15205801

CHARACTER ANIMATION OF LEGGED FIGURES

CROSS-REFERENCE TO RELATED APPLICATIONS

The present application claims priority under 35 USC §119 (e) of Provisional Patent Application bearing serial number 60/960,046, filed on September 13, 2007, the contents of which are hereby incorporated by reference.

TECHNICAL FIELD

The present invention relates to the field of character animation, and more specifically, to the animation of walking, running, jogging, or any other type of locomotion using feet.

BACKGROUND

The bipedal locomotion is one of the most important abilities of human beings, but it still remains a major issue in character animation due to the inherent complexity of the motion. A common difficulty encountered with animation is the so-called "footskate", which makes the foot look like it is sliding on the ground.

Kinematical methods for reproducing locomotion generally suffer from a robotic looking side-effect, while the use of dynamics produce more realistic motions but are quite expensive computationally.

Therefore, there is a need to improve on the existing techniques to reproduce locomotion for the purposes of animation.

SUMMARY

There is described herein a technique used in computational modeling for the animation of legged characters. The center of pressure under each foot is tracked as it moves to discrete positions along the bottom surface of the foot during a locomotive cycle. At least two feet are synchronized together, each foot having its own cycle in order to reproduce the motion in a realistic manner. The system is a normalized locomotion system adaptable to various characters' morphologies and fully tweakable in real-time.

In accordance with a first broad aspect of the present invention, there is provided herewith a method for representing locomotion for character animation, the character having at least one pair of feet, the method comprising: defining a cycle identifying a displacement of a center of pressure under a surface of each foot of the at least one pair of feet, the cycle corresponding to a type of locomotion and each phase of the cycle corresponding to a position of the center of pressure for a given position of the foot throughout the cycle; synchronizing the at least one pair of feet together by establishing a master- slave relationship, the master having a majority of a load supported by the at least one pair of feet and determining when to transfer the load to the slave in accordance with a set of rules; and transferring the load back and forth between the at least one pair of feet, the master-slave relationship being reversed every time the load is transferred.

In accordance with a second broad aspect, there is provided a system for digitally representing locomotion for character

animation, the character having at least one pair of feet, the system comprising: a processor in a computer; a memory- adapted to store a cycle identifying a displacement of a center of pressure under a surface of each foot of the at least one pair of feet, the cycle corresponding to a type of locomotion and each phase of the cycle corresponding to a position of the center of pressure for a ^' given position of the foot throughout the cycle,- and an application coupled to the processor and the memory, the application being configured for: synchronizing the pair of feet together by establishing a master-slave relationship, the master having a majority of a load supported by the pair of feet and determining when to transfer the load to the slave in accordance with a set of rules,- and transferring the load back and forth between the pair of feet, the master-slave relationship being inversed every time the load is transferred.

In accordance with a third broad aspect, there is provided a system for digitally representing locomotion for character animation, the character having at least one pair of feet, the system comprising: a foot position module adapted to determine a position of the at least one pair of feet and a position of a center of pressure according to a cycle, the cycle identifying a displacement of the center of pressure under a surface of each foot of the at least one pair of feet, the cycle corresponding to a type of locomotion and each phase of the cycle corresponding to a position of the center of pressure for a given position of the foot throughout the cycle; a synchronizing module adapted to synchronize the at least one pair of feet by creating a

master- slave relationship, the master having a majority of a load supported by the pair of feet, and to determine when to transfer the load to the slave in accordance with a set of rules; and a load transferring module adapted to transfer the load from the master to the slave.

While the description uses walking as a locomotion type to illustrate the invention, it should be understood that the invention is not limited to walking and can be extended to any type of locomotion and any type of gait. In addition, it should be understood that the phases of the walking cycle used in the description are not restrictive and may be varied as desired to produce a different gait.

BRIEF DESCRIPTION OF THE DRAWINGS

Further features and advantages of the present invention will become apparent from the following detailed description, taken in combination with the appended drawings, in which:

Fig. 1 is a flow chart illustrating a method for representing locomotion for character animation, in accordance with an embodiment ;

Fig. 2 is a table showing an example of the different phases in a walking cycle;

Fig. 3 illustrates an embodiment of the position of the pressure center under the foot throughout a walking cycle;

Fig. 4 illustrates an embodiment of a foot disc corresponding to the cycle shown in figure 2;

Fig. 5 illustrates an embodiment of the motion of the foot throughout the cycle shown in figure 2;

Figures 6A- 6D illustrates four types of locomotion having different cycles, in accordance with an embodiment;

Figures 7A- 7P illustrate an embodiment of the lower body of an animated figure throughout a walking cycle; and

Figure 8 is a block diagram of a system for representing locomotion for character animation, in accordance with an embodiment .

