This document summarizes a study analyzing and simulating a rocker-bogie exploration rover. Key points:
- Models of the mechanics and kinematics of the rocker-bogie rover configuration are presented to aid in design and control.
- An efficient method is outlined for solving the rover's inverse kinematics and performing quasi-static force analysis, accounting for factors like the manipulator, actuator limits, and wheel slip.
- A physical model is developed of the Lightweight Survivable Rover (LSR-1) rocker-bogie rover prototype. Experimental results confirm the validity of the models.
this ppt contains the robots which are used in space for investigating nearby planets from earth itself, the mechanism used for these rover is rocker bogie mechanism, which has the advantage to overcome the giant rocks.
Rocker bogie mechanism (mars rover) final year mini project final review paper BIRENDRA KUMAR PANDIT
The Rocker-Bogie Mobility system was designed to be used at slow speeds. It is capable of
overcoming obstacles that are on the order of the size of a wheel. However, when surmounting a
sizable obstacle, the vehicles motion effectively stops while the front wheel climbs the obstacle.
When operating at low speed (greater than 10cm/second), dynamic shocks are minimized when
this happens. For many future planetary missions, rovers will have to operate at human level
speeds (~1m/second). Shocks resulting from the impact of the front wheel against an obstacle
could damage the payload or the vehicle. This paper describes a method of driving a rockerbogie vehicle so that it can effectively step over most obstacles rather than impacting and
climbing over them. Most of the benefits of this method can be achieved without any
mechanical modification to existing designs – only a change in control strategy. Some
mechanical changes are suggested to gather the maximum benefit and to greatly increase the
effective operating speed of future rovers.
This is Part 2 of a 10 Part Series in Automotive Dynamics and Design, with an emphasis on Mass Properties. This series was intended to constitute the basis of a semester long course on the subject.
this ppt contains the robots which are used in space for investigating nearby planets from earth itself, the mechanism used for these rover is rocker bogie mechanism, which has the advantage to overcome the giant rocks.
Rocker bogie mechanism (mars rover) final year mini project final review paper BIRENDRA KUMAR PANDIT
The Rocker-Bogie Mobility system was designed to be used at slow speeds. It is capable of
overcoming obstacles that are on the order of the size of a wheel. However, when surmounting a
sizable obstacle, the vehicles motion effectively stops while the front wheel climbs the obstacle.
When operating at low speed (greater than 10cm/second), dynamic shocks are minimized when
this happens. For many future planetary missions, rovers will have to operate at human level
speeds (~1m/second). Shocks resulting from the impact of the front wheel against an obstacle
could damage the payload or the vehicle. This paper describes a method of driving a rockerbogie vehicle so that it can effectively step over most obstacles rather than impacting and
climbing over them. Most of the benefits of this method can be achieved without any
mechanical modification to existing designs – only a change in control strategy. Some
mechanical changes are suggested to gather the maximum benefit and to greatly increase the
effective operating speed of future rovers.
This is Part 2 of a 10 Part Series in Automotive Dynamics and Design, with an emphasis on Mass Properties. This series was intended to constitute the basis of a semester long course on the subject.
— This slide introduces a mars exploration robot based system that useful to explore the planet mars. Mars Rover Mongol Pothik is a semi-autonomous robot that is developed based on sensors and interactive applications. The robot is capable of completing human assistant tasks, Astronaut assistance task, collecting resource from planet mars, giving a feedback of soils condition such as temperature, moisture, pH. This robotics system includes a web based mother station from where the rover is controlled and given instructions to complete tasks. The mars rover will be used in planetary exploration research to explore life on mars. This rover has rocker-bogie suspension system, robotics arm, Drilling mechanism, live feed camera, aluminum wheels suitable to explore planet mars. This research is mainly focused on robotic system and computational efficiency. The system is consist of a GPS system for mapping purpose and smooth controlling features. In his paper we will discuss about different functionalities of mars rover. The end result will show the efficiency, impact and performance analysis of the system.
The Rocker-Bogie Mobility system was designed to be used at slow speeds. It is capable of
overcoming obstacles that are on the order of the size of a wheel. However, when surmounting a
sizable obstacle, the motion of the vehicle effectively stops while the front wheel climbs the obstacle.
When operating at low speed (greater than 10cm/second), dynamic shocks are minimized when
this happens. For many future planetary missions, rovers will have to operate at human level
speeds (~1m/second). Shocks resulting from the impact of the front wheel against an obstacle
could damage the payload or the vehicle. This paper describes a method of driving a rocker-bogie vehicle so that it can effectively step over most obstacles rather than impacting and
climbing over them. Most of the benefits of this method can be achieved without any
mechanical modification to existing designs – only a change in the control strategy. Some
mechanical changes are suggested to gather the maximum benefit and to greatly increase the
effective operating speed of future rovers.
A Design Of Omni-Directional Mobile Robot Based On Mecanum WheelsIJRESJOURNAL
ABSTRACT:As one of the important branch of mobile robotics, wheel mobile robot has long been paid atten tion to by the research people at home and abroad for its high load ability, positioning accuracy, high efficiency, simple control, etc. Mobile robot has close relation to many technologies suc-h as control theory, computer tech nology, sensor technology, etc. Therefore, research on the mobile robot has important significance
This is Part 4 of a 10 Part Series in Automotive Dynamics and Design, with an emphasis on Mass Properties. This series was intended to constitute the basis of a semester long course on the subject.
HELLO FRINDS THIS REPORT IS OF INDUSTRIAL TRAINING ON DIESEL LOCOMOTIVE TECHNOLOGY.
IT IS VERY HELP FULL FOR YOU .
