Patent Publication Number: US-2017354897-A1

Title: Spherical tire for a self-propelled vehicle

Description:
FIELD OF INVENTION 
     The present invention relates to transportation, and, more particularly, to an assembly for supporting a vehicle while traversing a ground or other surface. 
     BACKGROUND OF THE PRESENT INVENTION 
     A conventional device may include a spherical housing and an internal drive system including one or more motors coupled to one or more wheels engaged to an inner surface of the spherical housing. A biasing mechanism, including a spring and contact end, may be coupled to the internal drive system to provide diametrically opposing force between the wheels and contact end to allow for power to the motors to be transferred to the inner surface of the spherical housing, causing the self-propelled device to roll along a contact surface. The self-propelled device may rotate based on a combination of movement of its center of mass, independent power to the motors, and the force of the biasing mechanism against the inner surface. A magnetic coupling component may be included with the biasing mechanism. The magnetic coupling component may comprise ferrous metal or a permanent magnet, such as a neodymium magnet, to provide a magnetic field through the spherical housing to magnetically interact with external devices and/or accessories. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The disclosure herein is described by way of example, and not by way of limitation, in the figures of the accompanying drawings and in which like reference numerals refer to similar elements, and in which: 
         FIG. 1  schematically illustrates an assembly in accordance with the present invention; 
         FIG. 2  is an example block diagram illustrating a conventional system to control operation of a self-propelled device; 
         FIG. 3  is a schematic depiction of a conventional self-propelled device under control of a controller; 
         FIG. 4  schematically illustrates an example of a conventional self-propelled device; 
         FIG. 5  illustrates another example of a conventional self-propelled device; 
         FIG. 6  is an example block diagram for a computer system and the self-propelled device of  FIGS. 4 &amp; 5 ; 
         FIG. 7  shows UV-VIS spectra of a trithiocarbonate RAFT chain transfer agent, PNIPAM with a trithiocarbonate-end group and PNIPAM with a thiol group; 
         FIG. 8  shows transmission measurement of turbidity versus temperature for several PNIPAM polymers with CTA endgroups; 
         FIG. 9  shows the  1 H-NMR spectrum of a styrene-butadiene elastomer and a styrene-butadiene elastomer functionalized with PNIPAM. 
         FIG. 10  shows GPC curves for a styrene-butadiene elastomer and for three PNIPAM-functionalized styrene-butadiene elastomers; 
         FIG. 11  shows contact angle as a function of PNIPAM content of PNIPAM functionalized styrene-butadiene elastomer; 
         FIG. 12  shows the relative difference in contact angle above and below the LCST for PNIPAM functionalized styrene-butadiene elastomer; 
         FIG. 13  shows rheological properties as a function of temperature for a styrene-butadiene elastomer; 
         FIG. 14  shows rheological properties as a function of temperature for a graft copolymer of styrene-butadiene and PNIPAM, with 6 percent PNIPAM; and 
         FIG. 15  shows rheological properties as a function of temperature for a graft copolymer of styrene-butadiene and PNIPAM, with 4 percent PNIPAM. 
     
    
    
