Abstract:
A wheel base or mobile platform providing omnidirectional motion and control. At least two offset wheel assemblies are coupled to a platform that supports a load. Each offset wheel assembly has two wheels that share a common axis and a mechanical link that is pivotally coupled to a pivot point on the rigid platform and supports the two wheels in such a manner that the common axis is displaced from the pivot point. The common axis of the wheels is free to rotate about an axis parallel to the planes of rotation of the wheels. The platform may be turned in any direction specified by a user from any instantaneous configuration or velocity in accordance with a method uniquely specifying a torque to be applied to each of the wheels while each of the wheels is in rolling motion.

Description:
This application claims priority from provisional application No. 60/149,824, which was filed Aug. 19, 1999 and is hereby incorporated herein by reference. 
    
    
     TECHNICAL FIELD 
     The present invention pertains to a steering configuration for providing omnidirectional maneuverability, and, more particularly, to a steering arrangement having at least two pairs of offset wheels. 
     BACKGROUND OF THE INVENTION 
     A platform with omnidirectional mobility can move instantaneously in any specified direction across a surface from any current configuration of the platform. The word “arbitrary,” as used in this application and in any appended claims, will mean “as specified by a user.” Thus, an omnidirectional vehicle can be said to be movable in an arbitrary direction on a continuously smooth surface. 
     Omnidirectional platforms or mobility bases provide obvious advantages in applications where a vehicle transporting a human subject or other load is to be used in congested rooms with static and/or dynamic obstacles and narrow aisles such as commonly found in nuclear plants, offices, factory workshops and warehouses, eldercare facilities and hospitals. Such platforms provide for enhanced maneuverability for mobile robots or automated vehicles in industry, military, personal, healthcare and other applications. 
     Various deficiencies are apparent in existing mobility designs. Classical wheeled mobile platform design, such as employed in three-wheel skid steering type mobile robots or in four-wheel car type mobile robots, suffers from limited mobility due to the non-holonomic constraints of the wheels. Hence, the motion of these vehicles is not truly omnidirectional. While such vehicles can reach any position and orientation in a plane, they need very complex maneuvers and require complicated path planning and control strategies in these environments. It is thus highly desirable for robots and vehicles to have omni-directional mobility for such applications. 
     Two approaches for achieving omnidirectional or near omnidirectional motion capability can be distinguished: special wheel design and conventional wheel design. Most special wheel designs are based on the universal wheel concept, which achieves traction in one direction and allows passive motion in another direction. 
     One type of special wheel design, called a ball wheel mechanism, is described by West &amp; Asada, Design of Ball wheel Mechanisms for Omnidirectional Vehicles With Full Mobility and Invariant Kinematics,  Journal of Mechanical Design,  vol. 119, pp. 153-161 (June, 1997). In the design of West &amp; Asada, two rings of rollers hold a solid ball. The power from a motor is transmitted, through gears meshed with teeth on an active ring, to the solid ball via friction between the roller and the ball. The other ring roller is mounted to the chassis and its rollers are free to rotate. Thus the ball will have a free motion around the ring axis as a result of the motion of other balls for the mobility platform. With a minimum of three such ball wheel assemblies an omnidirectional mobility platform can be constructed. 
     Universal wheel designs may exhibit good omnidirectional mobility however they tend to be complicated in terms of mechanical structure. Another major drawback of these designs is the limited load capacity for platforms built based on these designs because of the fact that the loads are supported by the slender rollers in the universal design or by the contact point with the floor in the orthogonal wheel and ball wheel designs. There are also sensitive to floor conditions as the surmountable height is limited by the small diameter of the rollers. The universal wheel design is also susceptible to vibrations as the rollers make successive contact with the ground. Additionally, these designs are not well-suited to carpeted or dirty floors because of the nature of their mechanisms. 
     Conventional wheels are inherently simple. As used herein, a “conventional wheel” refers to a rigid circular ring capable of rotation about a central transverse axis of rotation by virtue of mechanical coupling (as by spokes, for example) of the ring to an axle coaxial with the axis of rotation. Conventional wheels may have high load capacity and high tolerance to floor non-idealities such as bumps and cracks, dirt and debris. Various designs have been conceived to increase the mobility for platforms using conventional wheels. The most common designs are those using steered wheels. The platform has at least two active wheels with both driving and steering actuators. It can move at arbitrary directions from arbitrary configurations. But these type of systems are not truly omnidirectional because they need to stop and reorient the wheels to the desired direction whenever they need to travel in a trajectory with non-continuous curvatures. 
