Patent Publication Number: US-2020298425-A1

Title: Morphable inertial appemdage, systems and associated methods

Description:
CROSS-REFERENCES TO RELATED APPLICATIONS 
     This application is a Non-Provisional of and claims the benefit of priority of U.S. Provisional Application No. 62/810,258 filed Feb. 25, 2019, the entire contents of which are incorporated herein by reference. 
    
    
     FIELD OF THE INVENTION 
     The invention pertains to mechanical and robotic systems, in particular locomotion mechanical systems that enable movements from one place to another, both in the three-dimensional space and in the sense of rotations. 
     BACKGROUND OF THE INVENTION 
     Traditionally, these types of movement required installation and use of actuators and structures with predefined mechanical and dynamic properties. In turn, these structures become redundant masses that adversely affect system performances when the hosts are not engaging in rapid manoeuvres. 
     While previous technologies have been developed to provide improved movement by using transferred forces/moments without ground contact, there currently exist no parallel appendage mechanisms utilizing augmentable or morphable inertial appendage to improve movement, particularly locomotion. Conventional technologies that sought to provide such improved movement include a serial link tail system and an angled haptic feedback system. 
     In regard to serial link tail systems, such as that described by Rone and Tzvi (2018), each motor must support the motors and structure downstream of its position, creating rotations that are suboptimal with changing centers of rotations. The weight and length of the end tail mass is also fixed, rendering its mechanical properties largely unchangeable. 
     In regard to angled haptic feedback devices, these devices utilize a remote center actuation system; however, they were typically designed for force-feedback and unable to perform in locomotion torque generation tasks. Such designs also typically require three or more motors for operation. 
     In another approach, use of a  3 -axes reaction wheel (often used in satellite applications) can supply rotation torques to its host, however, the wheel must spin at considerably high speeds in order to achieve sufficiently high impulsive torques. Generally, such designs are only suitable for slow response applications such as satellite re-orientation. Yet, in dynamic locomotion applications, mechanical and robotic systems are often required to respond in only a fraction of a second for balancing and maneuverability. 
     In yet another approach, use of a control moment gyroscope (often used in satellite applications) can supply a considerably larger amount of rotation torques to its host in a timely manner through rotating the axes of a single or multiples of spinning flywheels. However, the control moment gyroscope is mechanically more complex, and particularly, requires a sizeable amount of volume in the system body so that it can rotate continuously without colliding with other parts of the body or the ground. 
     Therefore, there exists a need for an approach that facilitates improved movement of a mechanical system while avoiding the drawbacks associated with conventional technologies described above. It would be further advantageous for an approach that could be readily applied to existing technologies systems. 
     BRIEF SUMMARY 
     In one aspect, the present invention pertains to a morphable inertial appendage that is attachable to a host mechanical system and that imparts inertial forces to the host in a timely manner to provide improved movement, while avoiding the drawbacks discussed above. 
     In some embodiments, the morphable inertial appendage system includes a morphable appendage that is morphable between an extended configuration and a retracted configuration by use of a morphing actuation system. The system can further include an additional actuator system operably coupled to the appendage that is configured to control movement of the appendage along one or more degrees of freedom. Typically, the morphable appendage comprises a distal mass disposed at or near the distal end of the appendage, the distal mass having a sufficient mass to impart a desired inertial force upon movement of the appendage (e.g. 100 g or greater depending on the forces desired). In some embodiments, the system utilizes a conjuncture of a morphable inertial appendage that enables variation of moments of inertia during operation, a parallel spherical five-bar manipulator that allows two motors to drive a payload (the morphable inertial appendage) at the same time for high-performance movements, and a software package that is robust and adaptive against variations in appendage and host operational states. 
     In some embodiments, the morphable inertial appendage system includes: a parallel motor actuator system, a tail retraction/extension actuator system, a spherical five-bar manipulator, and the morphable inertial appendage. In one aspect, utilizing motors in parallel (e.g. two motors or motor systems) provides smooth rotations at high torques. Since the motors operate in parallel, both motors contribute to the rotation of all three axes about the same rotational center. The appendage retraction/extension actuator system can be realized by any of: electric motors, electric servos, fuel engines, electromagnetic pistons, hydraulic pistons, gas pistons, pulley systems, or any combination thereof. The retraction/extension actuator system can be disposed on the host or on the appendage. In some embodiments, the morphable inertial appendage is designed with a telescopic mechanism that is actuatable by any of: cables and springs, lead-screw/ball-screw sliders, electromagnetic voice-coil(s) or any combination thereof. In other embodiments, the appendage is designed as a multi-bar-linkage folding mechanism. In some embodiments, the moments of inertia of the appendage can be readily changed by the telescopic or folding operations of the morphable inertial appendage, so that rotation movements can be made optimal. In some embodiments, the tail can be stowed away when not needed to provide a concise packaging and lower moments of inertia as needed. 