SO GO THROUGH IT .
**********************Best Of Luck ************************
INTRODUCTION OF INDIAN RAILWAY
DIESEL LOCOMOTIVE WORKSHOP .CHARBAGH
DIESEL ELECTRIC LOCOMOTIVE
WORKING MECHANISIM
IMPORTANT COMPONENTS OF LOCOMOTIVES
a) POWER PACK
b) FUEL SECTION
c) LUBE OIL CONTROL SECTION
i. FUEL INJECTION PUMP (FIP)
ii. INJECTORS
d) TURBO SUPER CHARGING (TSC)
e) BRAKES
f) COMPRESSOR / EXPRESSOR
g) GOVERNORS
h) TRACTION MOTER
i) BOGIE
j) GENERATOR
k) RADIATOR
l) ENGINE SECTION
m) CROSS HEAD
i. INLET AND EXHAUST VALVE
FAILURE ANALYSIS
a) MAGNAFLUX LAB
b) ULTRASONIC TEST
c) ZYGLO TEST
d) RDP TEST
This is a simple project for Induction Loop Vehicle Detector and Counter. It is very useful in counting car's and change its destination in tollbooth or parking area
Design and Fabrication of Wheel Chair using Rocker Bogie Mechanismijtsrd
Rocker bogie finds a vital role in determining the scientific analysis of objectives separated by many distance apart. The mobility design at present is quite a bit complex with many legs or wheels. The wheeled rover which is capable of driving over the rough terrain provided with high degree of mobility suspension system. The drive provided by the rocker bogie is simple and it mainly operated by the means of two motors. The motors are kept inside in order to make it more reliable and efficient. In overcoming the bumps in the natural terrain the wheels are operated simultaneously. By implementing this mechanism the vehicle can come through any obstacles it faces during the travel in the terrain. Arjun CP | Jithin Peter TK | C. Mohamed Meersa | Habeeb Rahman PP "Design and Fabrication of Wheel Chair using Rocker Bogie Mechanism" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-5 | Issue-4 , June 2021, URL: https://www.ijtsrd.compapers/ijtsrd42537.pdf Paper URL: https://www.ijtsrd.comengineering/mechanical-engineering/42537/design-and-fabrication-of-wheel-chair-using-rocker-bogie-mechanism/arjun-cp
it is presentation for future of robotics in 4 industrial revolutions. It has the content all about the mechatronics engineering. Again, I did a collection for all the resources together. here I use this info in a presentation for a seminar. here I share this to all the people who need this for technological resources. For the students of computer science, it is a collection for their research topic at a time.
A line follower robot, as the name suggests, is an automated guided vehicle, which follow a visual line embedded on the floor or ceiling.
Usually, the visual line is the path in which the line follower robot goes and it will be a black line on a white surface but the other way (white line on a black surface) is also possible.
Certain advanced line follower robots use the invisible magnetic fields as their paths.
— This slide introduces a mars exploration robot based system that useful to explore the planet mars. Mars Rover Mongol Pothik is a semi-autonomous robot that is developed based on sensors and interactive applications. The robot is capable of completing human assistant tasks, Astronaut assistance task, collecting resource from planet mars, giving a feedback of soils condition such as temperature, moisture, pH. This robotics system includes a web based mother station from where the rover is controlled and given instructions to complete tasks. The mars rover will be used in planetary exploration research to explore life on mars. This rover has rocker-bogie suspension system, robotics arm, Drilling mechanism, live feed camera, aluminum wheels suitable to explore planet mars. This research is mainly focused on robotic system and computational efficiency. The system is consist of a GPS system for mapping purpose and smooth controlling features. In his paper we will discuss about different functionalities of mars rover. The end result will show the efficiency, impact and performance analysis of the system.
The Rocker-Bogie Mobility system was designed to be used at slow speeds. It is capable of
overcoming obstacles that are on the order of the size of a wheel. However, when surmounting a
sizable obstacle, the motion of the vehicle effectively stops while the front wheel climbs the obstacle.
When operating at low speed (greater than 10cm/second), dynamic shocks are minimized when
this happens. For many future planetary missions, rovers will have to operate at human level
speeds (~1m/second). Shocks resulting from the impact of the front wheel against an obstacle
could damage the payload or the vehicle. This paper describes a method of driving a rocker-bogie vehicle so that it can effectively step over most obstacles rather than impacting and
climbing over them. Most of the benefits of this method can be achieved without any
mechanical modification to existing designs – only a change in the control strategy. Some
mechanical changes are suggested to gather the maximum benefit and to greatly increase the
effective operating speed of future rovers.
A Design Of Omni-Directional Mobile Robot Based On Mecanum WheelsIJRESJOURNAL
ABSTRACT:As one of the important branch of mobile robotics, wheel mobile robot has long been paid atten tion to by the research people at home and abroad for its high load ability, positioning accuracy, high efficiency, simple control, etc. Mobile robot has close relation to many technologies suc-h as control theory, computer tech nology, sensor technology, etc. Therefore, research on the mobile robot has important significance
This is Part 4 of a 10 Part Series in Automotive Dynamics and Design, with an emphasis on Mass Properties. This series was intended to constitute the basis of a semester long course on the subject.
HELLO FRINDS THIS REPORT IS OF INDUSTRIAL TRAINING ON DIESEL LOCOMOTIVE TECHNOLOGY.
IT IS VERY HELP FULL FOR YOU .
SO GO THROUGH IT .
