Procedural Locomotion of Multi-Legged Characters in Dynamic Environments

12 Pages·2017·2.36 MB·English

Procedural Locomotion of Multi-Legged Characters
in Dynamic Environments
AhmadAbdulKarim1 2,ThibautGaudin2,AlexandreMeyer1,AxelBuendia2 3,SaidaBouakaz1
1 Universite´ deLyon,CNRS
1 Universite´ Lyon1,LIRIS,UMR5205,F-69622,France
2 Spir.OpsArtificialIntelligence,Paris,France
3 CNAM−CEDRIC,292,rueStMartin,75003Paris,France
Abstract
(a)
We present a fully procedural method capable
of generating in real-time a wide range of
locomotion for multi-legged characters in
a dynamic environment, without using any
motion data. The system consists of several
independent blocks: a Character Controller, a
Gait/Tempo Manager, a 3D Path Constructor
(b)
and a Footprints Planner. The four modules
work cooperatively to calculate in real-time the
footprints and the 3D trajectories of the feet
and the pelvis. Our system can animate dozens
of creatures using dedicated level of details
(LOD) techniques, and is totally controllable
(c)
allowing the user to design a multitude of
locomotion styles through a user-friendly
interface. The result is a complete lower body
animation which is sufficient for most of the
chosen multi-legged characters: arachnids,
insects, imaginary n-legged robots, etc.
Keywords: Procedural Animation, Level
Of Details, Multi-Legged Characters, Dynamic Figure1:(a)Spidermodelavoidscratesflaggedasforbid-
Environments. denandstepsonothersflaggedassafe(b)Ant
modelonaheightmap(c)Imaginary5-legged
Robot.
1 Introduction
Real or imaginary animals make frequent ap-
pearances in video games, films and virtual that these virtual multi-legged characte rs per-
world simulations. In this context, animated form is locomotion: the ability to move in
virtual multi-legged characters like arachnids, these virtual worlds toward the points of in-
insects, crustaceans or any imaginary n-legged terest. These locomotion animations are quite
robots/creatures make these virtual worlds be- rich due to the variety of morphologies, gaits,
lievable and life like. The most common task body sizes/proportions and due to the complex-
ityoftheenvironmentwherethesemulti-legged presented approaches were dedicated or tested
characters move: overcoming objects, cross- onthefamilyofanimalsandcreaturespresented
ing uneven terrain, avoiding moving obstacles, in this paper, and to our knowledge, none ad-
etc. The challenge of modeling such motions dresses the performance issues with level of
arises from the lack of motion capture data detailstechniquesintroducedinoursystem.
inherent to the difficulty to obtain them and Data-driven techniques use input data to
by the fact that existing animation techniques produce the animation (like Motion Capture
mostlyaddresshuman-likecharacters[1]. Data). These techniques, although the most
We propose a system (See Figure 1) that natural looking, are fixed for a specific mor-
procedurally generates locomotion animations phology and a specific context. Physics-based
for dozens of multi-legged characters, without techniques are more generic and adapt better
any motion data, in real-time using dedicated to the environment. They do so by simulating
level of details (LOD) techniques, and with a theactualphysicalforces/torquesthatactonthe
reactive adaptation to a dynamic environment. articulated body. But they are computationally
Wefocusedongeneratingplausiblemovements expensive due to the number of equations to
[2] that are, at the same time, believable and solve, which limits the number of characters
fully controllable. Our technique produces a simulated at the same time. Several works
multitude of locomotion styles, generated out were proposed to overcome the problems of
of many input parameters like the creature the previous techniques or to mix them, like:
morphology, gait/tempo, the overall locomo- Adaptingthemotiondatatodifferentmorpholo-
tion speed, etc. These input parameters can gies (Motion Retargeting) using inverse kine-
be edited through a user-friendly interface in matics in [4, 5] or mesh based techniques in
real-time. We propose a foot path planning [6]. Using inverted pendulum model (IPM)
system that assign to each foot the best cou- [7] to avoid complex kinematics and dynam-
ple (footprint-trajectory), where the footprint ics calculations on the original multi-segments
is selected among several candidates, and the skeleton. In [8] they animate the upper body of
trajectoryisthe3Dpaththatreachthisfootprint. the character using Motion Capture data while
Our system generates plausible locomotion an- the lower body is animated using an IPM. In
imation at different level of details (LOD): the [9] they optimize their IPM controller using