     In one aspect, a morphable inertial appendage allows for various advantageous properties, for example, any of: new or enhanced locomotion capabilities of the host by use of the morphable inertial appendage, in terms of attitude (orientation) and translation (including height); direct torque control capability of the host without considering the control of the appendage; high speed and accurate appendage and host manipulation; separable yaw and pitch control for the appendage without dynamic coupling considerations; and ease in adoption and tuning of the inertial appendage system. Control of the inertia adjustable appendage system can be informed by feedback from any of: motor/joint encoders, inertial measurement units, torsional sensors, optical sensors, or any combination thereof. 
     In another aspect, the invention pertains to methods of use and control of a morphable inertial appendage. Such methods can include the use of the morphable inertial appendage for locomotion provisions, enhancements or augmentations in various applications, including any of: ground electro-mechanical systems (e.g., hopping and turning of robots); air electro-mechanical systems (e.g., air manoeuvres of fixed wing aircrafts); marine electro-mechanical systems (e.g., high-speed turning and stoppage of boats); and space electro-mechanical systems (e.g., precise attitude control of satellites). 
     In another aspect, the inertial appendage system can be used as a haptic feedback device for various applications, including any of: vehicle (e.g., air/sea/land/space) command generation; computer command generation; and medical device command generation. 
     In some embodiments, the augmentable morphable appendage allows transfer of forces to the mechanical system (i.e., “host”) to which it is attached without requiring high motor speeds to create these forces. For example, large torques can be supplied to the mechanical system to which the appendage is attached because the moments of inertia of the appendage are greatly amplified by the length the appendage extends from the host (e.g. tail length). In one aspect, the length of the appendage and the mass of the distal mass are determined to provide a desired inertial force, which may depend on the functional capabilities, size and mass of the host. In some embodiments, the distance the appendage extends is determined as a function of the distal mass and the desired inertial force. In some embodiments, the mass of the distal mass is determined as a function of the distance that the appendage extends and the desired inertial force. In some embodiments, the distal mass is 100 g or more (e.g., 150 g, 200 g, 300 g or more), while in other embodiments the distal mass is less than 100 g (75 g, 50 g, 25 g or less). In some embodiments, the appendage protrudes from the host a distance greater than 6 inches (e.g. 12 inches, 18 inches, 24 inches or more). In some embodiments, the appendage changes in length by 10% or more (e.g. 30%, 50%, 100%, 150%, 200% or more). In some embodiments, the appendage extends a variable distance depending on the inertial force desired. Since the appendage typically extends distally, it is referred to throughout the present application as a “tail”, however, it is understood that the appendage is not limited to a distally extended orientation and could be deployed in various other orientations or directions as desired for a given applications. The term “morphable” can refer to any change of position, length, size, shape or any combination thereof sufficient to change an inertia of the appendage. 
     Systems having such morphable appendages can be utilized in various applications, including but not limited to: locomotion robots, aerospace, defense (e.g. gun turret target acquisition and tracking), tracking applications (e.g. fire hose aim control); surgical robotics and animatronics. 
     In another aspect, the invention pertains to a high performance spatial-parallel-linkage leg. As described herein “leg” refers to a set of linkages between an upper deck and a distal foot that supports the robot device, either fully or partly in combination with one or more other legs. In some embodiments, the high performance leg is a 1-DOF 3RRR (revolute-revolute-revolute) spatial-parallel-linkage leg (“R” referring to “rigid link”), in other embodiments the leg is a 3-DOF 3RSR (revolute-spherical-revolute) spatial-parallel-linkage leg. Such legs have ability to provide higher torque and motion bandwidth, larger range of motion and structural stability such as hopping, to further improve maneuverability, energy efficiency and stabilization. These improved legs can be used in combination with any of the features described herein, or can be utilized on existing robotic system so to improve operation, functionality, maneuverability and efficiency thereof. 
