FACOLTÀ DI INGEGNERIA
Laurea Magistrale in Ingegneria Robotica e dell’Automazione
Control of a mobile robot for the execution
of Loco-Manipulation Tasks
Studente:
Salvatore Gerratana
Relatori:
Prof. Lucia Pallottino Ing. Danilo Caporale Ing. Alessandro Settimi
1 Introduction 3
2 State of the Art 5
2.1 Loco-Manipulation . . . 5
2.2 Tip-over Problem . . . 9
3 Hardware Setup 15 3.1 iRobot Create® 2 Programmable Robot . . . 15
3.2 OWI robotic arm . . . 15
3.3 RobotGeek Snapper Arm . . . 18
3.4 Usb Camera . . . 19 4 Control Software 21 4.1 Forward Kinematics . . . 21 4.2 Inverse Kinematic . . . 23 4.3 First Arm . . . 25 4.4 Second Arm . . . 25 4.5 Manipulation Primitive . . . 26 4.6 Locomotion Primitive . . . 28 5 Experiments 29 5.1 Grasping experiment . . . 29 5.2 Loco-manipulation experiment . . . 30 Bibliografy 38
The trend of using mobile robots in various scenarios, including unstructured envi-ronment, has increased the requirements on mobile robot performances. In particular, in this work the problem of performing combined manipulation and locomotion tasks is con-sidered. We show an innovative approach to solve locomotion and manipulation tasks. In particular, the aim is to study how manipulation planning can be made independent from locomotion planning. The idea to find an alternative solution to the hierarchical approach, generally used, bases his reasons on the request to have fluid movements. An autonomous mobile robot was developed and controlled for the execution of exem-plary tasks. A ROS based simulation environment has been developed, and experiment results on two hardware platforms are reported.
In recent years, mobile robots have widely spread in different fields of applications, from logistics in industrial plants as [1], to search and rescue missions as [2] and [3]. In these applications the need of performing combined manipulation and locomotion tasks arises in order to have an increase of execution speed or energy efficiency. The research of this field is present in various directions, as the tasks to be solved change according to the environment in which the robots operate, for example in [4], the authors analyze the problem of tip-over stability of the robot in Figure 1.1
Figure 1.1: Mobile robot for mining operation
These types of robot are used in a number of different applications such as mining robotics, bomb disposal, and search and rescue operations.
In this case, the authors exploited the front flippers to prevent tipping over. Based on this idea, a new method has been developed, named Force-Angle Stability Margin, and it is reported in [4].
Also in humanoid robots there is the problem of coordinating upper and lower body motions, as indicated in [5], where the authors focus on the generation whole body motions, coordinating walking and hands trajectories.
Figure 1.2: Image of robot model
One of the first prototypes of humanoid robots was developed by Honda Robotics with the the E series (Figure 1.3), but were mostly of semi-androids, followed by those of the P-series(Figure 1.4), which were more distinctly humanoid.
Figure 1.3: First of the serie E (E0 -1983)
Figure 1.4: First of the serie P (P1-1993)
In the next chapter relevant works existing in the literature are presented, also relative to the tip-over stability issue and possible criteria to prevent this issue in mobile robots.
2.1 Loco-Manipulation
As mentioned in the Introduction, Honda was one of the first industries to build prototypes of humanoid robots. The legged locomotion solution they found relies on the Zero Moment Point (ZMP) criterion, as indicated in [6].
They used ZMP, which is defined as the point on the ground about which the sum of all the moments of active force is equal to zero, to have it in a desired position in such away as to balance the ATGRF (Actual Total Ground Reaction Force) shown in the Figure 2.1:
Figure 2.1: Honda approach
They try to match the two points ZMP and ATGRF to avoid tip-over, but in reality, each mobile robot has variable mass center with the variation of its configuration, hence, there is the problem to estimate the position of the center of mass and define of the control laws that ensure dynamic stability.
the problem for example in [7], a control scheme of stability recovery and stability main-tenance is presented.