evaluation of the possible couples (footprint- Motion Capture data. In [10] they animate a
trajectory) may be adapted according to the quadrupedinreal-timeusingforwarddynamics,
desired LOD, typically depending on quality usingforcesdataextractedoutofrealquadruped
criteria such as the on-screen importance, vis- Motion Capture data. Finally, several papers
ibility, etc. These footprints and trajectories introduce a specific offline optimization pass,
may change in real-time in a reactive manner to accommodate for predefined environmental
according to the dynamic of the environment topologies and changes [11, 12]. The lack of
andtheobstacles. Finally,oursystemgenerates motion data and the difficulties to obtain them
the pelvis trajectory according to the overall for the family of animals and creatures that
desired direction, speed, the actual context of we simulate has led us to avoid data-driven
theenvironmentandthefeetpositionsandfeed- techniques. Inoursystemweconcentratedmore
backs. Thus, our procedural approach provides ongeneratingplausiblemovements[2],making
two important features for interactive applica- itmoreadapted(performancewise)toreal-time
tions: reactivityandcontrol. applicationsthanthephysics-basedones.
Procedural techniques use mathematical
formulas and algorithms to generate the loco-
2 Related Work
motion without any real motion data. They
There are several techniques for generating lo- do so using empirical and biomechanics con-
comotion, Multon et al. in [3] and Van Welber- cepts. These techniques offer high level of
gen et al. in [1] identified in their surveys the controllabilityoverdata-drivenones: practically
three major techniques: data-driven, physics- nomorphologicalconstraints,goodadaptability
based and procedural. Notice that few of the to the environment, etc. These techniques take
less computation time per character, making it itsmovementbasedon thefeetfeedback, butat
possible of animating several characters at the thesametimeitimposestheoveralltrajectory.
same time in real-time. However, they may When considering locomotion of multi-
suffer from the lack of naturality in the move- legged animals, the possibility of using real
ment, a disadvantage that we try to overcome data are strongly limited due to difficulties to
in this paper by integrating basic biomechanics capture the motion of real creatures like dogs,
principles. Wetookinspirationfromtheworkof horses, insects, spiders, etc. and is sometime
Boulicetal.in[13]onahumanwalkingmodel impossible like for an imaginary 5-legged char-
andtheworkofSinghetal.[14]thatshowhow acter. Thus, Girard et al. in [24, 25] propose a
avoidance in dynamic crowds can be improved fullyproceduralsystemtoanimatemulti-legged
usingbiomechanics-basedfootstepplanning. characters with visually plausible locomotion.
Inparalleltothelocomotionanimation,apath Their system is limited to planner terrains. Our
and footprints planning are needed in order to work can be considered as an extension into
navigate through the environment. In [15] they dynamicenvironments. Johansenin[26]adapts
search valid footprints using probabilistic nav- existing motion data (biped and quadruped) to
igation graphs that take into account posture the environment using inverse kinematics and
transition. Then,thesefootprintsaresubstituted footprintsprediction. In[27]theyanimateasix-
with corresponding motion clips. Lamarche legged character (a cockroach) using reduced-
in [16] generates navigation graphs and ceiling linear articulated body dynamics and gait pat-
information and uses these information to cal- ternsobservedinbiology. Wampleretal.in[28]
culate the best footprints around the optimized presentafullyautomaticmethodforgenerating
trajectory,andtogeneratethefinalmotionusing locomotion and gaits for legged animals based
motiondata,allowingfor3Dnavigationincom- on their shape and by the use of an off-line op-
plexenvironments. Pathplanningtechniquesare timization pass that results in believable anima-
also largely studied in robotics. In [17, 18, 19] tions. In[29]theyuseintelligentretargettingof
(H7HumanoidRobot™andBostonBigDog™) 2-4-6-legged Motion Capture data without any
their planner produce the footprints using feed- morphological constraint (the user can design
forward loops, correcting itself after each step theirowncreature). Theobjectiveofoursystem
for adaptation. In [20] (Honda ASIMO™) is to achieve similar results with the procedural
they plans a sequence of footstep positions to techniques in real-time without using any off-
navigate toward a goal location while avoiding line components, and with much more control
static and dynamic obstacles, their method uses inadynamiccomplexenvironment.