     In another aspect, the invention pertains to a high energy efficiency parallel-linkage leg. As described herein “leg” refers to a set of linkages between an upper deck and a distal foot that supports the robot device, either fully or partly in combination with one or more other legs. In some embodiments, the high energy efficiency leg is a 1-DOF 3RRR (revolute-revolute-revolute) parallel-linkage leg (“R” referring to “rigid link”), in other embodiments the leg is a 3DOF 3RSR (revolute-spherical-revolute) parallel-linkage leg. Such legs have higher resistance ability to decouple applied ground force and leg energy-stored spring force during movement, such as hopping, to further improve maneuverability, energy efficiency and stabilization. These improved legs can be used in combination with any of the features described herein, or can be utilized on existing robotic system so to improve operation, functionality, maneuverability and efficiency thereof. 
     Other features and advantages of the invention shall be apparent based upon the accompanying description, drawings, and claims. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  depicts an exemplary system comprising a parallel spherical five-bar manipulator, in accordance with some embodiments of the invention. 
         FIG. 2  depicts the range of motions of an inertial appendage assembly, in accordance with some embodiments. 
         FIG. 3  depicts a visualization of a telescopic appendage installed on a hopping robot, in accordance with some embodiments. 
         FIGS. 4A-4B  depict a visualization of a folding inertial appendage and the appendage installed on a hopping robot, respectively, in accordance with some embodiments. 
         FIGS. 5A-5C  depicts a prototype of an inertial appendage robotic system, in accordance with some embodiments. 
         FIGS. 6A-6E  depicts a scissor-style morphable inertial appendage, in accordance with some embodiments. 
         FIG. 7  depicts a chain matching mechanism of a morphable inertial appendage, in accordance with some embodiments. 
         FIG. 8  depicts a cable-driven mechanism of a morphable inertial appendage, in accordance with some embodiments. 
         FIGS. 9A-9G  depict a lead-screw style inertial appendages, in accordance with some embodiments. 
         FIGS. 10A-10C  depict a planar linkage leg design. 
         FIG. 11  depicts a 3RRR spatial parallel leg design, in accordance with some embodiments. 
         FIGS. 12A-12B  depicts a chain matching mechanism of a morphable inertial appendage and 1DOF 3RRR spatial parallel leg, in accordance with some embodiments. 
         FIGS. 13A-13C  depicts varying views of an agile dynamic robot having a scissor-like morphable inertial appendage and 3DOF 3RSR spatial parallel leg, in accordance with some embodiments. 
         FIG. 14  depicts varying sequential views of an agile dynamic robot having a morphable inertial appendage performing a forward somersault with a tail retraction and extension, in accordance with some embodiments. 
         FIG. 15  depicts varying sequential views of an agile dynamic robot having a morphable inertial appendage performing a continuous turn and hop, in accordance with some embodiments. 
         FIG. 16  depicts a 3RRR spatial parallel leg spring design, in accordance with some embodiments. 
     
    
    
     DETAILED DESCRIPTION 
     Although the disclosure hereof is detailed and exact to enable those skilled in the art to practice the invention, the physical embodiments herein disclosed merely exemplify the invention which may be embodied in other specific structures. While the preferred embodiment has been described, the details may be changed without departing from the invention. 
       FIG. 1  shows an exemplary embodiment of a mechanical system  100  utilizing a morphable inertial appendage  1 . Specifically, the mechanical system is a parallel spherical five-bar manipulator. Such systems can be configured for a variety of applications, however, such systems have particular applicability to locomotion. In this embodiment, the parallel spherical five-bar manipulator  100  consists of two driving motors  10  in parallel, followed by a spherical five-bar linkage system in which a shoulder arm  12  is attached to each of the motors  10  directly, upon which a connector arm  16  is installed via a passive rotary joint  14 . The morphable inertial appendage  1  (i.e. the fifth bar) is then attached to a connection of the two connector arms  16 . Such a configuration allows the morphable inertial appendage  1  to pivot at remote center  18 . In this embodiment, the morphable inertial appendage  1  is designed as a telescopic tail having a distal mass load  2 . While a particular five-bar manipulator is depicted here, it is appreciated that the morphable inertial appendage  1  can be used with various other manipulators and mechanical system designs in which an inertial force can be utilized to assist in movement of the mechanical assembly. 
     Movement of the inertial appendage is achieved by rotations of motors  10  in combination. When the two motors  10  move in the same direction (e.g. common mode), the appendage exhibits a pitch motion. When the two motors  10  move in the opposite directions (e.g. differential mode), the appendage  1  exhibits a yaw motion, as shown in the schematic  200  of  FIG. 2 . These movements of the inertial appendage  1  supply the necessary rotation torques to the host, with magnitude coefficients being augmentable by the distance and weight of the end mass. The inertial appendage system can also be used to transfer energy to a mechanical system for translational movements. By telescoping the distal mass load  2  to varying distances from the supporting structure (e.g., tail length), the inertial forces produced by movement of the distal mass load can be increased or reduced to impart a desired magnitude of force to the supporting structure. It is appreciated that these differing types of movement can be provided in differing modes or can be utilized as needed within a common operating mode. 