For the path planning they used a stability potential field, as shown in Figure 2.2 :
Figure 2.2: ZMP Path Planning
In particular is introduced a quantitative measure “α” for the degree of stability of the robot, and a more restricted area (Valid Stable Region), as in Figure 2.2, to limit the effects of external disturbances and they used a potential function that combines the center and the boundary of the stable region:
ϕ = ϕg(D1) + ϕp(D2) (2.1) where: ϕg = kg D2 1 ϕp= kp (D0+ D1)2 (2.2)
Hence the Planning of moving follow the law:
P (n + 1) = P (n) − δS × grad(ϕ)
In [9] the authors seek to exploit the degrees of freedom of the legs to increase manipulability of the system, while ensuring stability, as shown in Figure 2.3
Figure 2.3: Manipulabilty vs Locomotion
They try to maintain stability and manipulability avoiding singular configurations. The legged mechanism is controlled by means of the following potentian function U, which is then minimized:
U (re, rs, rw, f ) ≡ UZ+ Ua+ Ub (2.4)
That are respectively the functions of stability of the robot(Uz), manipulability of the
arm(Ua) and avoidance of singular-state of the robot(Ub), for example Uz :
Uz(re, rs, rw, f ) = KZ(xz− xd)2 (2.5)
where xz,xd,re, rs, rw,f are, respectively, current and desidered ZMP, tip arm position, shoulder
In [10] is proposed a motion planning method for mobile manipulators that has an imprecise mobile platform, when compared to their attached manipulator. In our work it has been decided to introduce a vision feedback to achieve a better performance in terms of tracking, both for the manipulation and the locomotion control. In [11] they apply a general framework for building complex whole-body control for highly redundant robots, as shown in Figure 2.4
2.2 Tip-over Problem
One of the problems that mobile robots and humanoids have in common when performing complex loco-manipulation tasks is the risk of tipping over or falling. In this section we review some literature on the criteria that exist to prevent such event for such robots. In [8], the authors make a hypothesis:that there are no large inertial accelerations therefore mostly a static analysis and the overturning stability is studied on an inclined plane, and they check if the weght vector g is within the support polygon, shown in Figure 2.5
Figure 2.5: Tip-over on inclined plane
The tip-over stability condition has been stated as follows: the weight vector g from the COG of the vehicle should intersect inside the convex polygon on the plane, whose vertexes are the ground contact points of the mobile robot, and the measure d , illustrated in 2.5 is
d = min w 2 − xproj, l 2 − yproj (2.6)
where: w is the width, instead l is the length of the support polygon.
In [13], instead, after solving the kinematics analysis and dynamics of the system, they determine the forces involved in the system, to avoid tip-over. Exploiting the 3 contact forces, respecting the inequalities Coulomb is obtained, it will be a necessary condition to realize the
movement of the Mobile Humanoid Robot decipted in Figure 2.6 fZ ≥ 0 µfZ ≥ q (f2 x+ fy2) (2.7)
Figure 2.6: Mobile Humanoid Robot
It will be a necessary condition, but not sufficient, to realize the movement of the Mobile Humanoid Robot. Furthermore several support plans have been undertaken to increase the robustness to the tip-over, and try to always stay within the CSP (Conservative Supporting Polygon) area, like illustrate in Figure 2.7
Figure 2.7: Several Planes Support
Another approach, different from ZMP, for Tip-over Stability criterion is presented in [14]. Their studies is suitable for a vehicle which is capable of adjusting its center-of-mass height, or
for a vehicle which carries a variable load, where the tip-over stability is sensitive to height, like illustrated in Figure 2.8
Figure 2.8: Force-Angle Method
where fr is the net force on C.M. This method is called as Force-Angle stability measure,
where α, is given by the minimum of the two angles, weighted by the magnitude of the force vector for heaviness sensitivity:
α = min(θ1, θ2) k fr k (2.8)
When α = 0 tip - over is occured.