a time-limited planning horizon. Comparing Finally, as our method tries to generate plau-
to our purpose of computer animation, robotics sibleandbelievablelocomotion,wecreatedour
have to deal with the complexity related to the controllers in a way that reflects many studies:
mobile robot mechanical constraints and with the effect of limb length and running speed on
therealworldphysicsthatwedonotfullyhave. time of contact and step length in [30], the
Most of previously cited techniques are Foot relationship between speed and step length in
placement driven locomotion, where the feet humans in [31], and animal gaits: galloping,
drive the locomotion and the overall trajectory trotting,pacing,etc.in[32].
of the center of mass. In [21] they generate lo-
comotionbyoverlayingMotionCapturedataon
3 Overall Locomotion Controller
predefinedfootplacement,whileTorkosetal.in
[22] generate the locomotion of a quadruped Locomotionistheactofmovingfromoneplace
usingexternalimposedfootprints,andreal-time to another. For most terrestrial animals that
physics. Thesetechniquessufferfromtheprob- means putting one foot in front of the others in
lem that the lower body (the legs) usually do a successive way until reaching the designated
not control the locomotion. On the contrary, point of interest (target). During a normal foot
the upper body imposes a logical trajectory movement there are two main phases explained
that the lower body tries to follow [23]. Our more in [33]: the stance phase where the foot
system respects this concept: the pelvis adapt is blocked on the ground and the swing phase
These four blocks work together in order to
generatethemovementofthefeetandthepelvis
in 3D. Now, to obtain the final lower body
Feet Path
Planning locomotionmovementweapplyaninversekine-
matics (IK) algorithm. We use a system called
P elvis theCyclicCoordinateDescent(CCD)algorithm
[34,35]whichcomputesthepositionandorien-
tation of the legs joints that connect the pelvis
with its feet. We chose the CCD because of
itsperformanceandsimplicity: itminimizesthe
error between the actual end effector position
andthedesiredonebyiterativelymodifyingthe
Figure2:SystemOverview
angleofthejoints.
where the foot flies in a parabolic-like curve 3.1 SystemParameters
toward its target without any ground contact.
(a) (b)
Locomotion cycle is the act of repeating these
feet movements, based on a certain rhythm or
tempo. Our system follows these principles
whengenerating-procedurallyandinreal-time-
the locomotion of the multi-legged characters. Figure3:Spider Model: (a) internal representation of
Themainadvantageoftheproceduralapproach the spider model with its IK system, in pink
is the projected bounding box, in blue the feet
is the reactivity as it adapts to the environment,
orientation.(b)theactualspider3Dmodel.
and the controllability (a list of all controllable
parameters is detailed in Section 3.1). Starting Our system generates the locomotion anima-
from an environment defined by a height map tions using several input parameters, that the
and several obstacles (moving or static), the user provides or controls in real-time. All the
overalllocomotionprocessiscomputedbyfour parameters(exceptthemorphologyparameters)
blocksasshownonFigure2. can be edited at any time by the user or by any
automaticcharactercontrollerwhenthefocusis
• Thecharactercontrolleristhecentralmain
toanimateacrowdofcreatures. Anoverviewof
structure that manages the overall loco-
alltheparametersfollows.
motion of the multi-legged character (See
Section 3.2). It relies on the three other • Multi-legged character morphology: the
structurestocomputethemotionofthefeet user provides an initial static skeleton that
andtheoverallpelvisdisplacement. can be associated with a skinned mesh.
To automatically map the morphology, the
• The gait manager regulates the feet tempo
user provides the system with the name
according to the movement patterns de-
of each leg hip joint and the name of its
finedbytheuser(SeeSection3.3).
endeffector(e.g.thejointbeforethefoot).