     One technique to use the conventional wheel for omnidirectional mobility is to use the active castor design as described by Wada &amp; Mori, Holonomic and Omnidirectional Vehicle with Conventional Tires,  Proc. IEEE Conf. on Robotics and Automation,  pp. 3671-3676, (April, 1996). Wada &amp; Mori describe an active wheel  10  fixed to a steering link  12 , as shown in FIG.  1 . Steering link  12  may be driven by a steering motor  14  and can rotate freely about a steering axis  16  fixed with respect to chassis  18  of the platform. Steering link  12  has an offset from the axis  20  of wheel  10 , as shown. With at least two sets of such wheels omnidirectional mobility can be achieved for a platform. Active control of dual-wheel castors is described by Wada in U.S. Pat. No. 5,924,512 which is incorporated herein by reference. 
     SUMMARY OF THE INVENTION 
     In accordance with one aspect of the invention, in one of its embodiments, there is provided a mobile base for providing omnidirectional maneuverability. The mobile base has a rigid platform and at least two offset wheel assemblies. Each offset wheel assembly has two wheels having axles aligned along a common axis. The axles are free to rotate about an axis parallel to the planes of rotation of the wheels. Each offset assembly further includes a mechanical link that is pivotally coupled to a pivot point on the rigid platform, and the mechanical link supports the two wheels in such a manner that the common axis of the wheels is displaced from the pivot point. The assembly also includes a rotary actuator for independently driving each wheel. 
     In accordance with alternate embodiments of the invention, the common axis of the two wheels of each offset wheel assembly may be substantially perpendicular to a line connecting the midpoint between the centers of the wheels to the pivot point. The mobile base in accordance may also have a user input device for steering the mobile base in a specified direction and with a specified velocity. Additionally, the mobile base may have at least one sensor for sensing a velocity of a wheel. At least one passive wheel may be provided for supporting the platform. 
     In accordance with a further aspect of the present invention, there is provided an omnidirectional vehicle. The omnidirectional vehicle has a support for supporting a load and at least two offset wheel assemblies. Each offset wheel assembly has two wheels having axles aligned along a common axis. The axles are free to rotate about an axis parallel to the planes of rotation of the wheels. A mechanical link pivotally coupled to a pivot point on the support supports the two wheels in such a manrner that the common axis is displaced from the pivot point. A rotary actuator is included in each assembly for independently driving each wheel. 
     In accordance with another aspect of the present invention, an offset wheel assembly for providing omnidirectional maneuverability includes two wheels having axles aligned along a common axis. The axles are free to rotate about an axis parallel to the planes of rotation of the wheels. A mechanical link having a long axis supports the two wheels, and a rotary actuator drives each wheel independently. 
     In accordance with a further aspect of the present invention, a method for providing omnidirectional control of a vehicle having a platform includes providing at least two offset wheel assemblies. Each of the offset wheel assemblies has two wheels that share a common axis and a mechanical link pivotally coupled to an offset link joint on the platform. The mechanical link supports the two wheels in such a manner that the common axis is displaced from the offset link joint. A user specified platform velocity is received, and the user specified platform velocity vector is transformed to obtain a unique joint velocity for each of the offset link joints. Each offset link joint velocity vector is transformed to obtain a unique rotational velocity for each of the wheels, and a torque is applied to each wheel to cause each wheel to attain the unique rotational velocity. The user specified platform velocity vector is thus achieved. In addition, at least one rotary actuator may be driven when applying the torque. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     The foregoing features of the invention will be more readily understood by reference to the following detailed description taken with the accompanying drawings in which: 
     FIG. 1 is a perspective view of a prior art active castor wheel; 
     FIG. 2 provides definitions of the nomenclature involved in the description of an offset active dual wheel assembly in accordance with an embodiment of the present invention; 
     FIG. 3 is a schematic drawing of an omnidirectional platform employing two offset dual wheel assemblies in accordance with an embodiment of the present invention; 
     FIGS.  4 ( a ) and  4 ( b ) are schematic drawings of an omnidirectional platform employing two offset dual wheel assemblies in accordance with another embodiment of the present invention; 
     FIG. 5 is a schematic top view of an offset dual wheel assembly in accordance with an embodiment of the present invention; 
     FIG. 6 is a schematic top view of an omnidirectional platform employing two offset dual wheel assemblies and two passive castor wheels in accordance with an embodiment of the present invention; 
     FIG. 7 is a schematic top view of an omnidirectional platform employing three offset dual wheel assemblies in accordance with an alternate embodiment of the present invention; and 
     FIG. 8 is a schematic top view of an omnidirectional platform employing four offset dual wheel assemblies in accordance with an alternate embodiment of the present invention. 
    
    
     The above drawings are to be interpreted as illustrative and not in a limiting sense. 
     DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS 
     A fundamental cause of the steering problem discussed in the Background Section of this Description is that wheels experience larger frictional forces when steering around a vertical axis than in rolling around the wheel axis. The scrubbing problem may be reduced by using two wheels separated at a distance and connected with a steering link, as described in U.S. Pat. No. 5,242,131, issued Sep. 7, 1993 and U.S. Pat. No. 5,704,568, issued Jan. 6, 1998, both to Watts and both incorporated herein by reference. Wheels in the dual wheel design are always rolling, even during steering, so that the frictional forces the wheel experiences are consistent and smaller while traction forces are greater than provided by a single wheel. 
     Referring now to FIG. 2, nomenclature is depicted as used to describe two wheels  24 ,  26  rotatable about axle  23  and coupled via rigid offset link  25  to platform  18 . Alternatively, two coaxial axles may be used. A “mobile base” will refer to the ground contacting portion of any vehicle or other mobile apparatus. For purposes of this description and any appended claims, a “platform” (or chassis) designates any rigid structure to which wheel assemblies are coupled. The point at which platform  18  is coupled to link  25  and thereby supported as designated by numeral  28 . The two wheels  24  and  26  of each offset wheel assembly may share a common axis  31  as shown, and the common axis  31  may be substantially perpendicular to a line connecting the midpoint  21  between centers of the wheels to the point  28 . The instantaneous velocity of support point  28  may be expressed in terms of a coordinate system defined by the instantaneous orientation of link  25  (i.e., in terms of orthogonal velocity components V S  and V f ) or in terms of a space-fixed coordinate frame (i.e., in terms of orthogonal velocity components V x  and V y ). S expresses the distance between axle  23  of wheels  24 ,  26  and support point  28 . V 2  and V 1  express the tangential velocities, at the surface, of wheels  24  and  26  respectively. Thus, in the link based coordinate system, the velocities of support point  28  are given, in terms of the wheel velocities, as:            [           V   f               V   s           ]     =       [           1   2           1   2               S   D           -     S   D             ]          [           V   1               V   2           ]         ,                          
     while the velocities are given, in a space-fixed frame, with respect to which link  25  is oriented at angle α, by:          [           V   x               V   y           ]     =         [           cos                 α             -   sin                   α               sin                 α           cos                 α           ]          [           V   f               V   s           ]       .                            
     In terms of this nomenclature, preferred embodiments of this invention provide a novel concept of wheel assembly design for omnidirectional mobility using convention wheels. Referring now to FIG. 3, a rigid body platform  18  may be supported by two points in a plane, the points designated by numerals  30  and  32 . The motion of rigid body platform  18  in the plane is fully specified in terms of the three degrees of freedom: translation in the X and Y directions and rotation by angle φ about a fiducial direction. Equivalently, the motion can be fully defined by the velocities at the two points  30  and  32 . Control of the velocities at the two points, as indicated by the subscripted variables, V, provides arbitrary (in the sense defined above), omnidirectional mobility for the rigid body platform. 
     Accordingly, an active dual wheel assembly  50 , (shown in FIG. 5 ) consisting of a pair of independently driven wheels  24  and  26 , separated at a distance D and connected with an offset link  25  to the platform  18  may be provided, in accordance with preferred embodiments of the present invention. By controlling the velocities of the two wheels, arbitrarily specified velocities may be achieved at the joint  30  of the link  25 . Referring to FIG. 5, each wheel  24 ,  26  is equipped with a rotary actuator, such as motor  40 , and a sensor  42  (such as a rotary encoder or tachometer, for example) to provide input to a processor  44  which provides wheel velocity control. Wheels  24 ,  26  are substantially coaxial and all wheels known in the mechanical arts are within the scope of the present invention, including but not limited to metal, rubber, or nylon wheels, or wheels having pneumatic tires. Motors  40  are coupled to respective wheels  24 ,  26  by drive  46  which may include a transmission  48 . Each motor may be connected to a wheel directly or via a flexible coupling, gear pairs, belts, etc. Each link joint  28  where link  25  is coupled to the platform may also have an optional sensor (such as an encoder) to measure the joint position relative to the platform for error compensation during platform motion control. The distance D between the two driving wheels and the distance S between the wheel axis and the offset link can be variable to suit the requirements of particular applications. With a minimum of two sets of such wheel assemblies, an omnidirectional mobility platform can be built as illustrated in FIG.  3 . 