     SUMMARY OF THE INVENTION 
     A support assembly for a vehicle in accordance with the present invention includes at least two spherical tires travelling on a road surface and rotating relative to the road surface and the vehicle and a drive system magnetically driving rotation of the tires relative to the drive system itself such that no portion of the drive system physically contacts the tires or the road surface. The tires each have an outer tread layer comprising a material having a first stiffness when dry and a second stiffness when wet, the first stiffness being greater than the second stiffness. 
     According to another aspect of the assembly, the drive system magnetically levitates the vehicle a first predetermined distance from the tires. 
     According to still another aspect of the assembly, the drive system magnetically levitates itself a second predetermined distance from an inner surface of the tires. 
     According to yet another aspect of the assembly, the tires are closed spheres having an interior space completely separate from external environment. 
     According to still another aspect of the assembly, the drive system comprises a first magnetically passive part and a second magnetically active part. 
     According to yet another aspect of the assembly, the first part generates only a constant magnetic field. 
     According to still another aspect of the assembly, the second part generates a constant magnetic field and a variable magnetic field. 
     According to yet another aspect of the assembly, the drive system maintains the vehicle at a substantially constant orientation relative to the drive system. 
     According to still another aspect of the assembly, the tires include a plurality off layers. 
     According to yet another aspect of the assembly, one of the plurality of layers mechanically supports a portion of a load determined by the vehicle. 
     According to still another aspect of the assembly, one of the plurality of layers comprises a tread for generating traction between the tires and the road surface. 
     According to yet another aspect of the assembly, one of the plurality of layers comprises an elastomeric layer for damping vibration caused by the tires traveling over the road surface. 
     Another support assembly for a vehicle in accordance with the present invention includes at least one spherical tire travelling on a road surface and rotating relative to the road surface and the vehicle. The tire has an outer tread layer comprising a material having polymeric backbone chain having a diene based elastomer selected from the group consisting of solution polymerized styrene butadiene rubber, emulsion polymerized styrene butadiene rubber, natural polyisoprene rubber, synthetic polyisoprene rubber, and polybutadiene and polymeric sidechains bonded to the backbone chain, the sidechains comprising a polymer selected from the group consisting of poly(N-isopropylacrylamide), poly(N-cyclopropylacrylamide), and poly(N, N-diethylacrylamide). 
     DETAILED DESCRIPTION OF EXAMPLES OF THE PRESENT INVENTION 
     An example conventional device, such as that described in U.S. Pat. No. 8,536,266, U.S. Pat. No. 9,090,214, and U.S. Pat. No. 9,211,920 incorporated by reference in their entirety herein, may include a spherical housing and an internal drive system including one or more motors coupled to one or more wheels engaged to an inner surface of the spherical housing. A biasing mechanism, including a spring and contact end, may be coupled to the internal drive system to provide diametrically opposing force between the wheels and contact end to allow for power to the motors to be transferred to the inner surface of the spherical housing, causing the self-propelled device to roll along a contact surface. The self-propelled device may rotate based on a combination of movement of its center of mass, independent power to the motors, and the force of the biasing mechanism against the inner surface. A magnetic coupling component may be included with the biasing mechanism. The magnetic coupling component may comprise ferrous metal or a permanent magnet, such as a neodymium magnet, to provide a magnetic field through the spherical housing to magnetically interact with external devices and/or accessories. 
     An example external accessory for the device may include a magnetic coupling component to magnetically couple with the magnetic coupling component of the biasing mechanism (e.g., the contact end). Accordingly, when the spherical housing of the self-propelled device is caused to roll, the external accessory can remain stably coupled to the contact end of the biasing mechanism via magnetic interaction through the spherical housing. 
     Either the self-propelled device, the external accessory, or both, may include a magnet (e.g., a neodymium magnet) to produce the magnetic field causing the magnetic interaction. Such interaction may involve a magnetic attraction in which contact occurs between the external accessory and the outer surface of the spherical housing. In such examples, friction may be reduced by coating the outer surface of the spherical housing and/or a contact surface of the external accessory with a substantially frictionless material. Additionally or alternatively, the magnetic interaction may involve a repulsive force including stability mechanism (e.g., one or more further magnets) to create stable magnetic levitation between the external accessory and the spherical housing. 
     As used herein, “substantially” means between 0° and less than 90° in the context of an angular rotation of the biasing mechanism while the self-propelled device is under operational control. Accordingly, a “substantially” stable, a “substantially” constant angle, or a “substantial” perpendicularity between the biasing mechanism (or spring component) and an external surface on which the self-propelled device rolls, means less than 90° with respect to that surface, and typically less than 45° while the self-propelled device is in a non-accelerated state. As further used herein, “substantially” in the context of friction between the outer surface of the spherical housing and the contact surface of the external accessory device, means a below normal frictional relation between two typical smooth surfaces (e.g., polished metal or wood surfaces). Thus, a “substantially” frictionless material means a material designed or manufactured for reduced friction. 
     One or more conventional examples described herein provide that methods, techniques, and actions performed by a computing device may be performed programmatically, or as a computer-implemented method. Programmatically, as used herein, means through the use of code or computer-executable instructions. These instructions may be stored in one or more memory resources of the computing device. A programmatically performed step may or may not be automatic. 
     One or more conventional examples described herein may be implemented using programmatic modules or components of a system. A programmatic module or component may include a program, a sub-routine, a portion of a program, a software component, and/or a hardware component capable of performing one or more stated tasks or functions. As used herein, a module or component may exist on a hardware component independently of other modules or components. Alternatively, a module or component may be a shared element or process of other modules, programs, and/or machines. 
     Some examples described herein may generally require the use of computing devices, including processing and memory resources. For example, one or more examples described herein may be implemented, in whole or in part, on computing devices such as digital cameras, digital camcorders, desktop computers, cellular/smart phones, personal digital assistants (PDAs), laptop computers, printers, digital picture frames, and/or tablet devices. Memory, processing, and network resources may all be used in connection with the establishment, use, and/or performance of any example described herein (including with the performance of any method and/or with the implementation of any system). 
     Furthermore, one or more examples described herein may be implemented through the use of instructions that are executable by one or more processors. These instructions may be carried on a computer-readable medium. Machines shown or described with figures below provide examples of processing resources and computer-readable mediums on which instructions for implementing examples may be carried and/or executed. In particular, the numerous machines shown with examples may include processors and various forms of memory for holding data and instructions. Examples of computer-readable mediums may include permanent memory storage devices, such as hard drives on personal computers or servers. Other examples of computer storage mediums may include portable storage units, such as CD or DVD units, flash memory (such as carried on smart phones, multifunctional devices, and/or tablets), and magnetic memory. Computers, terminals, network enabled devices (e.g., mobile devices, such as cell phones) may all utilize processors, memory, and/or instructions stored on computer-readable mediums. Additionally, examples may be implemented in the form of computer-programs, or a non-transitory computer usable carrier medium capable of carrying such a program. 
     Referring now to  FIG. 2 , a schematic depiction of an example self-propelled device  100  is shown. The self-propelled device  100  may move under control of another device, such as a computing device operated by a user. The self-propelled device  100  may be configured with resources that enable one or more of the following: maintain self-awareness of orientation and/or position relative to an initial reference frame after the device initiates movement; process control input programmatically, so as to enable a diverse range of program-specific responses to different control inputs; enable another device to control its movement using software or programming logic that is communicative with programming logic on the self-propelled device; and/or generate an output response for its movement and state that it is software interpretable by the control device. 
     The self-propelled device  100  may include several interconnected subsystems and modules. A processor  114  may execute programmatic instructions from a program memory  104 . The instructions stored in the program memory  104  may be changed, for example to add features, correct flaws, and/or modify device behavior. The program memory  104  may store programming instructions that are communicative or otherwise operable with software on a linked controller device. The processor  114  may execute different sets of programming instructions in order to alter the manner in which the self-propelled device  100  interprets or otherwise responds to control inputs from the linked controller. 
     A wireless communication port  110 , in conjunction with a communication transducer  102 , may exchange data between the processor  114  and other external devices. The data exchanges, for example, may provide communications, control, logical instructions, state information, and/or updates for the program memory  104 . The processor  114  may generate output corresponding to state and/or position information, communicated to the linked controller via the wireless communication port  110 . The mobility of the self-propelled device  100  may limit hard-wired connections. Thus, the term “connection” may be understood to mean a logical connection, such as a wireless link made without a physical connection to the self-propelled device  100 . 
     The wireless communication port  110  may implement the communication protocol and the transducer  102  may be an antenna suitable for transmission and reception of radio signals. Other wireless communication mediums and protocols may also be used in alternative implementations. Sensors  112  may transmit information about the surrounding environment and condition to the processor  114 . The sensors  112  may include inertial measurement devices, including a three-axis gyroscope, a three-axis accelerometer, and/or a three-axis magnetometer. The sensors  114  may provide input to enable the processor  114  to maintain awareness of the device&#39;s orientation and/or position relative to an initial reference frame after the device  100  initiates movement. Also, the sensors  112  may include instruments for detecting light, temperature, humidity, and/or measuring chemical concentrations or radioactivity. 
     A state/variable memory  106  may store information about the present state of the system, including, for example, position, orientation, rates of rotation, and/or translation about each axis. The state/variable memory  106  may also store information corresponding to an initial reference frame of the device  100  upon, for example, the device being put in use (e.g., the device being switched on), as well as position and orientation information once the device is in use. Thus, the device  100  may utilize information of the state/variable memory  106  in order to maintain position and orientation information of the device once the device moves. 