• The 3D path constructor is a utility struc- Out of these inputs our system detects the
turethatconstructa3Dtrajectoryofafoot number of feet, leg sections, the relative
usinganefficientdiscreterepresentationof hip positions and the initial feet relative
the environment that can be easily main- positions. The user also needs to provide
tained and updated with dynamic objects the system with the desired leg joint limits
(SeeSection4). (for our CCD algorithm), real body center,
projected body bounding box, body thick-
• The footprints planner evaluates for each
ness,andfinallytheprojectedfootshape(if
footallthepossibletargetsandtrajectories
itexists)anexampleisshownonFigure3.
inreal-time,andchoosesthebestcoupleof
footprinttargetand3Dtrajectory(SeeSec- • Gait/Tempo: using our interface, the user
tion5). designs for each foot the stance and swing
phase cycle. These cycles describe the multi-leggedcharactercenteronthisconvexhull
patternofthefeetmovement. Thefinalgait we get the needed pelvis height and by adding
canbesymmetricalorasymmetrical. the body thickness we get the actual pelvis
height. Atthesametimethecharactercontroller
• Locomotion speed: speed of the move-
adds an oscillating (sinusoidal) movement on
mentinmeter per second.
thispelvisheight,basedonthefeetphases. The
pitch angle of the multi-legged character body
• Stepheight: thepreferred footstep height
is calculated directly from the convex hull. It is
inmeter.
the slope of the line segment that contains the
• Feet spacing: the preferred position of projectedcenterofthemulti-leggedcharacter.
eachfoot,relativetothepelvis.
For Each Foot
3.2 CharacterController Stance F oot State? New to Swing Phase

Already in
The character controller is the coordinator of
Swing Phase
the overall system. It is in charge of two main
Do Nothing No For ced Replan? Yes
tasks: managing the movement of the feet and
Calculate Needed Target
computingthepelvis3Dmovementbasedonthe Check 3D
Trajectory Foot Path Planning
userneedsandonthefinalpositionsofthefeet.
Footprints 3D Path
(a) 4) Preferred Target Position 3) Naive Target Yes Valid? No Planner Constructor
Envi Position
ron
Figure5: Main job of the character controller per foot:
me
1) Initial Position
nt basedonthecurrentfootstateitcantakediffer-
2) Step Length entdecisions
Feet movement: Figure 5 explains how the
Vertical Slice in the Environment
character controller manages the movement of
(b) the feet (first task). At each time step, the
gait manager informs the character controller
about the feet that are going to enter swing
phase as detailed in Section 3.3. For each of
2) Final
1) Environment
Convex Hull these feet a preferred footprint target is calcu-
Convex Hull
3) Center
lated. As shown on Figure 4(a), the foot step
Projection
length is calculated based on the current speed,
Multi-legged Character Body multi-leggedcharactermorphologyandthefoot
Bounding Box Projection
relative position that the user can impose as
illustrated and explained directly on Figure 6.
Figure4:Theverticalsliceintheenvironmentcancontain
objects and obstacles, (a) computation of the After calculating this foot step length, we use
preferred footprint target for each foot. The the initial position of the foot to calculate the
naive target position is calculated by querying
preferred 3D target position in the environment
the environment about the elevation of the 2D
(SeeFigure4(a)).
point resulted from the initial position + the
steplength(b)Computationofthepelvis’height Finally, the character controller calls the foot
usingseveralconvexhullsthatcoverstheenvi- path planner to compute the 3D trajectory that
ronmentslicethatinterestsus
this foot will follow, as described in Section 5.
Pelvisdefaultmovement: the2Dmovement Feetthatwerealreadyinswingphasemayneed
of the pelvis on the ZX plan (assuming the anewa3Dtrajectory(path)forseveralreasons:
Y-axis is up) is calculated based on the speed a new pelvis orientation (when turning), a new
and orientation. While the computation of the desired relative position of the foot (Figure 6),
pelvis height is more complex, as shown on a new overall speed, or something changed in
Figure 4(b): we first construct a convex hull theenvironmentthusinvalidatingitscurrent3D
based on the ground height underneath it and trajectoryoritscurrenttarget. Inthesecasesthe
theactualpositionofthefeet. Byprojectingthe character controller processes this foot as if it
just started its swing phase, and therefore it is
Un-active Foot Currently in Foot 0
redirected to the previously explained foot path Swing Phase Feet Needle Foot 1
Foot 2
planning phase. Stance feet are blocked on the Foot 3
ground.