The same approach is presented in [15], instead in [16], the robot in Figure 2.9 has been studied
Figure 2.9: Mobile Robot
where is taking account of the tip-over analyzing contact forces. This, because during the tipping the contact forces on one or more wheels are null. Then the system changes the configuration in such a way that the forces are all uniform, by acting only on the configuration of the arm as the C.M. the mobile base is constant. The C.M. of the arm is:
rg = 1 mtot 3 X i=1 mirGi (2.9)
They are only used 3 of the 5 joints of the manipulator, where the jacobian is:
J = ∂rG
∂θ (2.10)
˙rg is a control input, and it is trying to maintain uniform contact forces between them:
F = 1
4(F1+ F2+ F3+ F4) (2.11)
The forces are then used as a weight coefficient to determine the control input to the tip-over avoidance algorithm as follows:
ui = (Fi− F )γ (2.12)
Where ui is the i-th wheel’s contribution to the control input, and γ is a three dimensional
base vector for the control.
Finally, the control input for the manipulator is determined as follows:
u =
4
X
i=1
ui (2.13)
The tip-over avoidance algorithm presented in this section is an example of Lyapunov based stability control.
Instead in [17] the authors introduces a new stability measuring method called Moment-Height Stability (MHS). They present the case of a static plan system (Figure 2.10) in which two external forces act. A rectangular support boundary polygon is considered
Figure 2.10: MHS Method f2d2− f1d1 > 0 Stability occur f2d2− f1d1 = 0 Critical case f2d2− f1d1 < 0 Instability occur (2.14)
The support boundary in Figure 2.11 has been considered with six edges for the general case
Figure 2.11: Poligon Support
The coordinate frame x0, y0, z0 has been attached to the base body. The point that the
manipulator arm is attached to the base is named F , which is considered as the origin of the body coordinate frame. After finding all the wrench acting on the system and reported in the reference system, it is possible to derive the moments go on the vertices of the polygon M1, M2,
. . . , M6.
p1, p2, . . . , p6 represents the coordinate of contact point on the ground, and the unit vectors
ˆ ai =
pi+1− pi
k pi+1− pi k (2.15)
The measure MHS α is calculated as:
α = hβmin(Iiγi· (Mi· ˆai)) (2.16)
3.1 iRobot Create® 2 Programmable Robot
For the Locomotion Task is taken the robotic solution of Figure 3.1Figure 3.1: Roomba
Roomba is a series of autonomous robotic vacuum cleaners. The disk-shaped robot, approxi-mately 30 cm in diameter and 8 cm tall, and it is able to turn in place.
3.2 OWI robotic arm
Figure 3.2: First Arm
This robot has 5 DOF with the technical details in Table 3.1
Table 3.1: Detail technical for First Arm Information
Weight 658 g Lifting Capacity 100 g Maximum Vertical Reach 30 cm Maximum Horizontal Reach 30 cm Wrist Motion Range 120° Elbow Motion Range 270° Base Motion (Shoulder) 180° Base Rotation Range 270°
This robotic arm is not being provided with sensors, so it has become necessary to introduce potentiometers connected with suitable supports to the outgoing shafts of the actuators, the choice is that of Figure 3.3
Figure 3.3: Potentiometers
It consist of a variable resistor, by the application of a moment on the external support, in the range [0°-180°] corresponding, respectively, at the [350-670] values obtained from the reading of Analog.
Table 3.2: detail technics for Potentiometer Information
Maximum Resistance 10 KΩ ± 30% Length 11 mm Rotational Life 1 M cycles
Weight 0.36 g Shaft Diameter 4 mm
For the first tests were mounted on various shafts of the engines just assuming linear range but the need to have available range wider angles, has required a more precise mapping, as shown in Figure 3.4
Figure 3.4: Fitting Curves
Through the Polyfit function of matlab, it was possible to make various interpolations of the curves, using the second order polimonial approsimation, and are taken the measures from analog read every 10°.