**********************Best Of Luck ************************
INTRODUCTION OF INDIAN RAILWAY
DIESEL LOCOMOTIVE WORKSHOP .CHARBAGH
DIESEL ELECTRIC LOCOMOTIVE
WORKING MECHANISIM
IMPORTANT COMPONENTS OF LOCOMOTIVES
a) POWER PACK
b) FUEL SECTION
c) LUBE OIL CONTROL SECTION
i. FUEL INJECTION PUMP (FIP)
ii. INJECTORS
d) TURBO SUPER CHARGING (TSC)
e) BRAKES
f) COMPRESSOR / EXPRESSOR
g) GOVERNORS
h) TRACTION MOTER
i) BOGIE
j) GENERATOR
k) RADIATOR
l) ENGINE SECTION
m) CROSS HEAD
i. INLET AND EXHAUST VALVE
FAILURE ANALYSIS
a) MAGNAFLUX LAB
b) ULTRASONIC TEST
c) ZYGLO TEST
d) RDP TEST
This is a simple project for Induction Loop Vehicle Detector and Counter. It is very useful in counting car's and change its destination in tollbooth or parking area
Design and Fabrication of Wheel Chair using Rocker Bogie Mechanismijtsrd
Rocker bogie finds a vital role in determining the scientific analysis of objectives separated by many distance apart. The mobility design at present is quite a bit complex with many legs or wheels. The wheeled rover which is capable of driving over the rough terrain provided with high degree of mobility suspension system. The drive provided by the rocker bogie is simple and it mainly operated by the means of two motors. The motors are kept inside in order to make it more reliable and efficient. In overcoming the bumps in the natural terrain the wheels are operated simultaneously. By implementing this mechanism the vehicle can come through any obstacles it faces during the travel in the terrain. Arjun CP | Jithin Peter TK | C. Mohamed Meersa | Habeeb Rahman PP "Design and Fabrication of Wheel Chair using Rocker Bogie Mechanism" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-5 | Issue-4 , June 2021, URL: https://www.ijtsrd.compapers/ijtsrd42537.pdf Paper URL: https://www.ijtsrd.comengineering/mechanical-engineering/42537/design-and-fabrication-of-wheel-chair-using-rocker-bogie-mechanism/arjun-cp
it is presentation for future of robotics in 4 industrial revolutions. It has the content all about the mechatronics engineering. Again, I did a collection for all the resources together. here I use this info in a presentation for a seminar. here I share this to all the people who need this for technological resources. For the students of computer science, it is a collection for their research topic at a time.
A line follower robot, as the name suggests, is an automated guided vehicle, which follow a visual line embedded on the floor or ceiling.
Usually, the visual line is the path in which the line follower robot goes and it will be a black line on a white surface but the other way (white line on a black surface) is also possible.
Certain advanced line follower robots use the invisible magnetic fields as their paths.
Electric Motor Driven Two Worm Gear Screw Jacks Lifting System For Small Scissor Lift Table Features:
1. Two cubical gearbox worm gear screw jacks.
2. Self locking function, precision positioning, synchronized travel speed.
3. Translating screw or travel screw type, with top plate end fitting.
4. Double input worm shaft with heat treated.
5. Single phase or 3-phases electric motor driven, direct to connect one jack.
6. Accessories cover flexible jaw couplings, connecting shaft, motor flange adapter.
Structural and Fatigue Analysis of Two Wheeler Lighter Weight Alloy WheelIOSR Journals
Importance of wheel in the automobile is obvious. The vehicle may be towed without the engine but
at the same time even that is also not possible without the wheels, the wheels along the tire has to carry the
vehicle load, provide cushioning effect and cope with the steering control. Generally wheel spokes are the
supports consisting of a radial member of a wheel joining the hub to the rim. The most commonly used materials
for making Wheel spokes are with features of excellent lightness, thermal conductivity, corrosion resistance,
characteristics of casting, low temperature, high damping property, machine processing and recycling, etc. This
metal main advantage is reduced weight, high accuracy and design choices of the wheel. This metal is useful for
energy conservation because it is possible to re-cycle. Spokes make vehicles look great but at the same time they
require attention in maintenance. To perform their functions best, the spokes must be kept under the right
amount of tension. The two main types of motorcycle rims are solid wheels, in which case the rim and spokes
are all cast as one unit and the other spoke wheels, where the motorcycle rims are laced with spokes. These
types of wheels require unusually high spoke tension, since the load is carried by fewer spokes. If a spoke does
break, the wheel generally becomes instantly unridable also the hub may break. Presently, for motor-cycles
Aluminium alloy wheels are used, currently now replacing by new magnesium alloy due its better properties
than Al-alloy. An important implication of this paper or the problem stated here is to “analyse the stress and the
displacement distribution comparing the results obtained”. In addition, this work extends Proper analysis of the
wheel plays an important role for the safety of the rider. This paper deals with the static &fatigue analysis of the
wheel. The present work attempts to analyse the safe load of the alloy wheel, which will indicate the safe drive is
possible. A typical alloy wheel configuration of Suzuki GS150R commercial vehicle is chosen for study. Finite
element analysis has been carried out to determine the safe stresses and pay loads
Links from the slides:
Rover Report June 13, 2013 - Curiosity's Cameras
http://www.youtube.com/watch?v=b2rwWECbEHg&feature=c4-overview-vl&list=PLE8C83FF0367EEF8C
Rover Report October 26, 2012 - ChemCam
http://www.youtube.com/watch?v=iDgv14Qtl1c&list=PLE8C83FF0367EEF8C
Rover Report March 15, 2013 - Evidence for Life?
http://www.youtube.com/watch?v=UUVmyI9yjyU
Rover Report July 11, 2013 - Trek to Mount Sharp Begins
http://www.youtube.com/watch?v=vluaivJqo9w#at=12
COMPARISON OF RESPONSE TO UNBALANCE OF OVERHUNG ROTOR SYSTEM FOR DIFFERENT SU...IAEME Publication
Rotor unbalance is most common fault found in the rotating machines. Methods
are adopted to analyze the position of unbalance and to bring its effect into acceptablelimit. Vibration analysis is the most common technique used to analyze the rotor
system. Research have been performed on rotor supported atboth ends, however lessstudy has been done for overhung rotor. In this paper the response of overhung rotoron isotropic support and anisotropic support subject tounbalance has been presented.and equations aresolved using MATLAB programming. The effect of unbalancehas been studied on thebode plot. Forward and Reverse whirl are observed through Campbell diagram andmode shapes are plotted.