     A clock  108  may provide timing information to the processor  114  by implementing a time-base for measuring intervals and rates of change. The clock  108  may provide day, date, year, time, and/or alarm functions. The clock  108  may allow the self-propelled device  100  to sound an alarm or alert at pre-set times. 
     An expansion port  120  may provide a connection for addition of accessories or devices. The expansion port  120  may provide for future expansion, as well as flexibility to add options or enhancements. For example, the expansion port  120  may be used to add peripherals, sensors, processing hardware, storage, displays, or actuators to the basic self-propelled device  100 . 
     In variations, the expansion port  120  may provide an interface capable of communicating with a suitably configured component using analog or digital signals. Thus, the expansion port  120  may provide electrical interfaces and protocols that are standard or well-known. Furthermore, the expansion port  120  may implement an optical interface. Example interfaces appropriate for the expansion port  120  may include the universal serial bus (USB), inter-integrated circuit bus (I2C), serial peripheral interface (SPI), and/or ethernet. 
     A display  118  may be included to present information to outside devices or users. The display  118  may present information in a variety of forms. In variations, display  118  may produce light in colors and patterns, sound, vibration, music, and/or combinations of sensory stimuli. The display  118  may operate in conjunction with actuators  126  to communicate information from physical movements of device  100 . For example, the device  100  may be made to emulate a human head, nod and/or shake to communicate “yes” or “no.” 
     In variations, the display  118  may be an emitter of light, either in the visible or invisible range. Invisible light in the infrared or ultraviolet range may be useful, for example, to send information invisible to human senses, but available to specialized detectors. In some examples, the display  118  may include an array of light emitting diodes (LEDs) emitting various light frequencies and arranged such that their relative intensity is variable and the light emitted is blended to form color mixtures. 
     The display  118  may include an LED array comprising several LEDs, each emitting a human-visible primary color. The processor  114  may vary the relative intensity of each of the LEDs to produce a wide range of colors. Primary colors of light are those in which a few colors may be blended in different amounts to produce a wide gamut of apparent colors. Many sets of primary colors are known, including, for example, red/green/blue, red/green/blue/white, and red/green/blue/amber. For example, red, green and blue LEDs together may define a usable set of three available primary-color devices comprising the display  118 . In other examples, other sets of primary colors and white LEDs may be used. The display  118  may further include an LED used to indicate a reference point on the device  100  for alignment. 
     A power cell  124  may store energy for operating the electronics and electromechanical components of the device  100 . The power cell  124  may be a rechargeable battery. Furthermore, an inductive charge port  128  may allow for recharging the power cell  124  without a wired electrical connection. In variations, the inductive charge port  128  may accept magnetic energy and convert it to electrical energy to recharge the power cell  124 . The charge port  128  may also provide a wireless communication interface with an external charging device. 
     A deep sleep sensor  122  may be included to place the self-propelled device  100  into a very low power or “deep sleep” mode where most of the electronic devices use no battery power. This may be useful for long-term storage or shipping. In variations, the deep sleep sensor  122  may be non-contact in that it senses through the housing of the device  100  without a wired connection. The deep sleep sensor  122  may be a Hall-effect sensor mounted so that an external magnet may be applied at a predetermined location on the device  100  to activate a deep sleep mode. 
     Drive actuators  126  may be included to convert electrical energy into mechanical energy for various uses. A primary use of the drive actuators  126  may be to propel and steer the self-propelled device  100 . Movement and steering actuators may also be referred to as a drive system or traction system. The drive system may move the device  100  in rotation and translation, under control of the processor  114 . Examples of drive actuators  126  may include, without limitation, wheels, motors, solenoids, propellers, paddle wheels, and/or pendulums. The drive actuators  126  may include two parallel wheels, each mounted to an axle connected to an independently variable-speed motor through a reduction gear system. Thus, the speeds of the two drive motors may be controlled by the processor  114 . 
     The drive actuators  126  may produce a variety of movements in addition to merely rotating and translating the self-propelled device  100 . Thus, in some variations, the drive actuators  126  may allow the device  100  to execute communicative or emotionally evocative movements, including emulation of human gestures, for example, head nodding, shaking, trembling, spinning, and/or flipping. In some variations, the processor  114  may coordinate the drive actuators  126  with the display  118 . For example, the processor  114  may provide signals to the drive actuators  126  and the display  118  to cause the device  100  to spin or tremble and simultaneously emit patterns of colored light. Thus, the device  100  may emit light and/or sound patterns synchronized with movements. 
     In further variations, the self-propelled device  100  may be used as a controller for other network-connected devices. The device  100  may contain sensors and wireless communication capability, and so it can perform a controller role for other devices. For example, the self-propelled device  100  may be held in the hand and used to sense gestures, movements, rotations, combination inputs, etc. 
       FIG. 3  is an example conventional schematic depiction of a self-propelled device  214  under control of a controller device  208 , such as a smart phone or tablet computing device. More specifically, the self-propelled device  214  may be controlled in its movement by programming logic and/or controls that can originate from the controller device  208 . The self-propelled device  214  may move under control of the computing device  208 , which can be operated by a user  202 . The computing device  208  may wirelessly communicate control data  204  to the self-propelled device  214  using a standard or proprietary wireless communication protocol. In variations, the self-propelled device  214  may be at least partially self-controlled, utilizing sensors and internal programming logic to control the parameters of its movement (e.g., velocity, direction, etc.). Still further, the self-propelled device  214  may communicate data relating to the device&#39;s position and/or movement parameters for the purpose of generating or alternating content on the computing device  208 . The self-propelled device  214  may control aspects of the computing device  208  by way of its movements and/or internal programming logic. The self-propelled device  214  may have multiple modes of operation, including those of operation in which the device is controlled by the computing device  208 , is a controller for another device (e.g., another self-propelled device or the computing device  208 ), and/or is partially or wholly self-autonomous. 
     The self-propelled device  214  and the computing device  208  may share a computing platform on which programming logic is shared in order to enable the user  202  to operate the computing device  208  and generate multiple kinds of input, including simple directional input, command input, gesture input, motion and/or other sensory input, voice input, or combinations thereof, enable the self-propelled device  214  to interpret input received from the computing device  208  as a command or set of commands, and/or enable the self-propelled device  214  to communicate data regarding that device&#39;s position, movement, and/or state in order to effect a state on the computing device  208  (e.g., display state, such as content corresponding to a controller-user interface). The self-propelled device  214  may include a programmatic interface that facilitates additional programming logic and/or instructions for using the device. The computing device  208  may execute programming that is communicative with the programming logic on the self-propelled device  214 . 
     According to some examples, the self-propelled device  214  includes an actuator or drive mechanism causing motion or directional movement. The self-propelled device  214  may be referred to by a number of related terms and phrases, including controlled device, robot, robotic device, remote device, autonomous device, and remote-controlled device. The self-propelled device  214  may be structured to move and be controlled in various media. For example, the self-propelled device  214  may move through media such as flat surfaces, sandy surfaces, and/or rocky surfaces. 
     As shown in  FIG. 4 , the self-propelled device  214  may correspond to a spherical object that can roll and/or perform other movements such as spinning. The self-propelled device  214  may include an external accessory  216  magnetically coupled to the self-propelled device  214  via magnetic coupling through the spherical housing of the device. The self-propelled device  214  may correspond to a radio-controlled aircraft, such as an airplane, helicopter, hovercraft, and/or balloon. The device  214  may correspond to a radio controlled watercraft, such as a boat or submarine. Numerous other variations may also be implemented, such as those in which the device  214  is a robot. 
     The self-propelled device  214  may include a sealed hollow envelope, substantially spherical in shape, capable of directional movement by action of actuators inside the envelope. The self-propelled device  214  may communicate with the computing device  208  using network communication links  210 ,  212 . One link  210  may transfer data from the computing device  208  to self-propelled device  214 . The other link  212  may transfer data from the self-propelled device  214  to the computing device  208 . The links  210 ,  212  may be separate unidirectional links or a single bi-directional communication link communicating in both directions. The links  210 ,  212  may not be identical in type, bandwidth, and/or capability. For example, the link  210  from the computing device  208  to the self-propelled device  214  may be capable of a higher communication rate and bandwidth compared to the link  212 . In some situations, only one link  210  or  212  may be established. Communication may then be unidirectional. 
     The computing device  208  may correspond to any device comprising at least a processor and communication capability suitable for establishing at least unidirectional communications with the self-propelled device  214 . Examples of such devices may include, without limitation mobile computing devices (e.g., multifunctional messaging/voice communication devices such as smart phones), tablet computers, portable communication devices, and/or personal computers. 
     The user  202  may interact with the self-propelled device  214  via the computing device  208  in order to control the self-propelled device  214  and/or to receive feedback or interaction on the computing device  208  from the self-propelled device  214 . As such, the user  202  may specify input  204  through various mechanisms of the computing device  208 . Examples of such inputs may include text entry, voice command, touching a sensing surface or screen, physical manipulations, gestures, taps, shaking, and combinations thereof. 
     The user  202  may interact with the computing device  208  in order to receive feedback  206 . The feedback  206  may be generated by the computing device  208  in response to user input. The feedback  206  may also be based on data communicated from the self-propelled device  214  to the computing device  208 , regarding, for example, the self-propelled device&#39;s position or state. Examples of feedback  206  may include text display, graphical display, sound, music, tonal patterns, modulation of color or intensity of light, haptic, vibrational, and/or tactile stimulation. The feedback  206  may be combined with input that is generated on the computing device  208 . The computing device  208  may thereby output content that is modified to reflect position or state information communicated from the self-propelled device  214 . 
