Assistive Robotics

Robotics structure and actuation systems

Lesson 2: robotics structure and actuation systems

Robot as a human system

Since we are going to be biomedical engineers, we can do a comparison between a robot and a human being. If we consider the brain, we can immediately map the supervision unit in which the intelligent algorithms and control system of the robot are placed. Obviously, the place, where decisions are taken, needs to be in connection with other different parts, in particular our brain will have contact with all nerve termination and our senses (vision, hearing, touching). They can be compared to all the sensor unit of the robot (cameras to simulate human vision, proximity sensor, or force sensor to simulate touch and so on), which are essential for the automatic machine to understand what happens and its internal behaviour, and can be divided in internal and external senses.

Then, the robot needs to have a mechanical structure (human’s body) to allow the robot to perform any kind of tasks, approach\moving somethings. All sensors, actuators, intelligent algorithms and control systems need to be in connection thanks to a bus and communication protocol. The sensor, which is a physical device, acquires the various signals (or electric impulses) that need to be passed to a processing unit (or everything there is inside). The way in which the quantity is passed from the sensor to the controller is performed through the bus and governed by a communication protocol, which is the language talked by different parts of the robot. If we see a robot as a system, it has all the units previously described. The robot has some tasks, a set of commands to do in a working environment: it performed the primary task (what I want the robot to do), but can be other task (which is the most intelligent part). Example: Roomba - first task is cleaning house, the others is mapping the house, avoid obstacle etc.

The control architecture is composed by a control system, which provides the correct impulse to the actuators that performs a mechanic action, typically allowing the motion of the robots. The electrical motion allows different parts of the robot to move but needs to be verify if the motion happens properly (feedback control). Unit sensor sends back to the control system to find the new values for the actuators. This loop works until the robot have something to do. The mechanical structure involves locomotion apparatus (wheels, tracks, legs) and manipulation apparatus (mechanical arm, end-effector, artificial hand). The actuation system provides the capability to exert an action (locomotion or manipulation), while the sensory system acquire data on the status of the robot (e.g., position, joint angles, etc.), thanks to proprioceptive sensors, or thanks to exteroceptive sensors acquire data on the external status of environment. At the end the control system it commands the execution of the action with respect to the goals. 1 Robotics structure and actuation systems.

Example of human robot where the locomotion is based on wheeled humanoid robot. In this example we can find different kind of interfaces, LEDs to simulate human like expression, tablet where we can put the requests and we have a feedback from the robot itself, the human interaction is a human like way of hand motion. Another example is the NAO: quite common robot used for education purpose. Nao has a lot of different actuators (right picture), typical connect to a motor because they are the part that can move. Furthermore, in the left part we can see all the sensors and we can observe that the number is very high. So, we can start to think that when a robot needs to interact in a human environment the robot needs to be equipped with many sensors, not only for security reason, but also to be more acceptable, to simulate something closer to the human act (speaking, communication).

Structure of a dynamic system

A robot is a dynamic system, whose structure can be separated into two components: kinematic skeleton: is based on the kinematics of the robot that includes all properties of the movement that depend upon the geometry of its mechanical structure (kinematic chain). Kinetics: is a law of dynamics that permits to study the conversion of the forces provided by the actuators into robot motion. If we want to make a comparison with our body we can assume that the kinetics is related to muscles, while kinematics to our skeleton.

Kinematic chain

Kinematics allows to represent positions, velocities and accelerations of specified points in a multi-body structure, independently from the causes (i.e., forces and torques) that may have generated the motion. To describe the kinematics of manipulators or mobile robots, it is necessary to define the concept of kinematic chains. A kinematic chain is a series of ideal links (rigid static body), connected by ideal joints (rigid mobile components). The ideal condition is reached when we do not consider mass, friction, elasticity, etc. are considered so we don’t consider the physical part of the problem.

Links/arms are idealized geometrical bars connecting two or more joints. Joints are idealized physical components allowing a relative motion between the attached links. Joints allow a single "degree of motion" (DOM) between the connected links. Joints may be of two types (in the present context): Revolute (or rotational) joints; they allow a rotation between the connected links; Prismatic (or translation) joints; they allow a translation between the connected links. Revolute joints are usually preferred for their compactness and reliability. Other types are possible, but will not be considered. 2 Robotics structure and actuation systems.

In the left side we can see the revolute joint, the red and blue components are two consecutive links, so the joint is the rigid component between these two links and allows a relative rotation along that axis between the red and blue part. On the right side we can find a prismatic joint: the joint allows a translation along one axis (in this case along ‘axis’). Revolute joints are the most common in the world, since they are more compact and reliable.