The micro-controller used for the reading from sensors and for controlling the arm has a inte-grated AT-Mega328 Processor with a Printed Circuit Board (Figure 3.5) adapted for interface with the Arduino’s motor shields
Figure 3.5: Micro-Controller
The robotic arm has not the appropriate preformance to perform the required tasks, so it was decided to adopt an alternative solution.
3.3 RobotGeek Snapper Arm
In order to have more performance, hence, an alternative solution to the robotic arm was taken (Figure 3.6)
Table 3.3: Details technical for definitive Arm Snapper Arm
DOF 5
Reach 28.5 cm
Controller Geekduino / Arduino Gripper Max Open 37 mm
Weight (With base and control panel) 1 kg / 2.2 lbs Weight (Without base and control panel) .75 kg / 1.65
Compared to the previous robotic arm, this last turns out to have a more rigid structure, it is also equipped with servo motors with integrated position control, allowing to reach higher positions with more precision, eliminating the measurement error of the potentiometers. It is also customizable to the modular units of the gripper present, which enable different grasping, in the Table 3.3 are shown the technical details of the robotic arm
3.4 Usb Camera
In the development of a manipulation control primitive, a usb camera has been used to implement a visual feedback control law. The goal is to have the capability of identifying an object to be grasped and provide feedback on the object pose to the arm control law. More details are given in Table 3.4
The camera used is a Trust Trino HD and the technical details are reported in Table 3.4.
Table 3.4: Details technics Information
Height 81 mm
Width 11 mm
Resolution 1280 x 720 Interface host USB 2.0 Maximum Frame Rate 30 fps
4.1 Forward Kinematics
To solve the forward kinematics has been choosen the Denavit-Hartenberg Convention, the fixed reference frame for the arm is shown in Figure 4.1
Figure 4.1: Fixed Frame for Arm
The corresponding DH’s Table is show in table 4.1
Table 4.1: DH’s Table Link d (m) θ a (m) α(°) 1 0 θ1 0 90° 2 0 θ2 0.09 0° 3 0 θ3 0.11 0° 4 0 θ4 0.11 0°
The position of the end effector is obtained using the following homogeneous transformation matrix Cθi −SθiCαi SθiSαi aiCθi Sθi CθiCαi −CθiSαi αiSθi 0 Sαi Cαi di 0 0 0 1
In Figure 4.2 an example of forward kinematics is shown for the set of angles q = [0, 160, −85, −40]
4.2 Inverse Kinematic
Inverse kinematics was solved in closed form, using the geometrical approach to find θ1 ,
and using algebrical approach to find θ2, θ3, θ4.
To find the first angle of robot is adopted the approach shown in Figure 4.3
Figure 4.3: Geometrical Approach
Hence θ1=atan(y,x), instead to find the others angles was used algebrical approach, because the
problem is reduced to a planar manipulator
∅ = θ1+ θ2+ θ3 pwx = px− a3c∅ = a1c1+ a2c12 pwy = py− a3s∅ = a1s1+ a2c12 (4.1)
Recasting the above equations is possible to obtain the remaining angles:
p2wr+ p2wz = a12+ a22+ 2a1a2c2 → c2 = p2 wx+p2wz−a21−a22 2a1a2 s2= ± √ 1 − c2
Hence the Inverse Kinematic is resolved, and setting the position of the end-effector found in Forward Kinematic, the solution found from Inverse Kinematic is shown in Figure 4.4
4.3 First Arm
For first arm has been developed a PI controller, based on the the measures from poten-tiometers. The block scheme is illustrated in Figure 4.5
Figure 4.5: Block scheme of the control loop of a single joint
4.4 Second Arm
The second arm has the servomotors with position controls integrated. A low-pass filter on the reference angular positions has been implemented to obtain smoother movement of the arm. The block scheme of the filter is illustrated in Figure 4.6
4.5 Manipulation Primitive
As mentioned before, a vision system has been integrated to improve location accuracy with respect to specific locations identified with markers and to objects to be grasped. To this purpose, the AprilTag library [18] has been used, which allows to recognize an object and provide a location in the fixed camera frame. AprilTags are an implementation of Augmented Reality Tags from Edwin Olson APRIL Laboratory, and they are capable of recognizing tags such those in Figure 4.7.