     The computing device  208  and/or the self-propelled device  214  may thus be configured such that user input  204  and feedback  206  maximize usability and accessibility for the user  202 , who may have limited sensing, thinking, perception, motor, and/or other abilities. This allows a user  202  with handicaps or special needs to operate the system  200 . 
       FIG. 4  schematically shows another conventional example of a self-propelled device  300 . The self-propelled device  300  may be of a size and weight allowing it to be easily grasped, lifted, and/or carried in an adult human hand. The self-propelled device  300  may include a spherical housing  302  with an outer surface that makes contact with an external surface as the device moves by rolling. The spherical housing  302  include an inner surface  304  and several mechanical and electronic components enclosed by the inner surface of the spherical housing. 
     The spherical housing  302  may be composed of a material that transmits signals used for wireless communication, yet are impervious to moisture and dirt. The spherical housing  302  may further be durable, washable, and/or shatter-resistant. The spherical housing  302  may also be structured to enable transmission of light and textured to diffuse the light. The spherical housing  302  may be a sealed polycarbonate plastic. The spherical housing  302  may comprise two hemispherical shells with an associated attachment mechanism, such that the spherical housing may be opened to allow access to internal electronic and mechanical components. 
     Several electronic and mechanical components may be located inside the spherical housing  302  for processing, wireless communication, propulsion, and/or other functions (collectively referred to as an “interior mechanism”). Among the components, examples may include a drive system  301  enabling the device  300  to propel itself. The drive system  301  may be coupled to processing resources and other control mechanisms. A carrier  314  serves as an attachment point and support for components of the drive system  301 . The components of the drive system  301  may not be rigidly attached to the spherical housing  302 . Instead, the drive system  301  may include a pair of rollers  318 ,  320  that are in frictional contact with the inner surface  304  of the spherical housing  302 . 
     The carrier  314  may be in mechanical and/or electrical contact with an energy storage component  316 . The energy storage component  316  may provide a reservoir of energy to power the device  300  and its associated electronic components. The energy storage component  316  may be replenished through an inductive charge port  326 . The energy storage component  316  may be a rechargeable battery. Such a battery may comprise lithium-polymer cells. Other suitable rechargeable battery chemistries/mechanisms may also be used. The carrier  314  may provide a mounting location for most of the internal components, including printed circuit boards for electronic assemblies, sensor arrays, antennas, and connectors, as well as providing a mechanical attachment point for internal components. 
     The drive system  301  may include motors  322 ,  324  and wheels  318 ,  320 . The motors  322 ,  324  may connect to the wheels  318 ,  320 , respectively, each through an associated shaft, axle, and gear drive (not shown). The perimeter of wheels  318 ,  320  may mechanically contact the inner surface  304  at essentially two points. These points may provide the drive mechanism of the spherical housing  302 , or ball, and may be coated with a material to increase friction and reduce slippage between the wheels  318 ,  320  and the inner surface  304 . For example, the wheels  318 ,  320  may include silicone rubber tires. 
     A biasing mechanism  315  may actively force the wheels  318 ,  320  against the inner surface  304 . A spring  312  and a spring end  310  may comprise the biasing mechanism  315 . More specifically, the spring  312  and the spring end  310  may be positioned to contact the inner surface  304  at a point diametrically opposed to the wheels  318 ,  320 . The spring  312  and the spring end  310  may provide additional contact force to reduce slippage of the wheels  318 ,  320 , particularly in situations where the interior mechanism is not positioned with the wheels at the bottom and where gravity does not provide adequate force to prevent the drive wheels  318 ,  320  from slipping. The spring  312  may provide a force to press the wheels  318 ,  320  and the spring end  310  against the inner surface  304 . 
     The spring end  310  may provide near-frictionless contact with the inner surface  304 . The spring end  310  may be a rounded surface configured to mirror a low-friction contact region at all contact points with the inner surface  304 . The rounded surface may include one or more bearings to further reduce friction at the contact point where spring end  310  moves along inner surface  304 . The spring  312  and the spring end  310  may be made of a non-magnetic material to avoid interference with sensitive magnetic sensors. However, the spring end  310  may include one or more magnetic components to magnetically couple to an external accessory device  330 . 
     The spring  312  may have a spring constant such that the wheels  318 ,  320  and the spring end  310  may be constantly engaged to the inner surface  304  of the spherical housing  302 . As such, much of the power from the motors  322 ,  324  may be transferred directly to rotating the spherical housing  302 , as opposed to causing the internal components (e.g., the biasing mechanism  315  and internal drive system  301 ) to slant or pitch. Thus, while motion of the self-propelled device  300  may be caused, at least partially, by pitching the internal components (and therefore the center of mass of the device), motion may also be directly caused by active force of the wheels  318 ,  320  against the inner surface  304  of the spherical housing  302  (via the biasing mechanism  315 ) and direct transfer of electrical power from the motors  322 ,  324  to the wheels  318 ,  320 . The pitch of the biasing mechanism  315  may be substantially reduced, and remain substantially constant (e.g., substantially perpendicular to the external surface on which the self-propelled device  300  moves). The pitch of the biasing mechanism  315  may increase (e.g., to over 45 degrees) during periods of hard acceleration or deceleration. Furthermore, under normal operating conditions, the pitch of the biasing mechanism  315  may remain stable or subtly vary (e.g., within 10° to 15°). 
     The spring end  310  may be formed of a magnetic metal attracted to a magnet. Such metals may include iron, nickel, cobalt, gadolinium, neodymium, samarium, and/or other metal alloys containing proportions of these metals. Alternatively, the spring end  310  may include a substantially frictionless contact portion, in contact with the inner surface  304  of the spherical housing  302 , and a magnetically interactive portion, in contact or non-contact with the inner surface  304 , including the above metals or metal alloys. The substantially frictionless contact portion can be comprised of an organic polymer such as a thermoplastic or thermosetting polymer. 
     Alternatively, the spring end  310  may be a magnet, such as a polished neodymium permanent magnet. The spring end  310  may produce a magnetic field extending beyond the outer surface of the spherical housing  302  to magnetically couple with the external accessory device  330 . Also, the spring end  310  may be comprised of a substantially frictionless contact portion and have a magnet included therein. 
     The magnetic component of the self-propelled device  300  may be included on any internal component, such as the spring  312  or the carrier  314 , or an additional component coupled to the biasing mechanism  315  or the carrier. The external accessory device  330  may include a magnetic component  332  to magnetically couple with the biasing mechanism  315  (e.g., the spring end  310 ). The magnetic component  332  may comprise a permanent magnet, such as a neodymium magnet. The magnetic component  332  may magnetically couple to the spring end  310 . As such, the magnetic field produced by the magnetic component  332  may extend through the spherical housing  302  to remain in magnetic contact with the spring end  310 . The magnetic component  332  of the external accessory device  330  may comprise a magnetic metal attracted to a magnet comprising the spring end  310 . 
     One or more of the spring ends  310  and the magnetic components may be comprised of any number of electro and/or permanent magnets. Such magnets may be irregular in shape to provide added magnetic stability upon motion of the self-propelled device  300 . The magnetic component  332  of the external accessory device  330  may be a single magnetic strip or multiple magnetic strips including one or more tributary strips to couple with a single or multiple correspondingly shaped magnets on the spring end  310 . Multiple magnets may be dispersed through the external accessory device  330  and the spring end  310  to provide additional stability. 
     The spring end  310  and external accessory device  330  may be in a stable magnetically repulsive state as the self-propelled device  300  moves. Either the magnetic component  332  or the spring end  310  may further include a superconductor material to substantially eliminate dynamic instability of a repelling magnetic force and allow stable magnetic levitation of the external accessory device  330  in relation to the spring end  310  while the spherical housing  302  slides therebetween. A diamagnetic material may be included in one or more of the self-propelled device  300 , spring end  310 , and/or the external accessory device  330  for stable magnetic levitation. Thus, without the use of guiderails or a magnetic track, the self-propelled device  300  may maneuver in any direction with the external accessory device  330  remaining in a substantially constant position along a vertical axis of the self-propelled device. 
     The external accessory device  330  may be in the form of any shape and may comprise any suitable material. A contact surface  334  of the external accessory device  330 , or a surface closest to the outer surface of the spherical housing  302  (during magnetic interaction), may correspond to the outer surface of the spherical housing  304 . Both the spherical housing  302  of the self-propelled device  300  and the external accessory device  330 , namely the contact surface  334 , may have substantially equivalent radii of curvature. This radius may be on the order of 10 cm to 30 cm. However, the radius may one meter up to the size of a human transportation vehicle and beyond. As such, magnetic coupling or interaction may be achieved using powerful electromagnets disposed within the self-propelled device  300  to couple with the external accessory device  330 , which may perform actions, carry payload, include a novel design, represent a character or figure, etc. 
     The contact surface  334  of the external accessory device  330  may be formed or coated with a substantially frictionless material, such as a synthetic compound or suitable polymer. Other suitable compounds may include polytetrafluoroethylene (PTFE), polyoxymethylene (POM), ultra-repellant surfaces, and/or liquid-impregnated surfaces and materials, such as slippery liquid infused porous surface (SLIPS). Further examples of substantially frictionless surfaces or coatings may include “ceramic alloys,” or “cermets,” which may be created by combining a metal alloy with a ceramic compound. A metal/ceramic alloy comprised of boron, aluminum, and magnesium (AlMgB 14 ) may be combined with the cermetic compound of titanium diboride (TiB 2 ) to provide a near-frictionless coating for the contact surface  334  of the external accessory device  330 . 
     The outer surface of the spherical housing  302  may comprise of any of the above substantially frictionless coatings or compounds discussed with respect to the contact surface  334  of the external accessory device  330 . Any combination of substantially frictionless coatings or compounds may be incorporated with respect to the outer surface of the spherical housing  302  and the contact surface  334  of the external accessory device  330 . 
     The spherical housing  302  may be formed to include an inner surface  304  more conducive to providing added friction using, for example, a rubber compound or other suitable synthetic compound, such as a silicone. The spherical housing  302  may include an outer surface having near-frictionless properties using coatings or compounds, as discussed above. 