     In the case of a hopping robot  300 , shown in  FIG. 3 , the inertial appendage assembly  310  includes an inertial appendage that telescopes between the extended and retracted configuration. In this embodiment, the inertial appendage assembly  310  attached thereto can pitch the telescoping inertial appendage  311  upwards such that the inertial forces from the distal mass  312  of the appendage compresses the robot&#39;s legs (obscured), storing mechanical potential energy, then pitch downwards such that the inertial forces from the distal mass  312  of the appendage further assist expansion of the robot&#39;s leg springs  301  and allow the robot  300  to take off. In this embodiment, the yaw and pitch movements of the inertial appendage  1  are controlled by the same approach as that described in  FIG. 1 . The telescoping movement of the inertial appendage  1  is facilitated by movement of a cable driven motor  302  disposed on the host, which is driven to wind or unwind cable  303  to adjust the length of the telescoping tail by compressing compression spring  313  to shorten the appendage or allowing compression spring  313  to expand to lengthen the appendage. This action can be further understood by referring to another view of a hopping robot shown in  FIG. 4B  in which the robot&#39;s legs  402  and leg springs  403  are clearly visible (although the appendage in this embodiment is folding rather than telescoping). 
     I. Morphable Inertial Appendage 
     While the concept of a morphable inertial appendage can be realized by various approaches, the present application presents several exemplary approaches: a telescopic mechanism, for example as shown in  FIG. 3 , and a folding mechanism, for example as shown in  FIGS. 4A-4B , a scissor like mechanism, for example as shown in  FIGS. 6A-6D , a chain matching mechanism, for example as shown in  FIG. 7 , a cable back-and-forth mechanism, for example as shown in  FIG. 8 , and lead-screw mechanism, for example as shown in  FIG. 9A-9G . 
     As described above, the telescopic appendage  311  enables augmentation of the appendage and host moments of inertia by means of extension and retraction of the end inertial mass along the appendage axis, such that the moments of inertia are increased at an extended state and decreased at a retracted state. The end mass  312  can also be moved to any intermediate position for a precise and optimal effect. In the embodiment shown, the stroke of the telescopic tail is about 170 mm, although it is appreciated it can be configured according to any stroke distance desired. While a particular design is shown in  FIG. 3 , it is appreciated that the telescopic appendage can be realized by any suitable mechanism, which may include any of: cables, pulleys, ball-screw sliders, lead-screw sliders, electromagnetic voice coils, or any combination thereof. For example, the embodiment shown in  FIG. 3  utilizes a universal pulley system  320  (shown enlarged at lower right without cable  303 ), system  320  having a cable limiter  321 , bearing  322 , and pulley  323 . 
     As shown in  FIGS. 4A-4B , the morphable inertial appendage  400  folds between the extended and retracted configuration. In this embodiment, the morphable inertial appendage  400  can be designed with linkages that folds such that augmentation or morphing of the appendage and host moments of inertia is provided by means of folding and unfolding. In this embodiment, we used planar  8 -bar-linkage design. Similar to the telescoping movement, this folding changes the distance of the distal mass of the appendage  400  from any supporting structure or host, thereby allowing for fine-tuned adjustment of the inertial forces imparted to the host. In some embodiments, the end mass can be folded inwards further than the distal mass of the telescopic appendage is capable of, however, its intermediate trajectory moves in an arc about the folding inertial appendage pivot joints, as shown in  FIG. 4A . As shown in  FIG. 4B , a hopping robot  410  can utilize a folding morphable inertial appendage assembly  400  having a movable appendage  401  with a distal mass  402  to facilitate hopping by utilizing inertial forces adjusted by folding appendage  401 . 
     Current research and development has demonstrated a working parallel spherical five-bar manipulator system that utilizes an inertial appendage, for example manipulator system  500  utilizing a telescoping inertial appendage  501  as shown in  FIGS. 5A-5C . Testing and simulations indicated that such a system can sustain repeated movements with a 200 g end load at a 30 cm extension distance from the host. The system operates utilizing control algorithms and software specifically developed to enable robust adaptive control of the inertial appendage. The functionality of the complete assembly for a variety of desired movements has been demonstrated in extensive simulations. 