Top View
Foot Target Position
Relative Interpolation Foot Current Needles
Position Relative Position Rotation
Direction
Character
Front
Feet with Equal Target Next Feet to enter
and Current Relative Swing Phase

Position
Figure8:Anexampleofafourfeet’sgaitasshownbythe
Figure6:8-LeggedCharacterFeetSpacingInterface gaitmanager. Withthisinterface, theusercan
editthepattern.
Pelvismovementrefining: Aftermovingthe
feet, the character controller refines the pelvis
movementbasedonthefeetfeedback(shownon Gaits interpolation/transition During a lo-
Figure 7). Each foot can choose a better target comotion cycle any creature changes its gait
that adapts better to the context (see Section 5). constantly in order to adapt to the environment.
In that case, the character controller averages To accommodate for this changes in the gait
theoffsetbetweenthepreferredfootprinttargets and to introduce more variety in the locomo-
(Figure 7 in blue) and the effectively chosen tion styles, our gait manager allows the transi-
one (in green). The controller incorporates this tion/interpolation between any needed gaits on
offset when it is quite significant, based on the the fly. Each swing phase sector has a start and
multi-leggedcharactermorphology,otherwiseit a finish, we compute the transition to another
discardsit. (destination) gait by simply interpolating the
2D Top View Foot start of the source sector toward the start of the
Chosen destination sector in the direction that does not
Target
pass by the finish of the destination sector. On
Pelvis
Figure 9(a) we chose the clockwise direction
Movement Direction
Pelvis whileonFigure9(b)wechosethecounterclock-
Foot Needed
wise one. By doing so, the interpolation does
Target
not pass by any area of the circle that the user
Figure7: Feet feedback: During the computation of the
doesnotwantto. Theinterpolationofthedura-
pelvisdisplacement,weusethefeetfeedback.
tionoftheswingphase(thesizeofthesector)is
quite straightforward, and the speed of all these
processes can be fixed in advance by the user.
3.3 GaitManager So,oneachstepandwhenthefootisnotactive
(in stance phase), we replace its disk with the
The role of the gait manager is to organize and
newdiskcalculatedintheinterpolationprocess,
visualize the pattern of the feet’s cycle and to
resultinginseamlessandlogicalinterpolation.
performthetransitionbetweenpatterns. Sincea
locomotioniscyclic,itseemednaturaltorepre-
4 3D Path Construction
sent the gait/tempo with circles. As illustrated
on Figure 8, each circle represents a foot, with During the swing phase, each foot has a cur-
thecoloredsectorsrepresentingtheswingphase rent position (source) and a desired footprint
portion of the foot movement. The feet needle target. The role of the 3D path construction is
activatessectorsanddeactivatesothersbasedon toconstructthefoot3Dtrajectorythatnavigates
its current position while turning. Activating a throughtheenvironment,fromthiscurrentposi-
sectormeansthatthecorrespondingfootshould tiontowardthefootprinttargetwithoutcolliding
enterintheswingphase. with any obstacle. This 3D path construction is
Source Gait Destination Gait
(a)
Foot 0
Foot 1
Sector
Start
(a)
Sector
Finish
Clockwise
Interpolation 1 2 3 4 5
(b)

(b)

Counter
Clockwise
Interpolation 1 2 3 4 5
Figure10: (a) We firstly construct the path in a 2D
Figure9:Interpolations Options: (a) deciding to do a voxel-basedrepresentationoftheenvironment
clockwise position interpolation based on the (yellowdots)andthengeneratethefinalcurve
actualdispositionofthegaitdisks(b)deciding (in black) with a selection of waypoints (red
todoacounter-clockwisepositioninterpolation dots). (b) Using the elevations map and the
previous 2D trajectory we construct the 3D
trajectory.
requested several times with different footprint
targets by the foot path planner as it will be

explained in Section 5. The environment itself
namic objects when they move near our multi-
can be very complex, and it can include several
leggedcharacter. Inordertoavoidlegscrossing,
objects represented by many triangles. That
we add for each foot the projection of the other
is why we have oriented this path construction
legsintotheobstacles’mapasforbiddencells.
process toward a discrete grid-based approach.