Kinematic chain is a series of links and joints. In this picture we can observe two different red part (links), two revolute joints and the blue one is a single link connecting the two joint and the other two links. So, we have three links and two joints composing a kinematic chain. Motor actuators will allow the rotation of joints allowing the motion of robot itself. Typically, all the joints are actuated, but when it doesn’t happen, they are called passive joint.

There are two chain types:

• Open chains (Serial Robots): there is only one link between two joints. The KC has tree-like structure;
• Closed chains (Parallel Robots): there are more than one link between two joints. The KC has the cycle-like structure. The parallel robots are the most common in industry: example - 3D printers sometimes have a parallel robot.

Degrees of motion (DoM) and degrees of freedom (DoF)

• The Degrees of Motion (DoM) is the number of independent motions that can be performed by a system.
• The Degrees of Freedom (DoF) of a mechanical system is the number of independent parameters that define its position in the Cartesian space.

Suppose a cone with one single point of contact with the plane. The system could perform only the rotation around the axis between the two links, so the degree of motion is equal to 1. Then, if we want to define orientation and position in the planar case, we must consider the position x and y in the point of contact and eventually the angle with respect to one of the axes formed by the cone. So, we have three DoF, because we need three independent parameters for defining position and orientation of the cone in the planar case.

In robotics, DoM and DoF are synonymous because for the robot is the same concept.

Degrees of motion calculation – the degree of motion d of a mechanical system composed by l links (base included) and n joints can be defined in accordance with the Kutzabach formula (for the Cartesian space). 3 Robotics structure and actuation systems.

In the 3D space instead, six independent parameters are required to describe the orientation and the position of one point: x,y,z position of the point and three angles that define the orientation. In the planar case (2D) we used the second formula called Grubler equation (m=3).

Joints are the circles and the links are the segment connecting the joint including the base and the last element is the end effector. In the case of the Open chain we will have 5 links and four joints, computing the formula we will find 4 degrees of motion. In the closed case both the number of joint and the number of links will be 6. The resultant degrees of motion are 3. In an open kinematic chain, each joint provides the structure a single DoM so the degrees of motion are equal to the number of joints. For this reason in robotic DoM and DoF are synonyms.

Kinematic redundancy

Going back to the open chain example, the number of DoM is equal to four while the DoF is three because we are in the planar case. Since n (DOM) > m (DOF), the robot is redundant. If the robot is in the 3D space, the DoF is six and DoM is four, so it is not redundant in this case. The robot with four DoM will be redundant for some task while not redundant for others. If we want as a task for the robot the motion of the end-effector in a particular point in the xyz space, we need to fix the position for this particular point (x,y and z position). The number of the parameters required is three and don’t mind the orientation. In this case, the robot will be redundant considering the task that has to perform.

Redundancy is a relative concept and depends on the specific task and what the robot has to do. So, the robot is redundant in planar case but is not in the 3D space. But if the task is to move the end effector only in a particular point, the robot is considered redundant for this specific task. A redundant robot can have different task. Let’s think about our body, only on the arm we have 7 DoM (3 wrist, 1 elbow, 3 shoulder) so human body is one of the most redundant robots in the world.

The kinematic redundancy allows to change the configuration of the manipulator in order to: avoid obstacles close to the robot; avoid joint position and velocity limits; improve the robot motion performance and make the robot like a fault tolerant system. For example, if we have 8 DoM and one of the joints fail (I.e. broken motor) we still have seven joints, so we can change our control system and perform the same operation without a joint (avoid losing the robot control).

The robots are classified by the kinematic type. The kinematic chain is a series of joints and links, where series means one after the other. Considering the series joints, starting from the base and going on, of the we can name the robot according to the presence of a Prismatic (P) or rotational (R) joint (remember that one joint means one degree of freedom). Each robot is characterized by workspace of its arm is the set of all positions that it can reach. This depends on a number of factors including the dimensions of the arm. 4 Robotics structure and actuation systems.

Cartesian = 3P = P-P-P

The shoulder is composed by three prismatic joints, with mutually orthogonal axes. Each DOM corresponds to a cartesian task variable. The task space is a sort of parallelepiped They provide an accurate positioning in the whole task space, but have a limited dexterity. The most common structures are lateral columns or suspended bridges. It can reach all the points inside the parallelepiped.

Cylindrical = 1R-2P = R-P-P

The shoulder has one revolute joint with vertical axis followed by two prismatic joints (one vertical the other horizontal). Each DOM corresponds to one cylindrical coordinate. The workspace is a cylindrical sector, can reach all the points in the cylinder expect the central axis for mechanical reason. The horizontal prismatic joint allows to reach horizontal spaces, but the accuracy decreases toward the arm ends. They are used mainly to move large objects.