       FIGS. 6A-6D  show the concept of a scissor-style morphable inertial tail  600 , with the incorporation of the proposed spherical five-bar manipulator  610 . The tail includes a scissor-type expandable rig  601  that extends longitudinally upon actuation.  FIG. 6A  shows the expandable rig partly retracted,  FIG. 6B  shows the rig fully retracted,  FIG. 6C  shows the rig fully expanded and  FIG. 6D  shows the rig fully retracted and rotated by movement of manipulator  610  attached to the proximal end of the rig.  FIG. 6E  shows the base actuator  602  (shown without the remainder of the scissor-type expandable rig), in which movable arms  602   a,    602   b  engage the first pair of parallel joints in the scissor-type rig so that as the subsequent joint slides along a center of the rig slides within slider  602   c,  the rig expands and contracts. Expandable rig  601  can operate in a conventional manner associated with scissor-type expandable rigs. In some embodiments, the power source cables of the motor wind along the scissor-type linkages, the motor directly drives (not spring driven) the distal end linkages and thus can control the scissor-type rig&#39;s length. In some embodiments, a parallel placed spring can help the rig maintain the expanded state. In addition, a slider extended from the SFB structure would provide the centers of the scissor-type tail a straight line along the tail&#39;s direction to slide in and strengthen the tail&#39;s stiffness. This also ensures the tail&#39;s stroke can be more than half of its longest length within only several loops of the four-bar linkages. The spherical five-bar manipulator  610  is in accordance with those described in previous embodiments, although it is appreciated that appendage  600  could be mounted on various other configurations of manipulators to provide same or similar functionality. In some embodiments, the motor is located at the distal end of the appendage such that the motor that is used to control the cables also serves as a distal load mass (see  1302  in  FIG. 13A ), although it is appreciated that the motor could be mounted elsewhere and that a distal mass similar to previous embodiments could be used. 
       FIG. 7  shows a telescoping inertial tail  700  actuated by a chain matching mechanism  702 ,  704 . This approach is advantageous in a space limited applications. As shown, two chains  703 ,  703 ′wrap around pulleys or capstans  704 ,  704 ′ which connects to one or more motors  705  (e.g. dual capstan motor or two motors). As the two chains are unwound, the chains engage each other and extend as rod  702  extending the telescoping tubes  701   a,    701   b,    703   c  outward. In the embodiment shown, a three-stage telescoping tube mechanism is applied with each of the three tubes being non-circular. Each tube has square sections both for inner and outer sections. The engaged chains forms a square-shape rod  702 , passing through the inside of the entire telescoping mechanism and anchoring to the distal end of the top tube  701   c.  The engaged two-chain rod drives the movement of the top tube  701   c,  creating the movement of the entire telescoping tube, thereby lengthening the entire appendage. In this embodiment, each chain wraps or curls around a pulley or capstan that connects to an independent motor/actuator or a single motor powering both capstans. It is appreciated that variations of the above embodiment can be realized. 
       FIG. 8  shows a movable inertial tail  800  actuated by a cable-driven back-and-forth mechanism. As cable  803   a,    803   b  is attached to one or both ends of rod  801  such that winding the cables about a motor-driven rotor  804  that moves the appendage in one direction to an extended position and winding the cables in an opposite direction moves the appendage in the opposite direction to a retracted position. In the embodiment shown, the cable back-and-forth mechanism binds the cable on the rotator  804  of the motor  805 , and the two ends of the cable are connected with the mass load  802  and the proximal end of the rod, respectively. The motor  805  is coupled to base plate  806  such that rotation controls the length of cable on both side of the rotor, determining the distance between the mass load and the fixed base portion  803 , which is secured to the host. The rod is connected with the base through the use of a linear bearing  807 . It is appreciated that variations of the above embodiment can be realized, such as one cable effecting movement in one direction and spring-loaded mechanism effecting movement in the opposite direction. 
       FIGS. 9A-9G  show embodiments of an extendable inertial appendage actuated by a lead-screw mechanism. As shown, the lead-screw mechanism uses a lead screw to adjust extend the telescoping rod, thereby adjusting the Mol of the appendage. 