THE INFLUENCE OF DRIVING AXLE LOCATION ON THE LATERAL FORCE OF VEHICLEIAEME Publication
The lateral force acting on the tires produces a side slip angle that affects the
directional stability of vehicle. This paper presents some research results of the
influence of driving axle location on the lateral force of vehicle with 4x2 wheel
formula when vehicle is turning. The single track dynamical models of FWD and RWD
vehicle while cornering are created. Based on these two dynamical models, the system
equations of motion built are enable to study the influence of driving axle location on
the lateral force. Some calculated simulation results are shown for illustration.
The cubic root unscented kalman filter to estimate the position and orientat...IJECEIAES
In this paper we introduce a cubic root unscented kalman filter (CRUKF) compared to the unscented kalman filter (UKF) for calculating the covariance cubic matrix and covariance matrix within a sensor fusion algorithm to estimate the measurements of an omnidirectional mobile robot trajectory. We study the fusion of the data obtained by the position and orientation with a good precision to localize the robot in an external medium; we apply the techniques of kalman filter (KF) to the estimation of the trajectory. We suppose a movement of mobile robot on a plan in two dimensions. The sensor approach is based on the CRUKF and too on the standard UKF which are modified to handle measurements from the position and orientation. A real-time implementation is done on a three-wheeled omnidirectional mobile robot, using a dynamic model with trajectories. The algorithm is analyzed and validated with simulations.
This paper deals with the dynamic characterization of an
automotive shock absorber, a continuation of an earlier
work Vibration is undesirable, not only because of the
unpleasant motion, the noise and the dynamic stresses,
which may lead to fatigue and failure of the structure, but
also because of the energy losses and the reduction in
performance which accompany the vibrations [1].
Vibration analysis should be carried out as an inherent part
of the design because of the devastating effects, which
unwanted vibrations could have on machines and
structures.
A Review of Shortcomings of Driving principle for Spherical Drive Systemspaperpublications3
Abstract: Spherical drive system is a relatively new field of research, and it holds a lot of potential due to a ball’s ability to be holonomic and rebound from collisions. In order to provide propulsion to such a completely closed sphere several methods have been put forward by different researchers. This article aims at putting together a definitive and complete list of the limitations of every propulsion system, so that future product designers and researchers may be able to decide on which propulsion system suits their purpose. This article will also help future researchers to identify and therefore find ways to overcome these limitations.
Modeling, Simulation, and Optimal Control for Two-Wheeled Self-Balancing Robot IJECEIAES
Two-wheeled self-balancing robot is a popular model in control system experiments which is more widely known as inverted pendulum and cart model. This is a multi-input and multi-output system which is theoretical and has been applied in many systems in daily use. Anyway, most research just focus on balancing this model through try-on experiments or by using simple form of mathematical model. There were still few researches that focus on complete mathematic modeling and designing a mathematical model based controller for such system. This paper analyzed mathematical model of the system. Then, the authors successfully applied a Linear Quadratic Regulator (LQR) controller for this system. This controller was tested with different case of system condition. Controlling results was proved to work well and tested on different case of system condition through simulation on matlab/Simulink program.
Inverse Kinematics Analysis for Manipulator Robot with Wrist Offset Based On ...Waqas Tariq
This paper presents an algorithm to solve the inverse kinematics for a six degree of freedom (6 DOF) manipulator robot with wrist offset. This type of robot has a complex inverse kinematics, which needs a long time for such calculation. The proposed algorithm starts from find the wrist point by vectors computation then compute the first three joint angles and after that compute the wrist angles by analytic solution. This algorithm is tested for the TQ MA2000 manipulator robot as case study. The obtained results was compared with results of rotational vector algorithm where both algorithms have the same accuracy but the proposed algorithm saving round about 99.6% of the computation time required by the rotational vector algorithm, which leads to used this algorithm in real time robot control.
Design and analysis of x y- positioning stage based on redundant parallel li...eSAT Journals
Abstract This paper presents the concept of a planar positioning stage based on a kinematically redundant parallel linkage. Basic kinematics and workspace analysis of base redundant manipulator is initially explained and the procedure of static analysis to predict the actuated joint torques is described. As there are six actuators in the linkage, the redundancy can be overcome by proper selection of the base joint variables. Also it is assumed that the motion is at a constant speed. A numerical example is shown with a straight line trajectory to illustrate the workspace and joint force calculation aspects of this linkage. The possible arrangement of the stage with electrostatic actuation and sensing are finally highlighted. Keywords: Kinematic redundancy, Parallel mechanism, Static analysis, and Workspace characteristics
A New Method For Solving Kinematics Model Of An RA-02IJERA Editor
The kinematics miniature are established for a 4 DOF robotic arm. Denavit-Hartenberg (DH) convention and the
product of exponential formula are used for solving kinematic problem based on screw theory. For acquiring
simple matrix for inverse kinematics a new simple method is derived by solving problems like robot base
movement, actuator restoration. Simulations are done by using MATlab programming for the kinematics
exemplary.