     When the self-propelled device  300  moves, the external accessory device  330  may remain magnetically coupled to the spring end  310  at a substantially constant position on top of the self-propelled device  300 . As such, while the self-propelled device  300  is being maneuvered, the biasing mechanism  315  may have a variable tilt angle relative to the plane of motion that remains somewhat minimal, but in most cases, does not typically exceed 45°, except during periods of relatively extreme acceleration or deceleration. However, during continuous and stable maneuvering of the self-propelled device  300 , the tilt of the biasing mechanism  315  may be closer to naught, or within 10°. During maneuvering, the azimuth may vary at any angle depending on independent power transferred from the motors  322 ,  344  to the wheels  318 ,  320 . 
       FIG. 5  illustrates an example conventional technique for causing motion of a self-propelled spherical device  400 . The self-propelled device  400  may have a sensor platform  404 , center of rotation  402  and center of mass  406  and contact a planar surface  412 . The drive mechanism for the device  400  may comprises two independently-controlled wheeled actuators  408  in contact with the inner surface of the spherical housing of the device  400 . 
     To achieve continuous motion at a constant velocity, the displacement of the center of mass  406  relative to center of rotation  402  may be maintained by action of wheeled actuators  408 . The displacement of the center of mass  406  relative to center of rotation  402  may be difficult to measure. Thus, it may be difficult to obtain feedback for a closed-loop controller to maintain constant velocity. However, the displacement may be proportional to the tilt angle  410  between the sensor platform  404  and the planar surface  412 . The tilt angle  410  may be sensed or estimated from a variety of sensor inputs. Therefore, the speed controller for the device  400  may be implemented to use the tilt angle  410  to regulate speed for the wheeled actuators  408  and maintain a constant speed across the planar surface  412 . The speed controller may determine the desired angle  410  to produce the desired speed and the desired angle set-point may be an input to a closed loop controller regulating the drive mechanism. This speed control technique may be extended to control turns and rotations of the spherical device  400  with feedback of appropriate sensed angles and angular rates. 
       FIG. 6  schematically shows a computer system upon which the above examples may be implemented. One or more components discussed with respect to the system  100  of  FIG. 2  may be performed by the system  500  of  FIG. 6 . The system  100  may also be implemented using a combination of multiple computer systems. The computer system  500  may include processing resources  510 , a main memory  520 , read only memory (ROM)  530 , a storage device  540 , and a communication interface  550 . The computer system  500  may include at least one processor  510  and a main memory  520 , such as a random access memory (RAM) or other dynamic storage device with instructions  522  to be executed by the processor  510 . The main memory  520  also may store temporary variables or other intermediate information during execution of instructions executed by the processor  510 . The computer system  500  may also include a read only memory (ROM)  530  or other static storage device for storing static information and instructions for the processor  510 . A storage device  540 , such as a magnetic disk or optical disk, may store information and instructions. For example, the storage device  540  may correspond to a computer-readable medium that triggers logic for maneuvering the self-propelled device  100 ,  200 ,  300 ,  400 . 
     The communication interface  550  may enable the computer system  500  to communicate with a controller device  580  via an established network link  552  (wireless and/or hardwire). Using the network link  552 , the computer system  500  may receive command instructions for maneuvering the self-propelled device  100 ,  200 ,  300 ,  400 . 
     The computer system  500  may implement the techniques described herein. Those techniques may be performed by the computer system  500  in response to the processor  510  executing one or more sequences of one or more instructions contained in the main memory  520 . Such instructions may be read into the main memory  520  from another machine-readable medium, such as the storage device  540 . Execution of the instructions contained in the main memory  520  may cause the processor  510  to perform the process steps described herein. Hard-wired circuitry may be used in place of, or in combination with, software instructions to implement examples described herein. Thus, the examples described are not limited to any specific combination of hardware circuitry and software. 
     The spherical shape of this concept may transform the way autonomous or any vehicles move. The spherical, shape may positively contribute to the safety, maneuverability, and comfort to match the demands of autonomous and any mobility. The multi-orientation tires may move in all directions, contributing to safety and comfort for passengers, as well as coping with any space limitations. Active anti-sliding technology may allow the tire to move as needed to reduce sliding from potential hazards, such as black ice or sudden obstacles. 
     The spherical shape may provide a smooth ride to address passenger comfort. The spherical shape may create a fluid, lateral movement to help the car overtake any obstacles without changing its driving direction. Further, because 360 degree turns are possible with the spherical shape, anticipated parking constrictions may be overcome, as less space is needed for cars fitted with spherical tires to pull into parking spots. Assuming public parking areas play the same role in the future, this could significantly increase the capacity of public parking areas without increasing their overall size. 
     A spherical tire/drive apparatus in accordance with the present invention may rely on magnetic levitation to carry the load of a vehicle. Such a spherical tire may be suspended from the vehicle by magnetic fields similar to magnetic levitation trains, which result in increased comfort and reduced noise for users. Such an apparatus may allow total integration of moving parts into the body of the spherical tire and/or the body of the vehicle (e.g., no moving parts or critical surfaces exposed to the environment). Further, a recharging system, through magnetic induction, may be totally isolated from the external environment. 
     The apparatus may simplify manufacturing and assembly as well as eliminate some components entirely, such as rims, steering system, axles, shock absorbers, springs, etc., thereby also reducing weight and cost. The magnetic levitation and control may eliminate all direct contact between the vehicle and the road thereby mitigating vibration, noise, and other undesired effects of direct contact. 
     The spherical tire may have several spherical tread layers, which may or may not mimic the functionality of conventional tire treads. The structure interior to the spherical tread may be an auxetic or normal foam material which is strong enough to take the load of the vehicle, but flexible enough to allow the tread to deform and generate an appropriate contact patch with the road. 
     A magnetic material layer and/or a diamagnetic layer may be located interior to the spherical tread structure for providing the levitation and control between tires and the vehicle. The vehicle may be permanently levitated away from the spherical tires or the alternate levitation, so that the vehicle/tires expend no energy when the vehicle is at rest and unused. Diamagnetic materials may generate a magnetic field only if they themselves are brought into an active magnetic field. 
     One part or all of the energy for the magnetic fields may come from a battery inside the spherical tire or a battery in the vehicle. The battery in the spherical tire may be charged and recharged by inductive transfer from a battery in the vehicle. 
     An electric motor inside the spherical tire may provide the tire and the vehicle mobility, similar to that described above. Alternatively, magnetic pulses may emote the tire and vehicle. The load bearing portion of the spherical tire may be constructed of graphene layers or layers of carbon-fiber. 
     As shown in  FIG. 1 , a support assembly  1000  for a vehicle  901  in accordance with the present invention may include at least two spherical tires  1010 , a drive system  1100  emoting the tires  1010  such that the vehicle  901  may be transported along a road surface. The vehicle  901  may be a car, golf cart, motorcycle, military transport, etc. The drive system  110  magnetically levitates the vehicle  901  a first predetermined distance from the tires  1010  and magnetically maintains the drive system  110  at a constant orientation relative to the road surface. A first part  1110  of the drive system  1100  may magnetically levitate itself a second predetermined distance from an inner surface  1020  of the tires  1010  such that the part  1110  is entirely enclosed within an interior space  1025  of each tire  1010 . Another part  1120  of the drive system  1100  may magnetically levitate  20  the vehicle  901  the first predetermined distance from the tires  1010 . Either part  1110  or  1120  of the drive system  1100  may be a magnetically passive component that responds to variations of a magnetic field. A corresponding other part  1120  or  1110  of the drive system  1100  may be a magnetically active component that generates variations in the magnetic field. Either component  1110 ,  1120  may itself generate a constant magnetic field. 
     The spherical tires  1010  may include several spherical layers  1030 . Some of the layers  1030  may function similarly to layers of a conventional pneumatic tire, such as the tread, the belts, the overlay, the carcass, etc. At least one of the layers  1035  may include a material responsive to a magnetic field variations such that each of the tires  1010  may be controllably rotated about a spherical center  1011  of the tires relative to the vehicle  901 , the drive system  1100 , and the road surface. 
     In the ongoing effort to further improve tire design, there is a tension among tire performance, rolling resistance (or fuel economy), and treadwear. Typically, for use in a consumer tire, a tread compound is designed to optimize these three performances. However, efforts to improve fuel economy often lead to compromises in performance and/or treadwear. For higher performance tires, the achievement better performance often comes with a compromise in treadwear and/or fuel economy. There is a desire therefore to develop elastomeric tread compounds, such as the spherical tread layer  1030  in  FIG. 1 , that may improve performance, fuel economy, and/or treadwear with little or no compromise in the other two. 
     Aqueous solutions of a variety of polar aprotic polymers exhibit a lower critical solution temperature (LCST). When these solutions are heated above the LCST, the intramolecular hydrogen bonding is preferred compared to the hydrogen bonding with water molecules. This leads to collapse of the polymer coils and a precipitation of the polymer from solution. This phase transition is reversible so that the polymer redissolves when the temperature is again decreased below the LCST. An example of an LCST polymer is poly(N-isopropyl acrylamide) (PNIPAM). Aqueous solutions of this polymer exhibit an LCST transition at about 33° C. 
     The combination of LCST polymers with elastomers offers the possibility of better control of elastomer performance in a variety of applications where the elastomer is exposed to water. Simple mixing of an LCST polymer with an elastomer results in a compound that will experience macrophase separation due to the lack of covalent bonds between the LCST polymer and the elastomer. Such a macrophase separation may have a detrimental effect on tread compound properties. 
     The spherical tread layer  1030  may include a rubber composition comprising: a copolymer comprising a polymeric backbone chain derived from a monomer comprising at least one conjugated diene monomer and optionally at least one vinyl aromatic monomer; and polymeric sidechains bonded to the backbone chain, the sidechains comprising a polymer capable of exhibiting a lower critical solution temperature (LCST); optionally, at least one additional diene based elastomer; and a filler selected from the group consisting of carbon black and silica. 
     The rubber composition may include a copolymer comprising a polymeric backbone chain derived from a monomer comprising at least one conjugated diene monomer and optionally at least one vinyl aromatic monomer; and polymeric sidechains bonded to the backbone chain, the sidechains comprising a polymer capable of exhibiting a lower critical solution temperature (LCST). 
     In one example, the copolymer may have the structure of Formula I: 
     
