1. The necessity to obtain a perfect cube, with straight edges and flat faces. It relates to the intention of creating perfectly geometrical flying shapes, but it is also induced by the fact that the cubes need to assemble while flying. If the edges are not perfectly straight, or if the faces become convex the cubes will not assemble properly.
2. The self-assembling properties. When two cubes connect to each other, they must still be able to use their motors to move in space. The thrusts of the motors of two connected cubes must add up in order to provide enough power to move them all. This led to the decision to place the ducted fans at the midpoint of each edge, and to guide the air streams towards the corners of the cubes with thin polycarbonate tubes.
3. The location of the sensors. The cube is by no way an optimal shape when it comes to sensory aptitudes, especially with large cubes (edge 160 cm or more). Obstacle avoidance would ideally require 24 sensors (one for each axis on each edge), which is hard to implement for reasons of cost, payload and energy requirements. The optimal sensor configuration is continuously being studied and updated for each project's needs.

After many design iterations and prototypes the structure reaches a stable stage with the last aerobots, christened t225c (edge length of 225 cm), the Tryphon. Its exosqueletton is made of twelve triangular trusses of carbon fiber rods and tubes assembled together by rapid prototyping joints.

SENSORS AND SOFTWARE
The mechatronic of the SAILS robots was developed in order to easily accept various sensors configuration. All the components are connected to an I2C communication bus managed by the central ultralight, Linux-based computer. Until now ultra-sounds sensors, light sensors, compass, altimeter have been tested and used for performances and demos. A video camera and accelerometer will be installed onboard in the very next phases. The sensors configuration can be quickly modified, thanks to quick-connect hubs.

The embedded control software has two mode: autonomous or teleoperated. This last mode allows the user to command position (through a USB numeric pad) which the controller then tries to stabilize. The autonomous mode is currently based on reactive behaviors. The two first automous algorithms were to stabilize itself according to a desired distance from a wall or a floor, and avoid obstacles while moving around. They use data collected from 12 ultrasounds sensors that have a 6-meters detection range. Many others specific behaviors were developed to trigger reactions to the robot's environment.

PAST PERFORMANCES AND FUTURE WORKS
The SAILS prototypes have been shown during major art events in several countries: Canada (Quebec Museum of Civilization), Belgium (Antwerpen Museum of Fashion), France (Grand Palais, Paris), Russia (Moscow Winzavod Center) and Czech Republic (Industrial Palace, Prague), among others. They also participated in several educational events.

Future developments involve the enhancement of the robustness of the aerobots for theatrical performances and public events; revision of the software to ensure maximal reliability during interactions with actors, so that planned interactions can be faithfully repeated in every performance; implementation of in-board camera/acceloremeter based control in order to give the aerobots a better knowledge of their pseudo-absolute position and microphones to open new human interaction possibilities.

Our principal objectives of design were to create a simple and reliable platform able to move on a rough terrain without finding itself in a position that would make it unusable, while minimizing dimensions, the mass, the number of actuators and the power consumption. The prototype is the result of analytical and numerical studies of kinematics and dynamics carried out on several geometrical models.

With only two motors actuating its six legs, the robot has a simplicity of control which goes hand in hand with the specifications required by the space context of the project. It has mechanical reflexes enabling him to adapt in an intelligent and automatic way to its environment and has a mechanical effectiveness seldom equalized for a walking robot.

The prototype was tested at the Canadian Space Agency on a terrain simulating Martian topography. The experiment performed on the analog site showed the viability of the concept selected: its reversibility, its handiness and its stability enabled it to cross the fields of rocks length into broad and with a remarkable speed of execution. The improvement of the system of transmission, the addition of the mechanism of compliance and the control of the tripod gait will certainly make it a potential candidate for the future robotized planetary missions.

Implementing the planarity constraint mechanically in a framework would be difficult. Instead, it is proposed here to proceed from the outset with a new mechanical construction, which is covered by US patent (No. 7,118,442). First, the faces are built as closed-loop planar linkages using a set of links forming the sides of the polygons. These links are connected by revolute joints at the corners, the axes of the joints being perpendicular to the plane formed by the face. This ensures the planarity of the faces for any configuration. Then, the sides of the faces are connected by revolute joints that lie on the edges of the polyhedron and intersect the joints of the faces at the corner of the faces. Therefore, all the joints associated to a given vertex of the polyhedron intersect at the vertex for any configuration. It is pointed out that the construction of PAFs only require one type of part. Moreover, for PAFs whose edges all have the same length, all the parts are identical.

