array}\right]\cdot v\left(k\right)\text{,}$$

where

$$\beta \left(k\right)=arctan\left(\frac{v_F\left(k\right)\cdot sin{\theta }_F\left(k\right)+v_R\left(k\right)\cdot sin{\theta }_R\left(k\right)}{2\cdot v_R\left(k\right)\cdot cos{\theta }_R\left(k\right)}\right)$$

and

$$v\left(k\right)=\frac{v_F\left(k\right)\cdot cos{\theta }_F\left(k\right)+v_R\left(k\right)\cdot cos{\theta }_R\left(k\right)}{2\cdot cos\beta \left(k\right)}\text{.}$$

The values $v_F\left(k\right)$, $v_R\left(k\right)$, ${\theta }_F\left(k\right)$ and ${\theta }_R\left(k\right)$ are the inputs. This implementation was inspired in the work described in  [6] and detailed in  [7].

A rhombic-like vehicle has a particular capability, where both drivable and steerable wheels can follow the same path, as illustrated in the left image of Fig. 3, which is identified as a line guidance approach. In general, each wheel can follow a different path keeping the structure of the vehicle, as illustrated in the right image of Fig. 3, which is identified as the free roaming approach. The relevance of these approaches will be addressed later in Section  2.

In ITER, the environment in all levels of TB and HCB is mostly composed of static and well-structured scenarios. Therefore, each level of the buildings can be modeled using a 2D map representation. The adopted representation is a set of 2D points in a global cartesian referential of ITER and a set of line segments, where each line segment connects two different points, as illustrated in the bottom images of Fig. 4. It is assumed no crossing between lines. In the case of intersection, a 2D point resulted from the intersection is created and each crossed line segment is split in two new line segments, one starting and the other ending in the splitting point, respectively.

The main challenge is to compute a trajectory to guide the vehicle from an initial vehicle configuration, $q_S$, to a final configuration, $q_F$, using the map representation and the vehicle model described above.

The paper is organized as follows. Section  1.2 summarizes the environment and its representation and describes the problem of trajectory optimization. Section  2 describes the two main approaches for trajectory optimization, namely the line guidance and free roaming, including the features of maneuvers and the maximization of common parts of different trajectories. Section  3 starts with a brief description of the software tool developed with the implementation of the algorithms and then presents the main results gathered within the scenarios of ITER. Finally, Section  4 summarizes the main conclusions and points for future work.

The trajectory optimization problem stated for the vehicle consists on evaluating a trajectory, i.e., a geometric path combined with a speed profile, which guarantees that the vehicle, departing from an initial configuration, achieves the specified goal without colliding with obstacles and taking into account a safety margin. Specific optimization criteria such as smoothness, path length and obstacle clearance are also considered during the planning phase as well as the vehicle characteristics (dimensions and kinematic constraints) and surrounding scenario.

To solve the trajectory optimization problem associated with the different missions specific information is required, which defines the inputs to the mentioned problem, as shown in Fig. 4:

• Vehicle model: the planning solutions depend directly on the vehicle configuration (geometric, kinematic and dynamic).

• Environment model: the model of the scenario where the vehicles have to move that constitute relevant information for the definition of a collision free optimal planned solution. From the original CAD models in 3D, it is only used their 2D projection at a floor level.

• Initial and goal conditions: the pair of vehicle pose (position and orientation relative to a given referential) determining how the vehicles start and finish its motion.

• Global trajectory(ies): most of the trajectories in TB share a large common path around the Tokamak, which is identified as a “ring” in each level. The maximization of different paths is also addressed, mainly in the TB to maximize the individual paths for each port in each level with the ring. Therefore, the trajectory of the ring is also assumed to be an input.

Together, these inputs define a motion query for the specified mission in the ITER scenarios and are fed into a trajectory planner. This planner generates a path to be carried out by the vehicles, i.e., a set of cartesian coordinates (for specific vehicle reference points) and respective orientations that geometrically describe the vehicle motion. In addition to the geometric feasibility of the solution, which shall guarantee that the vehicle reaches the goal configuration without colliding with obstacles, and considering the particular characteristics of the transportation problem inside the ITER buildings, it is desirable that the planned solution follows specific criteria requirements:

• Path clearance: increase the minimum distance of the vehicle to the surrounding obstacles of the scenario.

• Path smoothness: the planned solution shall be smooth, minimizing steering maneuvers and jerky motions.

• Path length: whenever possible find the shortest possible solution, so as to minimize the energy consumption of the on-board batteries.

• Maximization of common paths: the vehicle journeys may share common paths through the buildings.

The planner shall output a trajectory; therefore, the geometric solution (a path) is combined with a speed profile, which defines how to move the vehicle along the path at various speeds while satisfying the kinematic and dynamic constraints (maximum/minimum velocities and accelerations).