It will be noted that throughout the appended drawings, like features are identified by like reference numerals.

DETAILED DESCRIPTION

Figure 1 illustrates a method 10 for representing locomotion of a character in an animation. The character has a pair of legs and feet. It should be noted that the character could have more than one pair of feet in the case of a dog, for example. The first step of the method is the definition of a locomotion cycle for each foot 12. Locomotion is cyclic and can be decomposed into a plurality of organized phases which are repeated. Taking the example of walking, a cycle represents two steps, namely one step performed by the right foot and one step performed by the left foot. At the end of the walking cycle, each foot is back in the same position than that a,t the beginning of the cycle.

In one embodiment, the walking cycle may be decomposed into seven phases. They are Foot Strike, Midstance, Terminal Stance (heel-off) , Preswing (toe-off) , Initial Swing,

Midswing, and Terminal Swing. These phases can further be classified into two broader categories, namely the Stance Phase (Toe-Off and Heel-Strike) , and the Swing Phase. Figure 2 illustrates how each one of the seven phases is categorized for a pair of feet. Rows 20 and 22 are associated with the left foot and the right foot of the character, respectively. Rows 24 and 16 identify whether a particular phase is a stance phase or a swing phase, and row 28 identifies whether a particular phase belongs to the single support or double support category. At the beginning of the walking cycle, the left foot is in the Terminal Stance phase while the right foot is in the Terminal Swing phase. Each foot successively passes through each phase of the cycle while the character makes two steps. At the end of the walking cycle, each foot is back at its initial phase. Some parts of these phases correspond to simple support, meaning that the weight of the body is fully supported by a single foot, while other parts correspond to double support, meaning that the weight of the body is distributed over both feet.

It should be understood that a locomotion cycle may be decomposed into any number of phases. Furthermore, a cycle may correspond to fewer or greater than two steps . For example, in the case of a galloping horse, the two back legs are synchronized, which means that they touch the ground at the same time. In this case, a cycle may be defined as a single step. In another example, a character limps on the left foot every two steps. In this case, a cycle is defined by four steps, namely two normal steps performed by the right foot, and one normal step and one limping step performed by the left step.

In one embodiment, the Pressure Center (PC) under the foot is displaced to discrete positions throughout a complete cycle experienced during a walking motion. In this embodiment, the locomotion cycle is divided into eight phases and each phase is defined according to the position of the PC. Figure 3 illustrates an embodiment showing the different positions at which the PC is identified along the bottom surface of the foot. The Position "0" corresponds to the calcaneum (C), which is the heel bone. Position "1" corresponds to the astragal (A) , which is the bone in the ankle that articulates with the leg bones to form the ankle joint. Position "2" corresponds to the tarsus (T) , which are the cluster of bones in the foot between the tibia and fibula and the metatarsus. Position "3" corresponds to the metatarsus (M) , which is the middle part of the human foot that forms the instep and includes the five bones between the toes and the ankle. Position "4" corresponds to the phalanx (P) , which is the bone of the toe. Position ^U 5" corresponds to the off -toe (0), which is the tip of the toes. Position "6" corresponds to the swing position (S) and position "7" corresponds to the elevation position (E) . Position "8" is when the PC is back at the calcaneum (C) .

Using this cyclical property, a disc composed of each of these eight identified positions of the PC which describe the foot's motion during the complete cycle is illustrated in figure 4. Each phase can be seen as a key- frame interpolation from the previous phase on the disc . The key posture of each phase is defined as the maximum angle value for a flat foot relative to the ground. The cycle is completed with a floating value φe[0,8[ and loops, where "0" corresponds to

the PC positioned at the calcaneum (C) , "1" corresponds to the PC positioned at the astragal (A) , etc, as illustrated in figure 2.

With the foot disc, there is full control of the foot pressure center considered to move straight forward under each foot from C to 0 during the stance phases (φ in [0, 5]

*> CATMPO) , and backwards from 0 to C during the swing phases

(φ in ]5,8[ O OSEC) , as illustrated in figure 5. During the stance phase, the PC passes from the calcaneum (C) position to the off-toe position (0) and the . foot does not move forward with respect to the ground. During the cycle, each foot position is interpolated between the two key positions of the surrounding phases depending on the φ value.