Indeed, once the environment is converted and Start Position Pelvis Preferred Target
represented by our grid, the path computation
becomesindependentoftheobject’scomplexity.
We also have chosen this over a vectorial based
path planning because discrete algorithms are
easiertoimplement.
Grid-based representation of the environ-
ment. We convert the 3D environment near
theanimatedmulti-leggedcharacterintotwo2D
grids: the obstacles’ map and the elevations
map. The obstacles’ map describes the areas
of the environment where the feet are allowed
Figure11: An example of our environment discretiza-
to pass, as illustrated on Figure 10(a). The tion: pinkspheresrepresentstheground, yel-
black cells represent the obstacles, and we call low spheres contain the corner of an obsta-
them the forbidden cells. The elevations map cle, green spheres contain an obstacle edge,
blue spheres are an obstacle interior and red
contains the elevation of the highest obstacle in
spheresareanobstaclesizeincrease.
each cell as shown on Figure 11. These two
maps are computed using the terrain heightmap These maps are relatively small as they are
andtheobjects: theboundingboxofeachobject only computed around our animated multi-
isvoxelizedontothemaps. Concaveobjectsare legged character, speeding up calculations.
subdivided into convex ones. We pre-compute Since a foot could not be punctual, we use the
themap’srepresentationofstaticobjects. While bounding box of the foot shape to increase the
we compute the map’s representation of dy- size of the obstacles in the opposite direction
of the foot, as shown on Figure 12. Doing so preferredtargetcalculatedbythecharactercon-
guarantees the non penetration of the foot with troller can be too close to an obstacle). That is
theobstacles. whyinthisstepwecalculateandassigntoeach
foot the best trajectory toward the best target in
thecurrentenvironment.
Obstacle Foot Shape and
Orientation 5.1 PotentialFootprints
Our algorithm evaluates several footprint tar-
gets by exploring the potential cells around
Contextual Foot Center
new obstacle the preferred footprint (the one computed by

Figure12: We increase each obstacle size using the the character controller in Figure 11). Several
boundingboxofthefootanditsorientationin operations are done to do that. In both maps
ordertobetteravoidcollision.
(theobstacles’mapandtheelevationsmap),we
Path construction. Always with a perfor- firstly increase the size of the obstacles using
mance concern, we firstly compute the trajec- the foot shape (See Figure 12 and Figure 11 in
tory from the actual foot position toward the red). Secondly, to eliminate possible intersec-
targeted footprint in the ZX plan using the tion with other feet we fill the obstacles’ map
projections of the source and the target on the with the position of these other feet. Thirdly,
ZX plan (in black on Figure 11). Our system we identify all the -potential- cells that may
uses a shortest path computation that processes accept a footprint: all the non-forbidden cells
aWavefrontalgorithmcombinedwiththepoten- thatarenotasizeincreaseones(Figure13). For
tialfieldmethod[36]fortheobstacleavoidance. eachpotentialtarget,wecalculateascorebased
This method is quite similar to the well-known on several criteria’s: distance to the preferred
Dijkstra’sshortestpathalgorithm. footprint, difference of elevation between the
The resulting path off the wavefront algo- footprint and the surrounding cells, leading or
rithm is constructed out of several cells that we not to a feet crossing, etc. The combination of
call the naive cells of the plan (in yellow on all these criteria’s provides the final cell’s score
Figure 10). We refine these naive cells, using (footprint score) that we normalize between 0
queries of line of sight (no intersection with and1. Figure13showsthesescores.
a forbidden cell) to eliminate unwanted cells,
5.2 BestPairofFootprintandPath
and we obtain the final cells of the the plan (in
red). These cells are used to build the 2D path
represented by a parametric Hermite curve as
shownonFigure10)(a).