Mobility
The main interest of the PAFs is their mobility. Some of them are rigid structures while others are articulated mechanisms that deform with nice kinematic properties. Also, some of them are locally mobile but globally rigid. In other words, they can only move in their initial configuration. A kinematic chain with such properties, which is relatively rare, is often called shaky. In order to determine their mobility, i.e. how many degrees of freedom they have, a general method, which involves the first derivative of the constraints equations, is developed. Also, numerical simulations are performed in order to observe the flexed configurations or to find which are shaky PAFs. Finally, plastic models are built. Because of the flexibility of the plastic and the clearance of the joints, the plastic models are more flexible than they should be in theory. As a result, this allows to observe the flexing of the shaky PAFs, which do not significantly move in simulations. It is noted that the range of motion of the plastic models is limited by mechanical interference between adjacent parts.

Theory behind Accelerometer Arrays
In a few words, the work underway at the Laval University Robotics Laboratory is best summarized by the questions it aims at answering:

• What accelerometer arrays allow the estimation of what components of a rigid body moving in space?
• What is the minimum number of accelerometers required to estimate the trajectory of an object in space?
• How should accelerometers be positioned and oriented in order to give the best possible accuracy?
• How should we combine the accelerometer estimates in order to obtain robust estimates of the usual kinematics parameters (e.g.: the acceleration of a reference point, the angular acceleration and the angular velocity)?

In order to answer this last question, an accelerometer array was built by Guillaume Fournier and Philippe Gagnon, two students from the Laval University Department of Mechanical Engineering. Because of its octahedral geometry (an octahedron is a polyhedron with eight faces, just like certain dice that are used in board games), this accelerometer array was baptised Octahedral Constellation of Twelve Accelerometers (OCTA). A pair of orthogonal accelerometers (small black boxes on the photograph) is located at each of the vertices of the regular octahedron. Guillaume and Philippe shook this accelerometer array while recording its measurements and those of a reference magnetic sensor that was attached to it (the small gray box on the picture). This latter sensor provided a reference for the six-degree-of-freedom displacements of OCTA. Guillaume and Philippe applied an algorithm developed at the Laval University Robotics Laboratory to extract the angular velocity of OCTA from its accelerometer measurements. They then compared these estimates to those obtained through a time-differentiation of the magnetic displacement sensor estimates. A sample of the obtained results appears in the graph below, where one sees that the estimates computed from accelerometer measurements are close to those obtained from the magnetic displacement sensor (FOB).

In fact, to our knowledge, these are the most accurate angular-velocity estimates obtained from accelerometers ever observed. These results are promising, since accelerometers are less expensive than other sensors used for the measurement of the angular velocity. Well done Guillaume and Philippe!

The robotic hands developed in the laboratory up to this point, had an underactuation only in the fingers. Each finger was thus actuated by its own motor. In 1998 the company MDA Space Missions (previously SPAR Aerospace) contacted the laboratory in order to request the development of a hand for the well-known Canadarm. One of the specifications requested for this new hand was that it should be actuated by only two motors.

This led to the principle of a hand featuring under actuation among the fingers; the opening and closing of the fingers is controlled by only one motor. In fact, one motor is sufficient since it is not necessary for all three fingers to close independently, because all fingers will close to grasp an object as firmly as possible. If one finger is firmly wrapped around an object, the other fingers will continue to close until all fingers are firmly closed. The underactuation among the fingers is achieved through an innovative gear differential mechanism. A second motor allows the orientation of the fingers to be changed to achieve cylindrical, spherical and planar grasps.

A prototype of the highly underactuated self-adaptive 10-DOF robotic hand with 2 actuators was built in 1999. The new hand, SARAH (Self Adaptive Robotic Auxilary Hand), is slightly smaller and weighs only half as much as its 12-DOF predecessor (MARS Hand). It has the same mobility, but is actuated by only two motors.

The SARAH hand was built in collaboration with the Canadian Space Agency. Its design is covered by a US patent (No. 6,505,870) as well as by a pending WIPO patent. The current version is adapted as an end-effector to the SPDM of the Canadian Space Arm for the International Space Station.

This flexible gripper is adapted from the SARAH hand, which was developed by the Robotics Laboratory and originally designed for use in space. The SARAH hand includes three underactuated and orientable fingers, driven by only two motors. In order to satisfy the requirements of the waste retieval tasks, several components were redesigned. Among others, the new gripper has a significantly larger payload and is adapted to a nuclear environment. Also, the tip of the fingers is designed to grasp cans located in confined spaces, and are yet still capable of handling a variety objects. A plastic prototype of the new gripper (shown above) was built and tested successfully.

The model has 2 legs, of types RRU and RUS, and one passive Hooke joint on which the seat, controls and screen are mounted. The legs allow rotations to be carried out around a cone, while a motor added to the platform allows the platform to pivot in a plane normal to it. Thus a range of motion of ±60 degrees is possible.