Figure 6A- 6D illustrates four types of locomotions having different cycles, namely standard walking, tiptoe, backwards walking, and backwards tiptoe, respectively. Each locomotion type is associated with a respective cycle. The cycles are all decomposed into eight phases and each phase corresponds to a particular position of the PC under the foot. However, the position of the foot associated with a phase differs from one type of locomotion to another. Taking the example of the elevation phase (E) , the foot is parallel to the ground during standard walking and the foot is directed towards the ground during tiptoe, although the CP occupies the same position under the foot. As a result, a cycle is defined by the position of the CP and the spatial position of the foot associated with each phase of the cycle. Once the cycle has been defined, the spatial position of the foot is determined using the φ value.

Referring back to figure 1, the second step of the method 10 is the synchronization of the feet 14. In order to represent bipedal locomotion, two foot discs are used to represent the motion of each foot and the feet are synchronized together. A master- slave relationship is established between the two feet in order to distribute the load of the body amongst the two and synchronize the process. The last step of the method 10 is the transfer 16 of load back and forth between the pair of feet. Each foot has its own PC and a global pressure center (GPC) oscillates back and forth between the two PCs as a function of the load being displaced from one foot to the other during the motion. Whichever foot has a majority of the load becomes the master and the other foot becomes the slave. When the master is ready to transfer the load to the slave, the master will ask the slave whether he is ready to receive the load. If so, the load is transferred and the master- slave roles are reversed. If not, the master will adjust the speed of the master and of the slave such that the two can be ready for the transfer to occur at the same time. For example, the speed of the slave may be increased and the speed of the master may be decreased.

The GPC can be seen as a point moving on the ground along a line joining the PC from each foot. The position of the GPC on the feet PC's line is defined with a floating value p e [- 1, 1] coding the proximity to the left or the right PC. Once it is known if a foot can support the load or not and when it wants to transfer the load that it supports, synchronization occurs in the step by step process. When a foot reaches M, it asks the opposite foot if it is ready to carry the load (<p opposite in ]0,3] <* ^■ CATM) . If the opposite foot is in this

state, the foot transfers the load by throwing the p value at its opposite. If the opposite foot is not ready, the foot disc slows down and asks the opposite one to hurry up. The synchronization is thus ideal when the two foot phases are opposite (φleft = (φright+4) modulo (8) ) .

During the walking cycle, the motion of the GPC projected on the ground is not along a straight path. The p value oscillation from the supporting foot to the other one draws a path resembling a sinusoid. The GPC is in the sustentation polygon during the double support phases. If the notion of sustentation polygon is extended to always be the polygon formed by the feet projected on the ground (even during swing phases) , then the GPC remains in this polygon during the single support phases too, just integrating the unbalanced nature of this walking motion. If you ensure that the location of the center of gravity of the digital character is on a vertical line rising from the GPC on the ground, the center of gravity and the pressure centers can be reconciled, thus controlling the general center of gravity (and thus the pelvis) location. In one embodiment, the line rising from the GPC and passing by the center of gravity is perpendicular to the ground. In another embodiment, the line is not perpendicular to the ground and a shift exists between the projections of the GPC and the center of gravity on the ground. The position of the center of gravity can be adjusted during the walk via a normalized parameter which controls the shift. The shift also allows the control of the location of the center of gravity for specific gaits .

Figures 7A- 7P illustrate an embodiment for a full walking cycle. Only the lower part of the body is illustrated. The PC

for the right foot is represented by 5OA while the PC for the left foot is represented by 5OB. The GPC is represented by 52 and the path drawn by its motion on the ground is illustrated by 56 in figure 7P. Also illustrated is the center of gravity 54 of the walker as projected on the ground and as it moves during the walking cycle. The center of gravity 54 dynamically follows the GPC 52 (with a parameterized offset added to the center of gravity 54) . The upper part of the body is also used to determine shift from the GPC 52 target. The right PC 5OA and left PC 5OB are displaced under the surface of each foot throughout the cycle as per the example shown in figure 5.

The larger disc in the lower left-hand corner of each figure shows the position of the left and right feet throughout the cycle (as illustrated in figure 4) . The solid line illustrates the position of the left foot while the broken line illustrates the position of the right foot. For example, in figure 7A, the left foot is in the T phase (φleft = 2) and the right foot is in the S phase (φright = 6) . The shorter line in the smaller disc represents the load distribution and the style of the shorter line (i.e solid or broken) depends on which foot is the master at any given moment in the cycle. In figures 7A to 7G, the left foot is the master while the right foot is the slave. In figures 7H to 70, the right foot is the master while the left foot is the slave. In figure 7P, the master-slave relationship is again reversed, with the left foot becoming the master and the right foot acting as the slave.