       FIG. 9A  shows an extendable inertial appendage  900 ′ with a single lead screw rod  901 ′, which also acts as the rod and is actuated by a lead-screw servo motor. In this embodiment, motor  901 ′ is located at the distal end and serves as both the actuator and mass load  901 . It is appreciated that in other embodiments, the motor can be located elsewhere, such as at the proximal end. In this embodiment, the rotations of the motor cause the lead screw rod  901 ′ to screw toward the base  910 ′ of the appendage, shortening the entire appendage length. In this embodiment, the base portion needs sufficient space for the lead screw when the lead screw is screwed in when in the retracted configuration. 
       FIG. 9B  shows another embodiment of a lead-screw appendage  900  that uses three-stage telescoping tubes (top tube  901   c,  middle tube  901   b,  and bottom tube  901   a ). A motor rotates a small diameter lead screw rod  903  that is concentrically mounted with the bottom tube  901   a,  where the outer-side lead screw of the rod engages with the inner-side lead screw of the inner tube, as shown in  FIG. 9C . The outer-side lead screw of the inner tube then engages with the inner-side lead screw  903 ′ (see inner threads) at the bottom part of the top tube  901   c,  as shown in  FIG. 9D . The inner section of the middle tube  901   b  is a hexagonal shape  904   b,  as can be seen in  FIG. 9E , and is matched with the outer-side hexagonal shape  904   c  at the bottom part of the top tube  901   c,  as can be seen in  FIG. 9D , to maintain linear relation and prevent relative rotation between the telescoping sections. A small variation from the hexagonal shape to the round shape at the top part of the inner-side of the middle tube avoids the separation between the top tube and the middle tube. Similarly, the inner section of the bottom tube  901   a  is a round shape  905   a,  as shown in  FIG. 9F , and is matched with the outer-side round shape  905   c  at the bottom part of the middle tube, as shown in  FIG. 9G , to maintain linear movement. A small variation from the round shape to the hexagon shape at the top part of the inner-side of the bottom tube avoids the separation between the middle tube and the bottom tube and prevents their relative rotation. At last, the bottom tube  901   a  is fixed on the connector with stator of a motor. The inner lead screw rod  903  is controlled by the motor, and then transmitting the rotation to the inner tube, thus creating the linear motion of the top tube. In some embodiments, the mass load at the top of the top tube forces the entire tail to retract and the separation preventing mechanism on the tube can ensure the tail is able to extend. 
     It is appreciated that the above example of a morphable inertial appendage are exemplary and variations and modifications of the embodiments described above are in accordance with the concepts described herein. For example, many such embodiments can further utilize an additional spring-type mechanism to bias the appendage toward a particular configuration (e.g. extended, retracted or partly extended) to further increase speed and efficiency in moving or altering the shape of the appendage. 
     II. Spatial Parallel Linkage Leg 
     In another aspect, the invention pertains to an improved support leg that improves agility and maneuverability of robotic systems, particularly tail-inspired agile dynamic robots. This improved support leg can be realized as a 1-DOF 3-RRR-Spatial-Parallel-linkage Leg or a 3-DOF 3-RSR-Spatial-Parallel-linkage Leg. In the example below, the leg is controlled indirectly, for example by the swinging appendage (e.g. tail) through the reaction torque. Typically, in many dynamic robotic applications, a one-DoF energy-stored compliant springy leg is required.  FIGS. 10A-10C  shows conventional planar leg designs that include a central axial spring-type member  1003  and one or more two-member serial linkages  1101 . By contrast, in some embodiments, the improved support leg has higher resistance ability to decouple the applied ground friction force and leg energy-stored spring force during hopping and has a very high energy transfer efficiency during the body energy to the spring energy and the spring energy to the body energy in robot locomotion. 
       FIG. 11  shows an exemplary 3-RRR-Spatial-Parallel-Linkage leg  1100 . This leg design is particularly advantageous when used with a dynamic robot having a morphable appendage, for example, a dynamic hopping robotic system. In one aspect, each of three supports  1101  includes serial linkage chain including two bars  1101   a,    1101   b  connected by one revolute joint  1101   b.  At the connection point with upside and downside platform, another two revolute joints  1103   a,    1103 , respectively, are used to connect the chain. In this embodiment, the three revolute joints of the chain rotate in the same direction. The three chains are averagely distributed around the space, and the angles between each two of them is between 90 and 145, typically each being 120 degrees. These parallel mechanisms creates the linear motion between the upside and downside platform and results in the Center-of-Mass of the leg locates exactly on the center axis line. As can be seen, this design avoids the need for a one DOF spring actuated support in the center, which provides for markedly improved stroke length, stability of the structure and offset axis disturbance rejection, among other advantages. This design, when combined with use of a robot system having a morphable appendage allows the robot to achieve spectacular maneuverability, energy efficient locomotion, and robust stabilization to large perturbations, which may not be easily attained in the existing legged robots. Such a combination of features allows for robotic system that perform extreme locomotion maneuvers with ease by use of the morphable inertial appendage.  FIG. 16  shows another exemplary 3-RRR-Spatial-Parallel-Linkage leg  1600  that is substantially the same or similar to the configuration in  FIG. 11  except the three upper bars  1601  of the three supports  1601  are connected with three tension springs  1605  to provide energy-storage capability. 