       
         
         
             
             
         
       
     
     where X is a polymer derived from a monomer comprising at least one conjugated diene monomer and optionally at least one vinyl aromatic monomer; Z is a polymer capable of exhibiting a lower critical solution temperature (LCST); Y is a divalent group bonded to both X and Z; and n is the number of Y—Z] groups bonded to X. 
     In one example, the polymer X is a diene based elastomer comprising at least one carbon-carbon double bond. The phrases “rubber or elastomer containing olefinic unsaturation” or “diene based elastomer” as used herein are equivalent and are intended to include both natural rubber and its various raw and reclaim forms as well as various synthetic rubbers. In the description of this invention, the terms “rubber” and “elastomer” may be used interchangeably, unless otherwise prescribed. The terms “rubber composition,” “compounded rubber” and “rubber compound” are used interchangeably to refer to rubber which has been blended or mixed with various ingredients and materials and such terms are well known to those having skill in the rubber mixing or rubber compounding art. Representative synthetic rubbers are the homopolymerization products of butadiene and its homologues and derivatives, for example, methylbutadiene (i.e., isoprene), dimethylbutadiene and pentadiene as well as copolymers such as those formed from butadiene or its homologues or derivatives with other unsaturated monomers. Among the latter are acetylenes, for example, vinyl acetylene; olefins, for example, isobutylene, which copolymerizes with isoprene to form butyl rubber; vinyl compounds, for example, acrylic acid, acrylonitrile (which polymerize with butadiene to form NBR), methacrylic acid and styrene, the latter compound polymerizing with butadiene to form SBR, as well as vinyl esters and various unsaturated aldehydes, ketones and ethers, e.g., acrolein, methyl isopropenyl ketone and vinylethyl ether. Specific examples of synthetic rubbers include neoprene (polychloroprene), polybutadiene (including cis-1,4-polybutadiene), polyisoprene (including cis-1,4-polyisoprene), butyl rubber, halobutyl rubber such as chlorobutyl rubber or bromobutyl rubber, styrene/isoprene/butadiene rubber, copolymers of 1,3-butadiene or isoprene with monomers such as styrene, acrylonitrile and methyl methacrylate, as well as ethylene/propylene terpolymers, also known as ethylene/propylene/diene monomer (EPDM), and in particular, ethylene/propylene/dicyclopentadiene terpolymers. Additional examples of rubbers which may be used include alkoxy-silyl end functionalized solution polymerized polymers (SBR, PBR, IBR and SIBR), silicon-coupled and tin-coupled star-branched polymers. The preferred rubber or elastomers are polyisoprene (natural or synthetic), polybutadiene and SBR. 
     In another example, an emulsion polymerization derived styrene/butadiene (E-SBR) might be used having a relatively conventional styrene content of about 20 to about 28 percent bound styrene or, for some applications, an E-SBR having a medium to relatively high bound styrene content, namely, a bound styrene content of about 30 to about 45 percent. 
     By emulsion polymerization prepared E-SBR, it is meant that styrene and 1,3-butadiene are copolymerized as an aqueous emulsion. The bound styrene content can vary, for example, from about 5 to about 50 percent. In one aspect, the E-SBR may also contain acrylonitrile to form a terpolymer rubber, as E-SBAR, in amounts, for example, of about 2 to about 30 weight percent bound acrylonitrile in the terpolymer. 
     Emulsion polymerization prepared styrene/butadiene/acrylonitrile copolymer rubbers containing about 2 to about 40 weight percent bound acrylonitrile in the copolymer may also be contemplated as diene based rubbers for use in this invention. The solution polymerization prepared SBR (S-SBR) may have a bound styrene content in a range of about 5 to about 50, preferably about 9 to about 36, percent. The S-SBR can be conveniently prepared, for example, by organo lithium catalyzation in the presence of an organic hydrocarbon solvent. 
     In another example, cis 1,4-polybutadiene rubber (BR) may be used. Such BR may be prepared, for example, by organic solution polymerization of 1,3-butadiene. The BR may be conveniently characterized, for example, by having at least a 90 percent cis 1,4-content. The term “phr” as used herein, refers to “parts by weight of a respective material per 100 parts by weight of rubber, or elastomer.” 
     In one example, the polymer Z having a lower critical solution temperature (LCST) may include homopolymers and copolymers of various second monomers known to have LCST behavior, including but not limited to polymers of: acrylamides and substituted acrylamides, methacrylamides and substituted methacrylamids, acrylic acids and substituted acrylic acids, methacrylic acids and substituted methacrylic acids, vinyl alkyl ethers and substituted vinyl alkyl ethers, vinyl caprolactams and substituted vinyl caprolactams, and other monomers known to lead to polymers with LCST behavior, such as oligo(ethylene glycol) methacrylate and 2-(2-methoxyethoxy) ethyl methacrylate, and the like. 
     By “capable of exhibiting a lower critical solution temperature (LCST),” it is meant that in the presence of water, the polymer Z associates with the water to form a water-swollen polymer phase, wherein the water-swollen polymer phase will show an LCST transition when heated from a temperature below the LCST to a temperature above the LCST. The polymer Z is accordingly capable of exhibiting an LCST when the polymer Z exists as a side chain on the graft copolymer. 
     In one example, the polymer Z is a polymer of a second monomer of Formula II: 
     
       
         
         
             
             
         
       
     
     where R 1  and R 2  are independently selected from the group consisting of hydrogen, C2 to C6 linear alkyl, C2 to C6 branched alkyl, and C3 to C6 cycloalkyl, with the proviso that at least one of R 1  and R 2  is not hydrogen. 
     In one example, Z may be Formula (III) 
     
       
         
         
             
             
         
       
     
     where R 1  and R 2  are independently selected from the group consisting of hydrogen, C2 to C6 linear alkyl, C2 to C6 branched alkyl, and C3 to C6 cycloalkyl, with the proviso that at least one of R 1  and R 2  is not hydrogen, and m is the degree of polymerization of the hydrocarbon chain. 
     In one example, the polymer Z is a polymer of an N-substituted acrylamide derivative. 
     In one example, the polymer Z is a polymer of N-isopropylacrylamide, N-cyclopropylacrylamide, or N, N-diethylacrylamide. 
     In one example, the polymer Z capable of exhibiting a lower critical solution temperature has a weight average molecular weight ranging from about 500 to about 20000 g/gmol. 
     In one example, the polymer Z may be capable of exhibiting a lower critical solution temperature and have a lower critical solution temperature in a range of from about 0° C. to about 100° C. 
     In one example, the copolymer comprises from about 1 to about 20 weight percent Z. Y may be a divalent group bonded to both X and Z. In one example, Y is sulfur or oxygen. In one example, Y is sulfur. 
     Generally, Y originates as a terminal functional group of the polymer Z capable of reacting with a carbon-carbon double bond of the polymer X. Thus, as it exists in the copolymer Y links X to Z. In one example, the terminal functional group is a thiol group. Such a terminal functional group may be incorporated into the polymer Z during polymerization, for example, through use of a suitable chain transfer agent or terminating agent as is known in the art. The number n of Y—Z] groups may be bonded to X ranges from about 2 to about 30 in a given copolymer molecule. 
     The copolymer may be produced by various methods. In one example, the copolymer may be produced by functionalizing the polymer X with side chains of LCST polymer Z to produce a graft copolymer with an elastomer backbone and LCST polymer sidechains. A convenient way for the functionalization of a variety of elastomers is the thiol-ene reaction during which alkene moieties being present in the elastomers are transformed into thioethers by reaction with thiols. This reaction may proceed with vinyl groups as they are present in styrene-butadiene rubbers, butadiene rubbers, and polyisoprene rubbers. In order to allow the functionalization of the elastomers, the LCST polymers may feature thiol end groups. These can be introduced by reaction of thiocarbonylthio endgroups with nucleophilic agents. Polymers exhibiting thiocarbonylthio end groups can be produced by reversible addition-fragmentation chain transfer (RAFT) polymerization. One reaction scheme describes the use of PNIPAM as LCST polymer, however, this invention is not limited to that as any LCST polymer with a reactive end group, which for example can be produced by RAFT polymerization, can be used for the functionalization of the elastomer. 
     A first step of the method to produce the graft copolymer may be obtaining a first polymer comprising at least one carbon-carbon double bond. A second step of the method may be obtaining a second polymer. The second polymer may exhibit a lower critical solution temperature (LCST) and comprise a terminal functional group capable of reacting with the carbon-carbon double bond of the first polymer. In one example, the second polymer is obtained by polymerizing a second monomer in the presence of a thiocarbonylthio RAFT chain transfer agent to form a polymer comprising a terminal thiocarbonylthio group; and cleaving the terminal thiocarbonylthio group to a thiol group to form the second polymer comprising a terminal thiol group. 
     In one example, the terminal functional group of the second polymer is incorporated in the second polymer during polymerization through the mechanism of reversible addition-fragmentation chain transfer (RAFT). More details of the RAFT polymerization mechanism may be found by reference to Moad et al.,  Aust. J. Chem.  2005, 58, 379-410. RAFT polymerization of free-radical polymerizable monomers may be accomplished in the presence of a thiocarbonylthio RAFT chain transfer agent of Formula (IV): 
     
       
         