Figure 4.7: Tags
The ROS Software is used for control the arm, and for the Calibration of the Camera
Figure 4.8: Calibration
Camera calibration is used to estimate the scene’s structure in Euclidean space and remove lens distortion, a camera calibration has been performed with a grid, as shown in Figure 4.9 In Figure 4.9 a test of the vision system in the Rviz simulation environment[19] with the controlled arm has been performed.
Figure 4.9: A URDF model of the mobile manipulator has been developed and a snapshot of the manipulator tracking the tag pose is shown here.
Figure 4.10: Topics and Nodes
Uvc and apriltag are the nodes for image processing, tf’s node send the position of object detected, receive’s node calculate the Inverse Kinematic, and finally, the arm’s node send to serial the required angles to achieve desidered position. To achieve the grasping’s task has been adopted the filosofy of state machine shown in Figure 4.11
4.6 Locomotion Primitive
The iRobot platform is controlled in order to achieve a desired position. At the low level, a nonlinear tracking controller was used to steer the wheels towards a given position, based on [20]. At a higher level, a PI visual feedback loop has been implemented to adjust the reference position and correct drifts due to odometry, see Figure 4.12
Figure 4.12: PI Roomba
In Figure 4.13 the reference frames used for the robot control are illustrated. These are the locomotion frame (mettici una lettera sulla figura, tipo L), the base of the arm frame A, the camera frame C. Finally the gripper frame G (aggiungi un frame sul gripper). These are essential to calculate kinematic quantities during the cartesian control of the robotic arm.
5.1 Grasping experiment
The first experiment consists in the grasping a object while the mobile robot is not moving on the x-y plane. In the frame of Figure 5.1 the tag is reachable ,hence the position of end-effector approaches to the object.
Figure 5.1: Object to Grasp and Environment Setup
Below the frames showing the grasp’s execution
(a) position is not reachable (b) near to grasping position
(c) gripper open (d) gripper closed (e) lifting the oject
Figure 5.2: Frames
In details, these Frames correspond to the Machine State
the tag is not reachable
- in the frame of Figure 5.3b the tag is reachable, hence the position of end-effector approaching to the object.
- in the frame of Figure 5.3c the arm is on the object with gripper opened. - in the frame of Figure 5.3d the arm approach the object with gripper closed. - in the frame of figure 5.3e the arm lifts the object
5.2 Loco-manipulation experiment
The second experiment consists in the grasping an object while the robot is moving, hence this is a loco-manipulation task.
For this experiment was choisen the object shown in Figure 5.3
Figure 5.3: Object to Grasp and Environment Setup
It was prepared an environment, where to perform the tasks of loco-manipulation, in detail for this experiment the primitive of locomotion has been implemented in such a way as to comply with the tracking of the tag and perform a default trajectory.
The frames in Figure 5.4, show the execution of a Loco-Manipulation task
(a) only Locomotion Primitive (b) Locomotion with Manipula-tion Primitives
(c) Locomotion with Manipulation Prim-itives
(d) Locomotion with Manipulation Primitives
Figure 5.4: Loco-Manipulation Tasks
In details, the frame of Figure 5.4 represent
-the frame of Figure 5.4a shows the Roomba when approaching to the object, hence only Locomotion Primitive.
- the frame of Figure 5.4b shows the Roomba when approaching to object and the arm moving to grasping configuration
- the frame of Figure 5.4c shows the Roomba moving with the arm near to the grasping po-sition - in the frame of Figure 5.4d shows the Roomba moving, hence only locomotion primitive. Then this the approach used is different from the serial approach, infact as shown in Figure 5.4b this approach renders the manipulation primitive dependent from locomotion primitive.