     By combining a morphable appendage (e.g. swinging tail) with an improved springy support leg design, such as that of  FIG. 16 , the role of the morphable appendage in robot locomotion can be further expanded upon. A controller can control locomotion of the robot utilizing the morphable appendage without the movement limitations associated with the conventional axial leg support design, which allows for control strategies to realize extreme maneuvers such as energizing and maintaining a stable hopping motion, quick tail-inspired turn or forward somersault to demonstrate the advantages of having an external appendage in locomotion. 
     By combining a morphable inertial tail with a 3-DOF 3-RSR-Spatial-Parallel-Leg design, such as in agile dynamic robot  1200  in  FIG. 12 , the robot can perform more extreme maneuvers such as directional hopping, continuous somersaults in the air that are even maneuverability of conventional dynamic robots (or even human or animal capabilities). Thus, the 6-DOF robot provides a new platform to explore and expand upon robot agile locomotion. The 3-DOF 3-RSR-Spatial-Parallel-Leg design is particular advantageous in extreme 3D motion because it can offer higher motion and torque bandwidth, larger range of motion in pitch/yaw directions, larger stroke along the compression/extension axis as compared to conventional 3d hopping machine designs [for example, see M. H. Raibert, H. B. Brown, and M. Chepponis, “Experiments in balance with a 3D one-legged hopping machine,” The International Journal of Robotics Research, vol. 3, no. 2, pp. 75-92, 1984.] [Z. Batts, J. Kim, and K. Yamane, “Design of a hopping mechanism using a voice coil actuator: Linear elastic actuator in parallel (leap),” in Robotics and Automation (ICRA), 2016 IEEE International Conference on, May 2016.]. In typical 3D hopping leg designs, the proximal-end actuators need to undertake the weight of the distal-end actuators, significantly limiting the overall leg output force and motion bandwidth. The 3-DOF 3-RSR-Spatial-Parallel-Leg design can provide large stiffness and faster response at the distal end because through rigid mechanical linkages, three actuators can work simultaneously to support 1-DOF movement without undertaking another actuator&#39;s weight, while all three actuators can locate closely to the center of mass of the robot. 
     III. Agile Dynamic Robots 
     To fully utilize the advantage of the morphable inertial tail, a specialized tail-inspired dynamic robot has been developed. The tail-inspired agile dynamic robot consists of morphable inertial tail, host body and one or more support legs, for example, a single support leg. The leg can be a 1-DOF 3-RRR parallel leg or a 3-DOF 3-RSR spatial leg. In some embodiments, the proposed tail is particularly advantageous for a dynamic single leg hopping, for example as can be seen in  FIGS. 12A-13C . 
       FIGS. 12A-12C  show an agile dynamic robot  1200  comprising a movable appendage  1201  supported by a manipulator system  1202  that can change the orientation and/or attitude of the movable appendage  1201  thereby effect changes in inertia to facilitate dynamic movements, as described previously. The manipulator system  1202  is attached by additional gears  1203  that can further change the position of the appendage (e.g. pitch), which are powered by internal actuators  1204  (e.g. motors, servos, etc). The robot is support by a 1-DOF 3-RRR spatial parallel leg  1205 , such as that described in  FIG. 11 . 
       FIGS. 12A-12C  show an agile dynamic robot  1300  comprising a morphable appendage  1301  comprising a scissor-type expandable rig that is supported by a manipulator system  1303  that can change the orientation and/or attitude of the movable appendage  1301  that effect changes in inertia to facilitate dynamic movements. The manipulator system  1303  is attached by additional gears  1304  that can further change the position of the appendage (e.g. pitch), which are powered by internal actuators (e.g. motors, servos, etc). The robot  1300  is support by a 3-DoF 3-RSR-Spatial-Parallel-Leg  1305 , as can be seen the intermediate joint is spherical thereby providing further degrees of freedom within the support leg. 