The formula cars need high tire grip on racing challenge by reducing rolling displacement at corner or
double change lands. In this case study, the paper clarifies some issues related to suspension system with
inerter to reduce displacement and rolling angle under impact from road disturbance on Formula SAE
Car. We propose some new designs, which have an advance for suspension system by improving dynamics.
We optimize design of model based on the minimization of cost functions for roll dynamics, by reducing the
displacement transfer and the energy consumed by the inerter. Base on a passive suspension model that we
carried out quarter-car and half-car model for different parameters which show the benefit of the inerter.
The important advantage of the proposed solution is its integration a new mechanism, the inerter, this
system can increase advance in development and have effects on the vehicle dynamics in stability vehicle.
This work presents the kinematics model of an RA-
02 (a 4 DOF) robotic arm. The direct kinematic problem is
addressed using both the Denavit-Hartenberg (DH) convention
and the product of exponential formula, which is based on the
screw theory. By comparing the results of both approaches, it
turns out that they provide identical solutions for the
manipulator kinematics. Furthermore, an algebraic solution of
the inverse kinematics problem based on trigonometric
formulas is also provided. Finally, simulation results for the
kinematics model using the Matlab program based on the DH
convention are presented. Since the two approaches are
identical, the product of exponential formula is supposed to
produce same simulation results on the robotic arm studied.
Keywords-Robotics; DH convention; product of exponentials;
kinematics; simulations
The kinematics analysis and trajectory planning of Series robotIJRES Journal
In this paper, a series robot as the research object, using theoretical analysis, numerical simulation method of
combining, to carry out the overall performance analysis and optimization of industrial robots trajectory. For serial
robot, kinematics modeling. The establishment of a first-order influence coefficient method based on
second-order influence coefficient matrix, kinematic and dynamic analysis of performance indicators based on
both Jacobin matrix and Hessian matrix, and the actual size of the work and working space agencies, institutions
initially selected size. Finally, institutional performance indicators for institutional map drawing performance,
combined with the flexibility and maneuverability determine the size of a set of different institutions in the
optimal configuration, and its feasibility through simulation. According to the geometric characteristics of the
surface complex surface fragmentation process, solve the optimal value speed and coating spray width of the
overlapping area on each patch.
Wear Analysis on Cylindrical Cam with Flexible RodIJRES Journal
Firstly, the kinetic equation of spatial cylindrical cam with flexible rod has been established. Then, an
accurate cylindrical cam mechanism model has been established based on the spatial modeling software
Solidworks. The dynamic effect of flexible rod on mechanical system was studied in detail based on the
mechanical system dynamics analytical software Adams, and Archard wear model is used to predict the wear of
the cam. We used Ansys to create finite element model of the cam link, extracted the first five order mode to
export into Adams. The simulation results show that the dynamic characteristics of spatial cylindrical cam
mechanical system with flexible rod is closed to ideal mechanism. During the cam rotate one cycle, the collision
in the linkage with a clearance occurs in some special location, others still keep a continuous contact, and the
prediction of wear loss is smaller than rigid body.
Surrogate safety measures using bicycle vehicle modelsbijejournal
Surrogate Safety Measures (SSM) allow for analysis of crashes without having access to actual crash data
as those are difficult to obtain, being of rare event nature. This article, for the first time, uses kinematic and
dynamic bicycle models for vehicles for trajectory analysis to compute surrogate safety measures. The model
has two versions, with and without the consideration of adhesion coefficients depending on the road conditions.
Previously, only longitudinal models have been used and recently, a combined longitudinal and lateral model has
been used by the authors but with a single wheel model, which is being enhanced by using the bicycle model in
this paper.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology.
Abstract This paper presents the design and implementation of a quadcopter capable of payload delivery. A quadcopter is a unique unmanned aerial vehicle which has the capability of vertical take-off and landing. In this design, the quadcopter was controlled wirelessly from a ground control station using radio frequency. It was modeled mathematically considering its attitude and altitude, and a simulation carried out in MATLAB by designing a proportional Integral Derivative (PID) controller was applied to a mathematical model. The PID controller parameters were then applied to the real system. Finally, the output of the simulation and the prototype were compared both in the presence and absence of disturbances. The results showed that the quadcopter was stable and able to compensate for the external disturbances.
Abstract This paper presents the design and implementation of a quadcopter capable of payload delivery. A quadcopter is a unique unmanned aerial vehicle which has the capability of vertical take-off and landing. In this design, the quadcopter was controlled wirelessly from a ground control station using radio frequency. It was modeled mathematically considering its attitude and altitude, and a simulation carried out in MATLAB by designing a proportional Integral Derivative (PID) controller was applied to a mathematical model. The PID controller parameters were then applied to the real system. Finally, the output of the simulation and the prototype were compared both in the presence and absence of disturbances. The results showed that the quadcopter was stable and able to compensate for the external disturbances.
Closed-Form Solutions For Optimum Rotor in Hover and Climb
Analysis and simulation of a rocker bogie exploration rover
1. ANALYSIS AND SIMULATION OF A ROCKER-BOGIE
EXPLORATION ROVER
Hervé Hacot1
, Steven Dubowsky1
, Philippe Bidaud2
1
Department of Mechanical Engineering, Massachusetts Institute of Technology
Cambridge, MA 02139, USA
2
Laboratoires de Robotique de Paris - Centre Universiatire de Technologie
10-12 avenue de l’Europe - 78140 Vélizy - FRANCE
Abstract
Rovers will continue to play an important role in planetary exploration. Plans include the use of
the rocker-bogie rover configuration. Here, models of the mechanics of this configuration are
presented. Methods for solving the inverse kinematics of the system and quasi-static force
analysis are described. Also described is a simulation based on the models of the rover’s
performance. Experimental results confirm the validity of the models.