We sample this 2D curve and elevate it in
3D using the elevations map. Resulting way-
points are used as control points to define a 3D
Hermite curve: this curve represents our 3D
trajectorythroughtheenvironmentasshownon
Figure10(b).
Figure13: Potentialtargets: thecolorvariesfromgreen
(besttarget)(score=1)toblue(worsttarget)
5 Footprints and Feet Path (score = 0). Crossed cells are the cells
processed by our algorithm, in pink possible
Planning
trajectories,inblackthechosenone.
In Section 3.2, we explained that starting from Avoidance-wise. During the 3D path con-
the initial foot position the character controller struction (See Section 4), the forbidden cells in
calculates a preferred footprint target according the obstacles’ map designate the parts of the
to the locomotion parameters and the surround- environment that the 2D trajectory is going to
ingenvironment(Figure11). Butthesecalcula- avoid and go around. This 2D trajectory passes
tions do not take into consideration the actual through cells that have an elevation. The 3D
state of the foot and its preferences (e.g. the path constructor uses this elevation to construct
thefinal3Dtrajectory. Thesystemusesthisob- footprint target and 3D trajectory that this foot
stacles’maptoprocessanobstacle: eithergoing should follow. We calculate the length of this
arounditorgoingoverit. Ifthesystemwantsto 3D trajectory, and using the needed time given
go around an obstacle, it just needs to add it to bythecharactercontroller,wemovethefooton
the obstacles’ map as forbidden cells. In that thecurveataconstantspeed.
way, the resulting 2D trajectory will definitely Trajectory scoring. We generate for each
go around it. While if the system wants to go created 2D/3D trajectory a score based on the
overanobstacle,itdoesnotneedtodoanything applicationspecifications,likethetotallengthof
special as the obstacle is already present in thepath,theaccelerationandthecurvetangents
the elevations map. And the obstacle will be profile, etc. For instance, the system shown in
avoided accordingly based on its elevation. In theaccompanyingvideopreferstrajectoriesthat
ordertoachievethisavoidancedistinctioninan are more straight (direct) with less curvature,
optimal way in a complex environment (height a preference observed in biomechanics as it
map plus obstacles), our system discretize the minimizestheenergycost[37,38].
elevations map on the Y-axis into slices (for
instance slices of 10cm). For each slice, the 6 Level of Details techniques
system fills the obstacles’ map with the cells
(LOD)
thathavehigherelevationthanthisslice. Inthat
way, all calculated trajectories will go over all Ourmainalgorithm(Section5.2)executiontime
obstacles,objectsandpiecesoftheenvironment can be controlled easily when simulating many
that have an elevation lower or equal to the multi-legged characters in order to accelerate
slice’selevation. Atthesametime,allcalculated the simulation itself. This comes from the
trajectorieswillgoaroundallobstacles, objects ability of controlling the number of evaluated
and pieces of the environment that have an ele- couples (target-trajectory) and from the ability
vationhigherthanthechosenslice’selevation. of controlling the size of the slices used when
Soeachtrajectorycangoaroundorovereach avoiding obstacles. But in order to always
obstacle, which generates multiple trajectories have a plausible locomotion, we start applying
toward a target. Each one of these trajecto- this LOD after we find the first valid couple
ries has a score. Our search space is all the (target-trajectory), in this way we ensure that
possible trajectories that go from the starting the algorithm will assign to each foot a valid
pointtowardallthepossibletargets. Outofthis trajectorytowardavalidtarget(althoughitisnot
multitude of possibilities, our main algorithm thebestcouple).