         
             
             
         
       
     
     where R 3  is a free radical leaving group able to reinitiate polymerization, and Q is a functional group that influences the rate of radical addition and fragmentation. Suitable thiocarbonylthio RAFT chain transfer agents include dithioesters, trithiocarbonates, dithiocarbamates, and xanthates. In one embodiment, the thiocarbonylthio chain transfer agent is a trithiocarbonate. In one embodiment, the thiocarbonylthio chain transfer agent is selected from the group consisting of S-1-dodecyl-S-(αα′-dimethyl-α″-acetic acid) trithiocarbonate and 4-cyano-4-dodecylsulfanylthiocarbonylsulfanyl-4-methyl butyric acid. 
     Upon RAFT polymerization in the presence of a suitable thiocarbonylthio chain transfer agent, the chain-terminated polymer has the Formula (V): 
     
       
         
         
             
             
         
       
     
     where P n  represents the polymer chain exhibiting a LCST. 
     The chain terminated polymer of formula V may then be reacted with a suitable nucleophile to cleave the C—S linkage to obtain a second polymer of formula (VI) having a terminal thiol group of Formula (VI): 
       H—S—P n   (VI)
 
     In one example, the chain terminated polymer of Formula V is treated by aminolysis to obtain the thiol-terminated polymer of Formula VI. 
     A third step of the method may be reacting the second polymer with the first polymer to form a graft copolymer, the graft copolymer comprising a backbone derived from the first polymer and sidechains derived from the second polymer. During reacting of the second polymer with the first polymer, a second polymer may be linked to the first polymer through reaction of a terminal functional group of the second polymer with the unsaturated carbon-carbon bond of the first polymer. In one example, the thiol-terminated second polymer may be reacted with the first polymer in the presence of a free-radical initiator via a thiol-ene reaction, see for example  Macromolecules  2008, 41, 9946-9947. In one example, the free-radical initiator is selected from the group consisting of 2,4,6-Trimethylbenzoyldiphenylphosphine oxide and azobisisobutyonitrile (AIBN). 
     The rubber composition may optionally include, in addition to the copolymer comprising a polymer having a lower critical solution temperature (LCST), one or more rubbers or elastomers containing olefinic unsaturation. The phrases “rubber or elastomer containing olefinic unsaturation” or “diene based elastomer” are intended to include both natural rubber and its various raw and reclaim forms as well as various synthetic rubbers. In the description of this invention, the terms “rubber” and “elastomer” may be used interchangeably, unless otherwise prescribed. The terms “rubber composition,” “compounded rubber” and “rubber compound” are used interchangeably to refer to rubber which has been blended or mixed with various ingredients and materials and such terms are well known to those having skill in the rubber mixing or rubber compounding art. Representative synthetic polymers are the homopolymerization products of butadiene and its homologues and derivatives, for example, methylbutadiene, dimethylbutadiene and pentadiene as well as copolymers such as those formed from butadiene or its homologues or derivatives with other unsaturated monomers. Among the latter are acetylenes, for example, vinyl acetylene; olefins, for example, isobutylene, which copolymerizes with isoprene to form butyl rubber; vinyl compounds, for example, acrylic acid, acrylonitrile (which polymerize with butadiene to form NBR), methacrylic acid and styrene, the latter compound polymerizing with butadiene to form SBR, as well as vinyl esters and various unsaturated aldehydes, ketones and ethers, e.g., acrolein, methyl isopropenyl ketone and vinylethyl ether. Specific examples of synthetic rubbers include neoprene (polychloroprene), polybutadiene (including cis-1,4-polybutadiene), polyisoprene (including cis-1,4-polyisoprene), butyl rubber, halobutyl rubber such as chlorobutyl rubber or bromobutyl rubber, styrene/isoprene/butadiene rubber, copolymers of 1,3-butadiene or isoprene with monomers such as styrene, acrylonitrile and methyl methacrylate, as well as ethylene/propylene terpolymers, also known as ethylene/propylene/diene monomer (EPDM), and in particular, ethylene/propylene/dicyclopentadiene terpolymers. Additional examples of rubbers which may be used include alkoxy-silyl end functionalized solution polymerized polymers (SBR, PBR, IBR and SIBR), silicon-coupled and tin-coupled star-branched polymers. The preferred rubber or elastomers are polyisoprene (natural or synthetic), polybutadiene and SBR. 
     The at least one additional rubber may be of at least two of diene based rubbers. For example, a combination of two or more rubbers may be cis 1,4-polyisoprene rubber (natural or synthetic, although natural is preferred), 3,4-polyisoprene rubber, styrene/isoprene/butadiene rubber, emulsion and solution polymerization derived styrene/butadiene rubbers, cis 1,4-polybutadiene rubbers and emulsion polymerization prepared butadiene/acrylonitrile copolymers. 
     In one example, an emulsion polymerization derived styrene/butadiene (E-SBR) might be used having a relatively conventional styrene content of about 20 to about 28 percent bound styrene or, for some applications, an E-SBR having a medium to relatively high bound styrene content, namely, a bound styrene content of about 30 to about 45 percent. 
     By emulsion polymerization prepared E-SBR, it is meant that styrene and 1,3-butadiene are copolymerized as an aqueous emulsion. Such are well known to those skilled in such art. The bound styrene content can vary, for example, from about 5 to about 50 percent. In one aspect, the E-SBR may also contain acrylonitrile to form a terpolymer rubber, as E-SBAR, in amounts, for example, of about 2 to about 30 weight percent bound acrylonitrile in the terpolymer. 
     Emulsion polymerization prepared styrene/butadiene/acrylonitrile copolymer rubbers containing about 2 to about 40 weight percent bound acrylonitrile in the copolymer are also contemplated as diene based rubbers for use in this invention. The solution polymerization prepared SBR (S-SBR) may have a bound styrene content in a range of about 5 to about 50, preferably about 9 to about 36, percent. The S-SBR may be prepared, for example, by organo lithium catalyzation in the presence of an organic hydrocarbon solvent. In one example, cis 1,4-polybutadiene rubber (BR) may be used. Such BR can be prepared, for example, by organic solution polymerization of 1,3-butadiene. The BR may be characterized, for example, by having at least a 90 percent cis 1,4-content. The term “phr” as used herein, and according to conventional practice, refers to “parts by weight of a respective material per 100 parts by weight of rubber, or elastomer.” 
     The rubber composition may also include up to 70 phr of processing oil. Processing oil may be included in the rubber composition as extending oil typically used to extend elastomers. Processing oil may also be included in the rubber composition by addition of the oil directly during rubber compounding. The processing oil used may include both extending oil present in the elastomers, and process oil added during compounding. Suitable process oils include various oils as are known in the art, including aromatic, paraffinic, naphthenic, vegetable oils, and low PCA oils, such as MES, TDAE, SRAE and heavy naphthenic oils. Suitable low PCA oils include those having a polycyclic aromatic content of less than 3 percent by weight as determined by the IP346 method. Procedures for the IP346 method may be found in  Standard Methods for Analysis  &amp;  Testing of Petroleum and Related Products  and  British Standard  2000  Parts,  2003, 62nd edition, published by the Institute of Petroleum, United Kingdom. 
     The rubber composition may include from about 10 to about 150 phr of silica. In another example, from 20 to 80 phr of silica may be used. Siliceous pigments may be used in the rubber compound, including pyrogenic and precipitated siliceous pigments (silica). In one example, precipitated silica is used. Siliceous pigments employed may be precipitated silicas such as, for example, those obtained by the acidification of a soluble silicate, e.g., sodium silicate. 
     Such silicas may be characterized, for example, by having a BET surface area, as measured using nitrogen gas. In one embodiment, the BET surface area may be in the range of about 40 to about 600 square meters per gram. In another example, the BET surface area may be in a range of about 80 to about 300 square meters per gram. The BET method of measuring surface area is described in the  Journal of the American Chemical Society , Volume 60, Page 304 (1930). Silica may also be characterized by having a dibutylphthalate (DBP) absorption value in a range of about 100 to about 400, alternatively about 150 to about 300. Silica may have an average ultimate particle size, for example, in the range of 0.01 to 0.05 micron as determined by the electron microscope, although the silica particles may be even smaller, or possibly larger, in size. Various commercially available silicas may be used, such as, only for example herein, and without limitation, silicas commercially available from PPG Industries under the Hi-Sil trademark with designations 210, 243, etc.; silicas available from Rhodia, with, for example, designations of Z1165MP and Z165GR and silicas available from Degussa AG with, for example, designations VN2 and VN3, etc. 
     Carbon blacks may be used as a filler in an amount ranging from 10 to 150 phr. In another example, from 20 to 80 phr of carbon black may be used. Representative examples of such carbon blacks include N110, N121, N134, N220, N231, N234, N242, N293, N299, N315, N326, N330, N332, N339, N343, N347, N351, N358, N375, N539, N550, N582, N630, N642, N650, N683, N754, N762, N765, N774, N787, N907, N908, N990 and N991. These carbon blacks have iodine absorptions ranging from 9 to 145 g/kg and DBP number ranging from 34 to 150 cm 3 /100 g. 
     Other fillers may be used in the rubber composition including, but not limited to, particulate fillers including ultra high molecular weight polyethylene (UHMWPE), crosslinked particulate polymer gels and plasticized starch composite filler. Other fillers may be used in an amount ranging from 1 to 30 phr. 
     In one example, the rubber composition may contain a sulfur containing organosilicon compound. Examples of suitable sulfur containing organosilicon compounds are of the Formula (VII): 
       Z-Alk-S n -Alk-Z  (VII)
 
     in which Z is selected from the group consisting of 
     
       
         