1. Introduction
NASA recently started an ambitious exploration program of Mars [1]. Pathfinder is the first
rover explorer in this program [2],[3]. Future rovers will need to travel several kilometers over
periods of months and manipulate rock and soil samples. They will also need to be somewhat
autonomous. Rocker-bogie based rovers are likely candidates for these missions (see Figure 1).
The physics of these rovers is quite complex.
To design and control these, analytical models of how the rover interacts with its environment
are essential [4]. Models are also needed for rover action planning [5]. Simple mobility analysis
of rocker-bogie vehicles have been developed and used for design evaluation [6],[7]. In the
available published works, the rocker-bogie configuration is modeled as a planar system.
Improving the performances of a simpler four wheel rover has also been explored [8]. In this
work, actuator redundancy and the position of the center of mass of a vehicle (the Gophor) is
exploited to improve traction. The method relies on real-time measurements of wheel/ground
contact forces, which are difficult to measure in practice. Traction can also be improved by
monitoring the skiding of the rover wheels on the ground [9]. However, detailed models of the
full 3-D mechanics of rocker-bogie rovers have not been developed. Further models including
the manipulator’s influence are also required to effectively planning and controlling the actions
of these rovers. For example it is important for a planner to be able to predict if a rover can
successfully negotiate a given terrain obstacles, such as a ditch, without being trapped.
2. This paper describes a physical model of a rocker-bogie rover, the Lightweight Survivable
Rover (LSR-1). An efficient method of solving its inverse kinematics and its quasi-static force
analysis is outlined. The methods include the effects of the rover’s manipulator, actuator
saturation and tire-slip considerations. A graphical interface that enhances the understanding of
the physics of the model is also described.
2. The LSR-1 Design
Along with the Sojourner rover, the LSR-1 is representative of a class of NASA prototype
planetary rovers based on a rocker-bogie mobility configuration [10]. The LSR-1 vehicle has 20
cm diameter wheels and is approximately 100 cm in length, 70 cm wide, and 45 cm high. It is
equiped with a three degrees of freedom manipulator, whose payload is not negligible in the
rover mass ditribution. Six independently driven wheels are mounted on an articulated frame,
see Figure 1. The frame has two rocker arms connected to a main body. Each rocker has a rear
wheel connected to one end and a secondary rocker, called a bogie, connected to the other. At
each end of the bogie is a drive wheel and the bogie is connected to the rocker with a free
pivoting joint. The rockers are connected to the main body with a differential so that the pitch
angle of the body is the average of the pitch angles of the rockers. A more detailed description of
the design is given in [10].
Figure 1: A Rocker-Bogie Rover (LSR-1)
3. Model description
One of the principal purposes of this analysis is to serve as on-board tool for action planning
[5]. Hence it is important to keep the model as computationally simple as possible while
maintaining an acceptable level of fidelity. A key to achieving these objectives is to recognize
that the practical constraints of space systems, such as weight and power, require rovers to
travel at slow speeds, approximately 3 cm/s (for the LSR-1). Therefore, dynamic effects are
small and a quasi-static model adequately describes its behavior.
The terrain geometry is taken as input to the analysis. Rovers will have sensors such as stereo
cameras and laser range finding systems capable of providing this informationin the form of
maps of the local terrain [2,11]. The tire/soil characteristics are essential for the accurate
3. modeling of rover behavior [12]. However, these characteristics can be difficult to obtain. On-
line adaptive or identification methods, as well as pre-established estimates may be used to
provide this information. This area remains an open research topic. The analysis developed
here is intended to be sufficiently general to accomodate different soil/tire models.
3.1 Inverse Kinematics
The attitude and configuration of a rover as a function of the terrain on which it moves is
required to calculate the load distribution on the wheels, the rover’s stability, actuator outputs,
etc. The rover’s configuration, position and attitude can be fully defined by the following ten
parameters (see Figure 2).:
xB, yB and zB the inertial position of the vehicle;
ψ, Θ and φ: the yaw, roll and pitch angles
Θ1 ,Θ2, Θ3 and Θ4 : angles that define the configuration of the rocker-bogie mechanism
In the following kinematics analysis, the desired heading angle (ψ) and the inertial position of
the middle right wheel (x2r,y2r) are taken as input. Then, seven other independent variables
must be determined. The variables z2r, φ, Θ, Θ1, Θ2, Θ3 and Θ4 are chosen as unknowns.
From this set of ten variables, the remaining three system variables xb,yb, and zb can be easily
calculated.