picksupthebestcouple(target-trajectory)inan In our simulation and for off-screen charac-
intelligentway. ters, the algorithm stops directly when finding
Our algorithm (result shown on Figure 13) this first couple. While for the on-screen char-
loops on all the possible targets based on their acters, we limit the number of couples evalu-
score (in a descending way). For each one of ated after finding this first couple in a linear
these targets, the algorithm first generates the way based on the distance of that multi-legged
2D trajectory and scores it, if the score of the character from the camera. In this way for far
couple(target-trajectoryin2D)isbetterthanthe on-screen characters the algorithm stops also
current best couple found till now, it continues. when it finds the first couple. In the same way,
Thenitgeneratesthe3Dtrajectorybasedonthe for off-screen characters the algorithm tries to
2D one and scores it, if the score of the new go over any obstacle using no slices (not going
couple(target-trajectoryin3D)isbetterthanthe around any obstacle). While for the on-screen
currentbestcouple, thenittagsthisnewcouple characters,weincreasethesizeoftheslices(for
as the best one and continues. The algorithm example10cm,15cm...noslices)inalinearway
continuesevaluatingthecouplesuntilitreaches based on the distance of that character from the
a couple (target-trajectory in 3D) with a score camera. ThisLODcanberegardedas: themore
worse than the current best one, in this case it the character is far away from the camera (or
stopsandthecurrentbestcoupleisthebestone. off-screen) the less our algorithm worries if the
So,attheendofthealgorithmweobtainthebest chosen couple is comfortable. In next section
Table1:Averagecomputationtimefor1008-leggedcharacters
TotalforCharacters MapsPreparation CCDIKSystems AverageFPS
LOD 0.026s 0.004s 0.013s ~30fps
LODZoomed 0.028s 0.004s 0.006s ~30fps
NoLOD 0.045s 0.004s 0.013s ~18fps
we speak about the actual performance of our In LOD we make sure that all of the characters
real-timesystem. are in the field of view of the camera, while in
LOD Zoomed we zoom on one character and
makesurethatatleast50%ofthecharactersare
7 Results
shown on the screen. As we can observe, the
In our implementation, the environment is rep- maps preparation is fixed, as it is pre-computed
resented by two classes of objects: the terrain once,forallcharactersatthesametime. InLOD
and the obstacles. A height map defines the Zoomed the system loses some computation
terrainandisloadedwithoutanypre-processing time per character as there are more characters
analysis (See Figure 11 ). The obstacles are doing full search for the best couple, while in
mainly represented by crates with various sizes thesametimegainscomputationtimeintheIK
and orientations randomly generated on the ter- systems as we do not calculate the IK for the
rain (See Figure 1 and 14). These crates can be off-screencharacters.
staticorcanmoveontheterrain(Seetheaccom-
panying video). Without changing anything in
8 Conclusions
the system, we have tested it on different kinds
of terrain (flat surface, smooth terrain, regular We presented a system capable of procedu-
stairs, etc.) with different kinds of obstacles rally generating believable locomotion anima-
(static crates and moving ones). The size of the tion of several multi-legged characters (like
discretization maps used in our tests is 70×70 arachnids, insects, or any imaginary n-legged
with 7cm cells, which consumes little memory robots/creatures) in real-time with no a priori
and is precise enough since the maps describe motion data nor any information about the en-
only the environment close to each animated vironment. Our system is quite generic and can
character. Theanimatedmulti-leggedcharacters beappliedonavarietyofmorphologies. Inrun-
gaitsareinspiredfrombiologystudies[39,40] time the user can control many parameters like
thethegait,thespeed,thedirection,etc.
Nevertheless,thecurrentsystemassumesthat
the feet of the character can be represented by
a point. Our model does not include the feet’s
metatarsus, which has a great impact on the
naturalnessofthelocomotionwhenconsidering
more complex characters. As a future work, it
will be interesting to study this point, specially
for bipeds/humans. And to study the addition
ofaflexiblespine-likestructure,whichisessen-
Figure14: Simulationsnapshot.
tial when simulating quadrupeds [10]. We are
The results show that our system is well also planning on improving the pelvis behavior
adapted for real-time applications. In Fig- to incorporate dynamic-like balance reactions.
ure14andintheaccompanyingvideoweshow Our system can serve as input to higher level
many morphologically different characters ani- characters’controllersthatwouldliketoprovide
matedinreal-timeusingourtestmachine(Core more animations than only the locomotion, like
i7 2.7 GHZ, 8 GB RAM, 6870 ATI Radeon touching objects for discovering the environ-
HD with 1GB vRam). Table 1 shows average ment,studyinginsect’sbehavior,etc.
computation time for 100 8-legged characters.