Developments
In this work a control system for the execution of loco-manipulation tasks with mobile robots has been developed. A vision feedback has been used to reduce the drifts in the odometry of the mobile robot base, and to improve the accuracy of the robotic arm end-effector control. The problem of tipping over has been investigated and several solutions have been found in the literature. In Table 5.1 the investigated criteria are reported. Among these, some have been developed for mobile platforms and some for humanoid robots. The goal of future research in this direction is in developing innovative methods to prevent the tip-over of both mobile and humanoid robots while performing loco-manipulation tasks.
Table 5.1: Several Methods to solve tip-over problem
Method Papers
- Current and Future Perspective Zero Moment Point (ZMP) of Honda Humanoid Robot;
and his other applications - Stability Control for a Mobile Manipulator using a Potential Method; - Mobile Manipulation of Humanoid Robot - Experimental validation of tip over stability
of a tracked mobile manipulator; Force - Angle (FA) Margyn Stability - A New Measure of Tipover Stability
Margin for Mobile Manipulators; - Measure and Control of Stability for Mobile Robots - Stability Evaluation of Mobile Moment - Height Stability (MHS) Measure Robotic Systems using
Moment - Height Measure
- Center of Gravity Estimation and Control for a Field - Mobile Robot with a Heavy Manipulator; Using Contact Force and others method - Analysis of Dynamic Stability Constraints
using support polygon for a Mobile Humanoid Robot; - Tip-over Avoidance Algorithm for
Modular Mobile Manipulator
Finally this suggests to increase the performance of the vision system, in a manner, such to have a higher frame rate, such as to enable more velocity in locomotion and grasping tasks.
Foremost, I would like to express my sincere gratitude to my advisor Prof. Lucia Pallottino for the continuous support and encouragement of my Master’s Thesis.
I would also like to show my gratitude to the Eng. Danilo Caporale and Eng. Alessandro Settimi for their valuable inputs and able guidance.
1.1 Mobile robot for mining operation . . . 3
1.2 Image of robot model . . . 4
1.3 First of the serie E (E0 - 1983) . . . 4
1.4 First of the serie P (P1- 1993) . . . 4
2.1 Honda approach . . . 5
2.2 ZMP Path Planning . . . 6
2.3 Manipulabilty vs Locomotion . . . 7
2.4 Hierarchical Approach . . . 8
2.5 Tip-over on inclined plane . . . 9
2.6 Mobile Humanoid Robot . . . 10
2.7 Several Planes Support . . . 10
2.8 Force-Angle Method . . . 11 2.9 Mobile Robot . . . 11 2.10 MHS Method . . . 13 2.11 Poligon Support . . . 13 3.1 Roomba . . . 15 3.2 First Arm . . . 16 3.3 Potentiometers . . . 16 3.4 Fitting Curves . . . 17 3.5 Micro-Controller . . . 18 3.6 Definitive Arm . . . 18 3.7 Camera . . . 19
4.1 Fixed Frame for Arm . . . 21
4.2 Forward Kinematic . . . 22
4.3 Geometrical Approach . . . 23
4.4 Inverse Kinematic . . . 24
4.5 Block scheme of the control loop of a single joint . . . 25
4.6 Low Pass Filter . . . 25
4.8 Calibration . . . 26
4.9 A URDF model of the mobile manipulator has been developed and a snapshot of the manipulator tracking the tag pose is shown here. . . 27
4.10 Topics and Nodes . . . 27
4.11 State Machine . . . 27
4.12 PI Roomba . . . 28
4.13 Reference Systems . . . 28
5.1 Object to Grasp and Environment Setup . . . 29
5.2 Frames . . . 29
5.3 Object to Grasp and Environment Setup . . . 30
3.1 Detail technical for First Arm . . . 16
3.2 detail technics for Potentiometer . . . 17
3.3 Details technical for definitive Arm . . . 19
3.4 Details technics . . . 20
4.1 DH’s Table . . . 21
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