         
             
             
         
       
     
     where R 4  is an alkyl group of 1 to 4 carbon atoms, cyclohexyl or phenyl; R 5  is alkoxy of 1 to 8 carbon atoms, or cycloalkoxy of 5 to 8 carbon atoms; Alk is a divalent hydrocarbon of 1 to 18 carbon atoms and n is an integer of 2 to 8. 
     In one example, the sulfur containing organosilicon compounds are the 3,3′-bis(trimethoxy or triethoxy silylpropyl) polysulfides. In one example, the sulfur containing organosilicon compounds are 3,3′-bis(triethoxysilylpropyl) disulfide and/or 3,3′-bis(triethoxysilylpropyl) tetrasulfide. Therefore, as to formula VII, Z may be 
     
       
         
         
             
             
         
       
     
     where R 5  is an alkoxy of 2 to 4 carbon atoms, alternatively 2 carbon atoms; alk is a divalent hydrocarbon of 2 to 4 carbon atoms, alternatively with 3 carbon atoms; and n is an integer of from 2 to 5, alternatively 2 or 4. 
     In one example, the sulfur containing organosilicon compounds includes 3-(octanoylthio)-1-propyltriethoxysilane, CH 3 (CH 2 ) 6 C(═O)—S—CH 2 CH 2 CH 2 Si(OCH 2 CH 3 ) 3 , which is available commercially as NXT™ from Momentive Performance Materials. In another example, the sulfur containing organosilicon compound is Si-363. The amount of the sulfur containing organosilicon compound in a rubber composition may vary depending on the level of other additives that are used. Generally speaking, the amount of the compound may range from 0.5 to 20 phr. In one example, the amount will range from 1 to 10 phr. 
     It is readily understood by those having skill in the art that the rubber composition would be compounded by methods generally known in the rubber compounding art, such as mixing the various sulfur-vulcanizable constituent rubbers with various commonly used additive materials such as, for example, sulfur donors, curing aids, such as activators and retarders and processing additives, such as oils, resins including tackifying resins and plasticizers, fillers, pigments, fatty acid, zinc oxide, waxes, antioxidants and antiozonants and peptizing agents. As known to those skilled in the art, depending on the intended use of the sulfur vulcanizable and sulfur-vulcanized material (rubbers), the additives mentioned above are selected and commonly used in conventional amounts. Representative examples of sulfur donors include elemental sulfur (free sulfur), an amine disulfide, polymeric polysulfide and sulfur olefin adducts. In one embodiment, the sulfur-vulcanizing agent is elemental sulfur. The sulfur-vulcanizing agent may be used in an amount ranging from 0.5 to 8 phr, alternatively with a range of from 1.5 to 6 phr. Typical amounts of tackifier resins, if used, comprise about 0.5 to about 10 phr, usually about 1 to about 5 phr. Typical amounts of processing aids comprise about 1 to about 50 phr. Typical amounts of antioxidants comprise about 1 to about 5 phr. Representative antioxidants may be, for example, diphenyl-p-phenylenediamine and others, such as, for example, those disclosed in  The Vanderbilt Rubber Handbook  (1978), Pages 344 through 346. Typical amounts of antiozonants comprise about 1 to 5 phr. Typical amounts of fatty acids, if used, which can include stearic acid comprise about 0.5 to about 3 phr. Typical amounts of zinc oxide comprise about 2 to about 5 phr. Typical amounts of waxes comprise about 1 to about 5 phr. Often microcrystalline waxes are used. Typical amounts of peptizers comprise about 0.1 to about 1 phr. Typical peptizers may be, for example, pentachlorothiophenol and dibenzamidodiphenyl disulfide. 
     Accelerators are used to control the time and/or temperature required for vulcanization and to improve the properties of the vulcanizate. In one example, a single accelerator system may be used, i.e., primary accelerator. The primary accelerator(s) may be used in total amounts ranging from about 0.5 to about 4, alternatively about 0.8 to about 1.5, phr. In another example, combinations of a primary and a secondary accelerator might be used with the secondary accelerator being used in smaller amounts, such as from about 0.05 to about 3 phr, in order to activate and to improve the properties of the vulcanizate. Combinations of these accelerators might be expected to produce a synergistic effect on the final properties and are somewhat better than those produced by use of either accelerator alone. In addition, delayed action accelerators may be used which are not affected by normal processing temperatures but produce a satisfactory cure at ordinary vulcanization temperatures. Vulcanization retarders might also be used. Suitable types of accelerators may be amines, disulfides, guanidines, thioureas, thiazoles, thiurams, sulfenamides, dithiocarbamates and xanthates. In one example, the primary accelerator is a sulfenamide. If a second accelerator is used, the secondary accelerator may be a guanidine, dithiocarbamate, or thiuram compound. 
     The rubber ingredients may be mixed in at least two stages, namely, at least one non-productive stage followed by a productive mix stage. The final curatives, including sulfur-vulcanizing agents, may be mixed in the final stage which may be called the “productive” mix stage in which the mixing typically occurs at a temperature, or ultimate temperature, lower than the mix temperature(s) than the preceding non-productive mix stage(s). The terms “non-productive” and “productive” mix stages are well known to those having skill in the rubber mixing art. The rubber composition may be subjected to a thermomechanical mixing step. The thermomechanical mixing step generally comprises a mechanical working in a mixer or extruder for a period of time suitable in order to produce a rubber temperature between 140° C. and 190° C. The appropriate duration of the thermomechanical working varies as a function of the operating conditions, and the volume and nature of the components. For example, the thermomechanical working may be from 1 to 20 minutes. 
     The rubber composition may be incorporated in a variety of rubber components of the tire, such as the spherical tread layer  1030  of  FIG. 1 . For example, the rubber component may be a tread (including tread cap and tread base), sidewall, apex, chafer, sidewall insert, wirecoat or innerliner. 
     Vulcanization of the spherical tire may be carried out at conventional temperatures ranging from about 100° C. to 200° C. In one example, the vulcanization is conducted at temperatures ranging from about 110° C. to 180° C. Any of the usual vulcanization processes may be used such as heating in a press or mold, heating with superheated steam or hot air. 
     A spherical tread layer  1030  in accordance with the present invention may imitate, or bio-mimic, nature. For example, the tread layer  1030  may mimic the pattern of brain coral. A groove bottom in the tread layer  1030  may comprise a material, such as that described above. The material may react similar to a natural sponge, stiff when dry and softer when wet to deliver adequate driving performance and aquaplaning resistance. Such a texture may absorb water on the road and eject water from the tire footprint through centrifugal force to reduce the risk of aquaplaning. Thus, when dry, the material at the groove bottoms may stiffen the tread for improved dry performance and handling. When wet, the material at the groove bottoms may soften, leading in effect to deeper grooves and better wet traction. 
     It is contemplated for examples described herein to extend to individual elements and concepts described herein, independently of other concepts, ideas or system, as well as for examples to include combinations of elements recited anywhere in this application. Although examples are described in detail herein with reference to the accompanying drawings, it is to be understood that this disclosure is not limited to those precise examples. As such, many modifications and variations will be apparent to practitioners skilled in this art. 
     Accordingly, it is intended that the scope of this disclosure be defined by the following claims and their equivalents. Furthermore, it is contemplated that a particular feature described either individually or as part of an example may be combined with other individually described features, or parts of other examples, even if the other features and examples make no mentioned of the particular feature. Thus, the absence of describing combinations does not preclude rights to such combinations. 
     While certain examples have been described above, it will be understood that the examples described are by way of example only. Accordingly, this disclosure should not be limited based on the described examples. Rather, the scope of the disclosure should only be limited in light of the claims that follow when read in light of the above description and accompanying drawings.