     Referring again to FIG. 3, the velocity coordinates of the three .degrees of freedom of the rigid platform are: Ω, the angular velocity of the center line  33  between points  30  and  32  with respect to a fixed direction in the space-based frame, and V cx  and V cy , the translational velocities of the rigid platform in the space-fixed frame. The kinematic relations among the rigid platform  18  and the velocities of the four wheels may be expressed as follows: 
     Designating the velocities of the rigid platform, with respect to each of its degrees of freedom, as follows:            p   v     ≡     [           V   cx               V   cy             Ω         ]       ,                          
     and the joint velocities of the pivot points, as follows:            q   v     ≡     [           V   x1               V   y1                     V   x2               V   y2                 ]       ,                          
     the velocities of the two pivot joints may be expressed in terms of the velocities of the rigid platform uniquely as: 
     
       
           {dot over (p)}   v   =J   v   {dot over (q)}   v , 
       
     
     where the Jacobian velocity transformation is given by:            J   v     =     [           1   2         0         1   2         0           0         1   2         0         1   2                 1   B        sin                 φ             -     1   B          cos                 φ             -     1   B          sin                 φ             1   B        cos                 φ           ]       ,                          
     and B is the spacing between pivot points  30  and  32 , and φ is the instantaneous angle between center line  33  and the space-fixed x axis. 
     Solution for {dot over (q)} v  (by inversion of J v ) determines the requisite pivot point velocities uniquely. 
     The pivot point velocities, in turn, determine the requisite rotation rates of each of the offset castor wheels, again, uniquely, since the relation between the pivot point velocities and the tangential velocities of wheels  24  and  26  is as given above. Thus, to achieve a desired motion of the platform, the torque to be applied by the respective rotary actuators is readily determined. 
     Additional description is provided in the preprint entitled “Omni-Directional Mobility Using Active Split Offset Castors,” by Dubowsky et al., attached hereto as an appendix, and incorporated herein by reference. 
     FIG.  4 ( a ) illustrates a common problem with vehicles using some dual-wheel approaches. The wheels  24  and  26  do not both maintain contact with the ground  35 . This causes a loss of traction, and hence a loss of control of the vehicle. Although some compliance in the wheel and the mechanical structure will alleviate this problem, it is often not sufficient. A simple but effective solution, which does not require a form of independent suspension, is illustrated in FIG.  4 ( b ). Joints  34  and  36  have been added to the assembly to compensate for uneven ground surfaces. The wheels  24 ,  27 ,  26 , and  29  have axles  37  aligned along a common axis  31 . The axles  37  are free to rotate about an axis  39  parallel to the planes of rotation of the wheels  24  and  26 . This additional degree of freedom insures that all of the wheels  24   27 ,  26 , and  29  maintain contact with the ground  35 . In this manner, loss of traction in the wheels is prevented and control of the platform is maintained. More particularly, joints  34  and  36  may be passive joints. 
     The omnidirectional platform of the various embodiments of the present invention may be controlled either by on-board processors  44  or off-board computers connected by wires or via wireless means. 
     In order to achieve fully omnidirectional mobility, two active dual wheel assemblies  50  are provided, as depicted in FIG.  3 . Additionally, one or more passive castor wheels  52  may be provided to support platform  18 , as shown in FIG.  6 . Castor wheel  52  may present a non-consistent friction problem, and, in certain embodiments of the invention, it may be advantageous to provide three active dual wheel assemblies  50 , as shown in FIG.  7 . In this manner, additional traction and stability may be achieved. Similarly, four or more active dual wheel, assemblies  50  may be provided, in accordance with alternate embodiments of the invention, as shown in FIG. 8. A user input device  54  (shown in FIG.  6 ), such as a steering wheel, joystick, etc., is provided for allowing a user, conveyed by the platform or otherwise, to specify the direction and/or magnitude of desired motion. User input device  54  may be a computer. 
     Since preferred embodiments of the present invention use conventional wheels, the structure of the wheel assembly may be simple and may provide high mechanical strength. Mobility platforms based on this concept may advantageously have high loading capacity and be less sensitive to floor conditions and other non-idealities on the application environments. The dual wheel design effectively alleviates the problem of scrubbing during steering. The dual wheel design also increases the traction of the platform and increases the disturbance force rejection capability. Compared with other dual-wheel design, the platform based on this invention does not need to stop and reorient the wheels when tracking a trajectory with discontinuous curvatures. 
     This invention can be used to build intelligent mobile robotic devices with omnidirectional mobility capability for applications that need excellent maneuverability in congested environments with dynamic obstacles. Typical devices can be the medicine, food, and file dispatching robots in hospitals; personal assistive robots such as smart walkers and wheelchairs for elderly or disabled people in private home and eldercare facilities; and material handling robots in workshops and warehouse. It may also be used in conjunction with mobile platforms on which robotic manipulators, observation, and surveillance equipment can be mounted for applications in both military and industry. 
     The described embodiments of the invention are intended to be merely exemplary and numerous variations and modifications will be apparent to those skilled in the art. All such variations and modifications are intended to be within the scope of the present invention as defined in the appended claims.