Figure 2: Kinematic parameters of the Rover
Since the six wheels are independently driven, the wheel motions along the ground are
considered as inputs to the analysis. From this input, the rover position and configuration is
calculated iteratively to satisfy these closed-loop equations [4]:
Φ = Θ1 +Θ 3( )/ 2 −γ (1)
z2r = zcenter,2r (2)
z2r − z3r = cos(Θ) ⋅(l3 ⋅sin(Θ2 ) − l4 ⋅ sin(Θ2 + β)) (3)
z2r − z1r = cos(Θ) ⋅ (l3 ⋅ sin(Θ2 ) + l2 ⋅ sin(Θ1 + α) − l1 ⋅sin(Θ1)) (4)
z2r − z1l = cos(Θ) ⋅ (l3 ⋅sin(Θ2 ) + l2 ⋅sin( Θ1 + α) − l1 ⋅ sin(Θ3 )) + w ⋅ sin(Θ) (5)
4. z2r − z2l = cos(Θ) ⋅ (l3 ⋅ sin(Θ2 ) + l2 ⋅ sin(Θ1 +α ) − l2 ⋅ sin(Θ3 +α ) − l3 ⋅ sin(Θ 4) + w ⋅ sin(Θ) (6)
z2r − z3l = cos(Θ) ⋅(l3 ⋅sin(Θ2 ) + l2 ⋅ sin(Θ1 +α ) − l2 ⋅sin(Θ3 +α )
+ l4 ⋅sin(Θ 4 +β ) + w ⋅ sin(Θ)
(7)
where r and l refer to the right and left sides of the vehicle respectively, and γ is the angle Θ1
when the rover is on a flat surface. The wheels centers positions are then deduced by solving
this system. This gives seven equations in seven unknowns. These iterative solutions are
obtained using numerical methods such as steepest descent and Newton’s method. Because of
the highly non-linearity of these equations and because the ground profile is not continuously
differentiable, these methods can fail to converge to a solution.
It is possible to solve accurately the above inverse kinematics by simplifying the problem. From
the profile of the ground, Θ can be approximated. Then, the model is broken into two
problems. Using this approximate value of Θ, the models of the right and left sides are solved
directly. Finally, Θ is corrected while maintaining the values for z2r, Θ1, Θ2, Θ3 and Θ4. For a
complete description of this approach see [4]. The average error between the wheel contact
point and the ground profile is less than one percent of the wheel diameter (.2 cm). This error is
on the same order as the errors due to other factors, such as tire compliance. The method is
computationnaly very efficient (less than 10 iterations are usually enough to find a solution).
3.2 Force Analysis
With the pose of the rover calculated, the quasi-static force analysis can be performed. The
quasi-static force balance is used to determine if the rover wheels will slip, if the rover will slide
or tip over. It can also be used to estimate the amount of energy consumed and if any actuator
are near saturation. The system center of mass position is computed and is input to the force
analysis, as well as external forces. Through these terms the manipulator configuration and task
forces enter the analysis. It is assumed that with the LSR’s relatively rigid wheels, a large
moment in any direction does not exist at the ground contact point. Ignoring these moments
prevents the three-dimensional force analysis from becoming highly statically indeterminate.
The normal and the tangential forces between the i
th
wheel and ground are Ni and Ti
respectively, see Figure 3.
Assuming that the vehicle roll angle is small, The transverse forces acting at the wheel contact
point (Fy1 to Fy6) will be relatively small. Further, by assuming that each of these forces has the
same magnitude, Mxl, Mxr, Mzl and Mzr can be computed (the width of each of the rocker-bogie
assembly is small as compared to the width and height of the vehicle, hence Mxl, Mxr, Mzl and
Mzr are only function of Fyi). The resulting equations of static equilibrium for the body are:
Fxr + Fxl = 0 (8)
(Fxr − Fxl )
w
2
+ Mzr + Mzl = 0 (9)
5. Fzr + Fzl − Wz = 0 (10)
(Fzl − Fzr )
w
2
+ Mxr + Mxl = 0 (11)
The system of equations (8)-(11) permits the values Fx, Fz, My that are applied from the body to
each rocker to be calculated. These forces and moments are then considered inputs to the planar
problem shown in Figure 3. The equations of equilibrium in the planar case are:
F ⋅ux =∑ Ti + Ni( )
i=1
i =3
∑ ⋅u x + Fx = 0 (12)
F ⋅ uz =∑ Ti + Ni( )
i=1
i= 3
∑ ⋅ uz − Fz = 0 (13)
My,body =∑ T1 × RA + N1 × RA + T2 × MA + N2 × MA + T3 × FA + N3 × FA+ M y = 0 (14)
My,bogie =∑ T2 × MB + N2 × MB+ T3 × FB + N3 × FB = 0 (15)
These equations are solved with the following constraints on the wheel torques:
1) Ti ≤ µ Ni : no slip i
th
wheel (or will just slip).
2) Ni ≥ 0 insures i
th
wheel ground contact.
3) τi ≤ τ max to insure the i
th
wheel motor does not saturate.
Where τi is the i
th
wheel motor torque. Note that τi is related to the wheel tangential force Ti by
the wheel radius. The method of finding a solution under these constraints is detailed in [4].
Figure 3: 3-D and 2-D Force Analysis
he set of equations (12-15) is underdetermined (four equations and six unknowns). Three of
the unknowns are directly commanded (the wheel torques), therefore they affect the normal
forces magnitudes. This interesting feature is used in the design of a traction controller based on
fuzzy logic [4].
6. The model has been tested on the MIT MOD I rocker-bogie experimental test-bed. Figure 4
shows the results and the comparison to the analysis. For these experiments the rover was
standing on a flat surface. The normal force changes with respect to torque changes have been
measured with a load cell. The dashed line represents experimental results, and the solid line
represents analytical model results.
In Figure 4, the changes in the rear, middle and front wheels normal forces as a function of the
motor torques are plotted.
8
6
4
8
6
4
8
6
4
6
4
2
6
4
2
6
4
2
4
2
0
4
2
0
4
2
0
Rear Normal force Changes Middle Normal force Changes Front Normal force Changes
RearNormalForve(N)RearNormalForceRearNormalForce(N)
MiddleNormalForve(N)MiddleNormalForce(N)MiddleNormalForce(N)
FrontNormalForve(N)FrontNormalForce(N)FrontNormalForce(N)
Rear Wheel Torque (mN-m)
Front Wheel Torque
Middle Wheel Torque
Rear Wheel Torque (mN-m)
Front Wheel Torque
Middle Wheel Torque
Rear Wheel Torque (mN-m)
Front Wheel Torque
Middle Wheel Torque
-200 200
-200 200
-200 200
-200 200
-200 200
-200 200
-200 200
-200 200
-200 200
Figure 4: Measured and simulated variations of the normal forces on the wheels.