Polar or spherical = 2R-1P = R-R-P

The shoulder has two revolute joints (one vertical, one horizontal axis) followed by a prismatic joints (with axis orthogonal to the last one). Each DOM corresponds to one polar coordinate. The task space is a spherical sector that may include part of the floor, to allow the manipulation of objects there. The structure is less rigid than the previous ones, and the accuracy decreases with the elongation of the prismatic arm. The RRP can reach all the spherical point.

SCARA = 2R-1P = R-R-P

The shoulder has two revolute joints followed by one prismatic joints (all with parallel/vertical axes). The correspondence between DOM and cartesian coordinates is true only for the vertical component. The effect of gravity is compensated by the structure itself. The structure is rigid in the vertical component and compliant in the horizontal components. This robot is mainly used for small components manipulation and vertical soldering or assembly tasks (e.g., in electronic boards assembly)

Articulated or anthropomorphic = 3R = R-R-R

The shoulder has three revolute joints: the first one is vertical, the other two are horizontal and parallel. The structure is similar to the human body, with trunk, arm and forearm, with a final wrist. No correspondence between joint and cartesian coordinates. Task space is a sort of sphere sector. It is one of the most common structures in industry, since it provides the best dexterity. Its accuracy is not constant inside the task space. 5 Robotics structure and actuation systems.

Robot performance

Robots are not only classified according to the joint but are kinematically classified also according to the following performance:

• Workspace: is composed by all points that can be reached by any position and orientation of the end-effector.
• Accuracy: is the ability of a robot to position its end-effector at a preprogrammed location in the workspace. Accuracy is a function of the precision of the arm kinematic model (which is only simplified rigid-body kinematic configuration) the precision of the world, tool, and fixture models. Thus, manipulator accuracy becomes a matter of matching the robot geometry to the robot solution in use by precisely measuring and calibrating link lengths, joint angles, and mounting positions.
• Repeatability: represents the ability of the manipulator to return repeatedly to the same location. It depends on the method of teaching or programming the manipulator. Most manufacturers intend this figure to indicate the radius of a sphere enclosing the set of locations to which the arm returns when sent from the same origin by the same program with the same load and setup conditions. Repeatability is important when performing repetitive tasks such as blind assembly or machine loading. Depends on the precision of the robot with respect to the model.
• Resolution: represents the smallest incremental motion that can be produced by the manipulator.

In an ideal situation workspace, accuracy and repeatability has be as greater as possible, while the resolution should be very small for very precise movement, in reality it is not possible, we have to find a tradeoff between time, costs and performances.

Robot design

Robots are now often designed for specific applications and to perform limited sets of tasks. Robot design focuses on the number of joints, physical size, payload capacity, and the movement requirements of the end-effector. Payload capacity example: Amazon drone cannot delivery all kind of objects because of payload capacity that can delivery only that weighing less than 5 kg. If we have a reliable control system, we will be able to achieve with the same situation higher accuracy.

The configuration of the movable skeleton and the overall size of the robot are determined by task requirements for reach, workspace, and reorientation ability. These features affect the precision of end-effector path control needed for applications. They also define the absolute positioning capability necessary for small part assembly, the repeatability needed for material and package handling, and the fine resolution that allows precise, real-time sensor-based motions. A critical concept in robotic system design is the range of tasks the robot is expected to perform. The robot should be designed to have the flexibility it needs to perform the range of tasks for which it is intended. This determines the topology of the robot mechanism and the actuator system. The choices of geometry, material, sensors, and cable routing follow from these basic decisions.

Actuators

The electric, hydraulic and pneumatic motors and other elements that cause the links of the mechanism to move are called actuators. Actuators can be built in many different ways, most prominently: electrical motors, pneumatics and valves. In this course we will only deal with electrical motors due to the fact that are widespread and more used also thanks to the greater availability of electricity with respect to fuels. A servomotor is a rotary actuator or linear actuator that allows for precise control of angular or linear position, velocity and acceleration. We can find:

• Pneumatic: characterized by pneumatic energy (compressor), pistons or chambers mechanical energy is difficult to control accurately (change of fluid-compressibility) no trajectory control. It is commonly used for opening/closing grippers (some part of the robot such as hands) or as artificial muscles (McKibben actuators) 6 Robotics structure and actuation systems.
• Hydraulic: provide hydraulic energy (accumulation tank) and is regulated by pumps/valves mechanical energy. Advantages: no static overheating, self-lubricated, inherently safe (no sparks), excellent power-to-weight ratio, large torques at low velocity (w/o reduction); disadvantages: needs hydraulic supply, large size, linear motion only, low power conversion efficiency, high cost, increased maintenance (oil leaking).
• Electrical: are widely used in robotics, and are the only one that we are going to study. Advantages: power supply available everywhere, low cost, large variety of products, high power conversion efficiency, easy maintenance, no pollution in working environment; disadvantages: overheating in static conditions (in the