In one embodiment, during the stance phases, some gait parameters tuned in real-time allow to personify the foot

motion: heel-strike and toe-off factors, and foot aperture. The heel strike factor controls the slope of the foot when the heel touches the ground which corresponds to the calcaneum position (C) of the foot disk. The toe-off factor controls the slope of the foot when the foot takes off from the ground, which corresponds to the off-toe (0) of the foot disk. The foot aperture controls the opening angle of the foot which corresponds to the yaw angle about the vertical line rising from the ankle bone. During the swing phases, the PC of the foot is moving along a path computed in real-time at each new step, and tuned by the desired normalized step length and some user-defined gait parameters, such as step width, back/fore swing normalized heights, limping factor, etc .

The control of the global speed of the digital character walking is directly related to the normalized step length and to the speed of each foot disc (the φ value variation step) which corresponds to the common notion of step frequency. Some other normalized gait parameters allow the user to tune in real-time all the needed values to personify gait, for example pelvis swing down/up/side amplitudes, shoulders swing/twist amplitudes, and arms swing/roll amplitudes.

Due to the nature of the described technique, which uses normalized data, it is thus fully applicable to every digital character morphology (leg, foot, and toe length) . Every acceptable walking speeds are controllable. The gait of a specific character or a specific gait for a specified character can be personified in real-time by tuning normalized parameters or loading some preset parameters for typical walking styles. The foot discs can be changed in

real-time to integrate high-level gait topologies such as tip-toe or backwards walking, as illustrated in figure 5.

While a running motion differs from a walking one (no double support phase but a flight phase) , the CP motion under each foot is the same for these two locomotion cadences. Therefore, the technique described herein is fully applicable to make a digital character run. It just has to change its rule to permit transfer of the load before the foot strikes.

The transitions between different paces in different locomotion types (e.g. standing to walking to running to walking to standing) are fully transparent for the user. All transitions may be handled by varying the disc speeds and the load transfer rules, in real-time or not. In addition, the user can exhibit control on the digital human balance not only during the walking/running process, but also during the standing, small-step turning, and pelvis swaying processes.

The PC positions (φ values) and the p value are varied to move the general center of gravity in the sustentation polygon, thus ensuring a natural balance. In addition, the synchronization of multiple foot discs together can be used for multi-legged characters with an even number of legs.

It should be understood that the method illustrated in figure 1 may be executed by a machine provided with a processor and a memory. The cycle identifying a displacement of the center of pressure under the foot and the associated foot positions are stored into the memory. The processor is then configured to execute the steps of synchronizing the pair of feet and transferring the load back and forth between the pair of feet.

Figure 8 illustrates one embodiment of a system 100 for representing locomotion of a character in an animation. The system 100 comprises a foot position module 102, a synchronizing modulel04, and a load transferring module 106. The foot position module 102 is provided with a memory in which the foot disk corresponding to the defined type of locomotion is stored. The foot disk comprises reference foot positions during locomotion. Each reference foot position is associated with a position of the CP under the foot and a φ value.

The foot position module 102 is adapted to determine the position of the pair of feet and the position of the CP of each foot. The foot position module 102 accesses the foot disk stored in its internal memory. During locomotion, the foot position module determines the next position of each feet and the next position of the CPs according to the foot disk. It should be understood that locomotion may be represented by two different foot disks, one for the right foot and the other one for the left foot. In this case, the foot position module 102 determines the position of each foot according their respective foot disk.

The synchronizing module 104 receives the position of the CP of each foot from the foot position module position 102. The synchronizing module 104 determines which foot is the master using the position of the CP of each foot. In one embodiment, the synchronizing module 104 generates a global pressure center and the master is determined according to the position of the global pressure center. A floating value p e [-1, 1] may be associated with the position of the GPC on the feet

PC's line. In this case, the synchronizing module 104 determines the master according to the p value.

The synchronizing module 104 is further adapted to determine when the load has to be transferred from one foot to the other and transmits this information to the load transferring module 106. Upon reception of this information, the load transferring module 106 transfers the load and the master- slave roles are reversed. The synchronizing module 104 also adjusts the position of the center of gravity according to the position of the global center of pressure.

In one embodiment, the synchronizing module 104 determines whether the slave is ready to receive the load. If so, the synchronizing module 104 asks the load transferring module 106 to transfer the load and the mater- slave roles are reversed. If not, the synchronizing module 104 adjusts the speed of the master and of the slave. When it determines that the master and the slave are ready for the load transfer, the synchronizing module 104 reverses the master-slave roles and asks the load transferring module 106 to transfer the load.

It should be noted that the present invention can be carried out as a method, can be embodied in a system, a computer readable medium or an electrical or electro-magnetic signal.

The embodiment (s) of the invention described above is (are) intended to be exemplary only. The scope of the invention is therefore intended to be limited solely by the scope of the appended claims.