The errors between the model and the actual system are caused by several factors. In the
analytical model, when the effect of a wheel torque is considered, the other motors torques are
taken as zero. However, the friction of the highly geared motors creates an unknown static
torque opposing the commanded torque. Also, since the experimental rover is not equipped with
torque sensors, the output torque cannot be known very accurately. Finally, unmodeled friction
in the rocker-bogie joint can also be shown to create some errors. Nonetheless analytical model
predicts the trends seen in the experimental system quite well.
7. 4. Simulation
The model has been implemented into a simulation. It shows the rover in its environment,
moving over specified terrains and is a valuable tool for evaluation. A graphical interface has
also been developed, to enhance the understanding of the system (see Figure 5). A number of
variables useful for performance evaluation are computed and displayed including the normal
forces on the rover wheels. The torque saturation for each wheel (the ratio between the actual
torque and the saturation torque), the slip ratio Sr that is defined and computed as: Sr =
µ
,
where Ti, Ni and µ are the traction and normal forces and the local coefficient of friction under
the ith
wheel respectively are also shown. Stability margin is defined as the ratio between the
angle necessary to tip over the rover at a given time and the angle to tip over the rover when on a
flat surface [13].
The kinematics parameters (link lengths, etc) can be changed during the simulation, therefore the
simulation can be used for optimisation studies. Other control panel keys interface with the user,
such as Pause, Play Fast Forward, etc. buttons. This way, the user can focus on specific areas.
Torque
Slip ratio
Torque
Slip ratio
Simulation Speed
Time: 330.7 s
Distance traveled : 428.2 cm
Energy consumed
Stability Margin
Wheel1 Wheel 2 Wheel 3
Rover
top view
Figure 5: Rover Simulation Graphics Software
5. Summary and Conclusions
A simple and computationally efficient rocker-bogie rover model is presented. Under reasonable
assumptions, it is possible to determine the rover attitude and configuration, given its position
and ground characteristics, and whether the rover will slide, tip over or maintain its balance.
The model includes the affect of the manipulator. The mechanics of the rover has been
8. developed, and the over-actuation of the system leads to the ability to affect the normal forces by
applying specific wheel torques. This property has been verified experimentally and can be
used for the design of an active traction control. A graphical interface has been designed to
enhance understanding of the system.
6. Acknowledgements
This work is supported by the NASA Jet Propulsion Laboratory under contract no. 960456 The
authors would like to acknowledge the support of Dr. Paul Schenker and his research team at
JPL. The support and encouragement of Guillermo Rodriguez of JPL is also acknowledged.
7. References
[1] Mars Pathfinder: www.mpf.jpl.nasa.gov
[2] Hayati, S., et. al., “The Rocky 7 Rover: A Mars Sciencecraft Prototype”, Proceedings of the
1997 IEEE International Conference on Robotics and Automation, pp. 2458-64, 1997.
[3] Schenker, P., et. al., “Lightweight Rovers for Mars Science Exploration and Sample Return,”
Intelligent Robots and Computer Vision XVI, SPIE Proc. 3208, Pittsburg, PA, October, 1997.
[4] Hacot, H., The Kinematic Analysis and Motion Control of a Planetary Rover, Masters Thesis,
Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA,
May, 1998.
[5] Farritor S., Hacot H., Dubowsky S., “Physics Based Planning for Planetary Exploration”,
Proceedings of the 1998 IEEE International Conference on Robotics and Automation.
[6] Linderman, R., Eisen, H., “Mobility Analysis, Simulation and Scale Model Testing for the
Design of Wheeled Planetary Rovers”, In Missions, Technologies, and Design of Planetary Mobile
Vehicle, pages 531-37, Toulouse, France, September 28-30, 1992.
[7] Chottiner,J. E., 1992, “Simulation of a Six-Wheeled Martain Rover Called the Rocker-Bogie”,
M.S. Thesis, The Ohio State University, Columbus, Ohio
[8] Sreevinasan, S., Wilcox, B., “Stability and Traction Control of an Actively Actuated Micro-
Rover”, Journal of Robotic Systems-1994, pp. 487-502
[9] Van der Burg, J.,Blazevic,P., “Anti-Lock Braking and Traction Control Concept for All-
Terrain Robotic Vehicles” IEEE International Conference on Robotics and Automation, pages
1400-05, April, 1997
[10] Bickler, B., “A New Family of JPL Planetary Surface Vehicles”, In Missions, Technologies,
and Design of Planetary Mobile Vehicle, pages 301-306, Toulouse, France, September 28-30,
1992.
[11] Matthies, L., Balch, T., Wilcox, B., “Fast Optical Hazard Detection for Planetary Rovers using
Multiple Spot Laser Triangulation” IEEE International Conference on Robotics and Automation,
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[12] Ben Amar, F., Bidaud, P., “Dynamics Analysis of off-road vehicles”, Proceedings of the 4th
International Symposium on Experimental Robotics 4, pages 363-371.
[13] Papadopoulos, E.G., Rey, D.A., "A New Measure of Tipover Stability Margin for Mobile
Manipulators" 1996 IEEE International Conference on Robotics and Automation, Minneapolis,
MN, pp.487-94, 1996.