     In some embodiments, when incorporating the robot with the 1-DOF compliant leg, one motor mounted on the body is used to control the leg landing angle. When using the 3-DOF 3-RSR spatial parallel leg, three motors on the body together control the leg simultaneously. Electrical board, motors, sensors utilized for such control can be disposed within the host body. The 3-RSR-Spatial-Parallel-Leg allows for achieve a large range of multi-directional movement control to be achieved while the movable appendage assists in balancing the host as well as a source of dynamic power to energize dynamic movements. 
     One particular application for the tail-inspired agile dynamic robot is to achieve a somersault, while maintaining balance and control of trajectory. The retraction of the morphable inertial appendage speeds up the rotation significantly, facilitating an early completion of the forward somersault even at low forward speed. This feature prevents the ground contact with the long tail or the host body. 
       FIG. 14  shows sequential views of a somersault movement described above of an agile dynamic robot  1400  utilizing a movable appendage  1401  attached to a host  1402  that is supported by springy 1 DOF legs  1402 .  FIG. 15  shows sequential views of a continuous hop and turn movement by an agile dynamic robot  1500  utilizing a movable appendage  1501  attached to a host  1502  that is supported by springy 1 DOF legs  1502 . It is appreciated that such movement can further be realized by agile dynamic robots having a single springy support leg, such as that described in  FIG. 16 , or a 3-RSR spatial parallel leg as described above. 
     II. Control Software Package 
     In another aspect, the invention pertains to control software configured to control the morphable inertial appendage so that movement and morphing of the morphable appendage is coordinated to facilitate a desired movement and/or inhibit an undesired movement of the mechanical assembly or host. Such control software can be embodied in programmable instructions recorded on a non-transitory medium, typically one or more processors of a control unit operably coupled with the appendage. Typically, the control software receives inputs corresponding to a state and/or a movement of one or more components or linkages of the mechanical system to which the appendage is attached such that the augmentation/morphing of the appendage and/or movement of the appendage is coordinated with a desired or commanded movement of the mechanical system. The control unit of the appendage may be separate from the mechanical system or integrated within an overall control unit of the mechanical system or host. 
     In some embodiments, control and estimation software for the morphable inertial appendage system is provided such that precise and accurate torques can be supplied to the host. The controller software is adaptive and robust such that its operation is safe and optimized at different tail postures, different inertial tail extension levels, and host operational states. Undesired gravitational and dynamic effects of the appendage system can therefore be cancelled by the software. This robust and adaptive behavior is particularly advantageous, as the parasitic effects would normally adversely affect system performance. Retuning of the controller is also unnecessary due to the robust and adaptive nature of the control software. 
     Methods of controlling such an augmentable or morphable appendage are also provided. Such control methods can include: receiving an input corresponding to a desired state or movement of all or at least a portion of a mechanical system or host, the system having a morphable appendage attached thereto; determining a modified state of the morphable appendage that facilitates the desired state or movement; and augmenting or morphing the appendage to the modified state such that inertial forces from the modified appendage facilitate the desired state or movement of the mechanical system. In some embodiments, the method can further include determining a movement of the morphable appendage. The movement of the appendage may also be associated with a current movement or anticipated movement of the host to which it is attached. In some embodiments, the method can include determining multiple modified states of the appendage or a dynamic changing state of the appendage during a complex movements or series of desired movements of the host. Such methods can further include coordinating augmenting or morphing of the appendage during movement of the appendage and/or movement of the attached mechanical system or host. 
     III. Practical Applications 
     The morphable inertial appendage described herein can be utilized to improve and control movement of various types of mechanical systems, including but not limited to robotics, aircrafts, defense and satellites. 
     In some embodiments, the systems utilize the concepts described herein to provide agile locomotion of ground robots, including energy pumping, dynamic manoeuvres, and attitude stabilization of a hopping robot. In some embodiments, such systems are used to provide agile aerobatic manoeuvres of aircrafts in the absence of aerodynamic forces. In other embodiments, these systems can be used to provide rapid and precise attitude control of satellites. In other embodiments, these systems can be used in defense applications, for example, providing smoother and faster target tracking for gun turrets. In still other embodiments, the system provides instrument manipulation in manufacturing and surgical robots, for example, enabling smoother rotation and displacement control of the end surgical instrument. In other embodiments, these systems can be used for actuation in animatronics. 
     The foregoing is considered as illustrative only of the principles of the invention. Furthermore, since numerous modifications and changes will readily occur to those skilled in the art, it is not desired to limit the invention to the exact construction and operation shown and described. While the preferred embodiment has been described, the details may be changed without departing from the invention, which is defined by the claims.