Real-time Horse Gait Synthesis Ting-Chieh Huang Yi-Jheng Huang Wen-Chieh Lin Department of Computer Science National Chiao Tung University, Taiwan ftchuang,ichuang,[email protected] Abstract digital special effects. In computer animation, Horse locomotion exhibits rich variations in animals are a very common character. To gen- gaits and styles. Although there have been many erate more realistic animal animation, the data- approaches proposed for animating quadrupeds, driven approach, which relies on real motion there is not much research on synthesizing horse data as synthesis or editing resources, seems to locomotion. In this paper, we present a horse be a good candidate. Nevertheless, it is not con- locomotion synthesis approach. A user can venient and sometimes even difficult to capture arbitrarily change a horse’s moving speed and quadruped motion although we are now able to direction and our system would automatically collect a great amount and variety of human mo- adjust the horse’s motion to fulfill the user’s tions using commercial motion capture devices. commands. At preprocessing, we manually In this paper, we propose a synthesis approach capture horse locomotion data from Eadweard to animate quadruped motion based on a small Muybridge’s famous photographs of animal motion database. In particular, we focus on gen- locomotion, and expand the captured motion erating horse locomotion as it is basic and es- database to various speeds for each gait. At sential motion while exhibiting large variations. runtime, our approach automatically changes Moreover, this is also a challenging problem as a gaits based on speed, synthesizes the horse’s horse has six different gaits and changes its gaits root trajectory, and adjusts its body orientation at different speeds. If we can solve the gait tran- based on the horse’s turning direction. We sition problem of horse, the proposed approach propose an asynchronous time warping ap- should be applicable to the gait transition prob- proach to handle gait transition, which is critical lem of other quadrupeds. for generating realistic and controllable horse We propose a realtime system that allows locomotion. Our experiments demonstrate a user to arbitrarily change a horse’s moving that our system can produce smooth, rich and speed and direction. Our system automatically controllable horse locomotion in real time. changes the horse’s gaits according to its speed. We construct a motion database by manually Keywords: character animation, motion capturing horse postures from Eadweard Muy- synthesis, quadruped gait synthesis bridge’s series pictures of 11 locomotion using MAYA. In order to let a horse walk or run at 1 Introduction arbitrary speed, we expand our horse locomo- tion data by time warping the captured motion Character animation has been studied in com- to various speeds based on zoological studies puter graphics for many years. With the rapid [1]. The studies show that a horse’s stride length development of computer hardware and graph- at stance phase increases with its progressing ics algorithms, 3D animation techniques are speed, while the contact time of a stride de- now wildly used in cartoons, video games and creases as a power function of its speed. To be able to generate smooth gait transition moment on one image. Different with above between two arbitrary gaits at any phase of a methods which can only capture 2D informa- stride, we propose an asynchronous time warp- tion, statistical analysis has also been applied ing method to handle the gait transition prob- to capture 3D information[5]. In biomechanics lem. We also develop an on-line root trajectory and zoology, Alexander et al. [6, 7, 8, 9] de- generation and body orientation adjustment ap- veloped dynamic similarity hypothesis, which proach to control the global position and orien- explains the relationship between animal size, tation of the horse. Instead of using the same speed, mass and external forces. Hoyt et al.[1] generic time to blend the motion of two gaits showed that a horse’s step length increases with for all four legs, our asynchronous time warp- its speed while its feet’s time of contact with the ing method performs time warping at each leg ground decreases as a power function of speed. separately. We blend each leg’s motion of two These findings and other research on animal gaits at its own generic time and gradually ad- behavior strategies [10, 11] help us to develop just each leg’s pace to ensure that the four legs our gait synthesis approach. would converge to the new gait. Furthermore, In computer graphics, many methods were our root trajectory generation and body orienta- proposed to simulate quadruped motion. Inverse tion adjustment approach computes the position Kinematics (IK)-based approaches [12, 13, 4] and orientation based on each foot’s ground con- usually decide animal footprints first, and then tact state at each time frame. combine physically-based approaches to con- The contributions of this paper are propos- trol the body movement. Instead of driving ing: 1) a real-time horse gait synthesis ap- quadruped motion by skeletons, mesh-based proach that can automatically change a horse’s approaches generate the motion of mesh sur- gait smoothly according to the speed and direc- face directly [14, 15, 16, 17]. Another main tion specified by a user; 2) An asynchronous stream of generating quadrupeds locomotion time warping method that can generates smooth is the controller-based approaches, which can gait transition between any two gaits; 3) A root produce realtime interaction and deal with un- trajectory generation and body orientation ad- expected circumstances[18, 19, 20, 21]. Al- justment method that preserves horse gait style though Marsland and Lapper[20] also worked while the horse turns and/or changes speed. on horse locomotion generation, they focused only on the trot gait in their simulation. In contrast, we address to synthesize all gaits of a 2 Related work horse in real time. Coros et al.[21] combined a PD controller system and an internal virtual Generating quadrupedal motions receives much force system to simulate an integrated set of research attention in robotics and computer an- gaits and skills for a physics-based quadruped. imation. It also benefits from many research Besides, optimization-based approaches were studies in zoology and biomechanics. We refer also widely used. Wampler et al. proposed the readers to an excellent survey by Skrba et a sampling-based derivative-free optimization al. [2] for an overview of quadruped animation method under the spacetime optimization for- techniques including quadruped motion capture mulation to automatically synthesize plausible and simulation. gaits for different skeletons[22]. People have long been interested in There are also many quadruped simulation quadruped motions and analyzed them using approaches mixing the above approaches. Kry different motion capture devices. Comparing et al.[23] used the natural vibration modes of with human motion, it is hard to capture ani- the body that are related to morphological pa- mal motion. The famous work by Eadweard rameters such as the shape, size, mass, and joint Muybridge [3] was the first attempt to capture stiffness to generate efficient locomotion. Tsai animal motions, in which a series of 24 cameras et al.[24] proposed a physically-based method, was used to take photos of animal’s locomotion. which is able to adjust the original motion Kokkevis et al. [4] used chronophotography to meet adaptation requirements when animat- technique to record many phases of a single ing 3D virtual characters. Sims[25] proposed a novel system creating virtual creatures that User Desired Speed & Direction move and behave in simulated 3D physical worlds. He used genetic algorithm to evolve the Capture Motion from morphologies and the neural systems of those Gait Muybridge’s photographs Transition creatures. Horse In robotics, various quadruped robots have Root Trajectory Motion been created. Sony AIBO is a Japanese robot Synthesize Motions at Generation & dog, which is able to see and move around while Various Speed Body Orientation Adjustment maintaining balance[26]. Boston Dynamics pro- duced ’BigDog’ and ’LittleDog’[27, 28, 29]. Preprocessing Runtime BigDog has the animal alike legs that can absorb Figure 1: Overview of our horse locomotion the shocks from the ground. LittleDog, which generation system. is capable of walking on rough terrains, is built for studying animal locomotion. SCOUT used one degree of freedom legs to produce walking, climbing, and galloping animation[30]. In contrast to the existing work on quadruped animation, we address the gait transition and synthesis problem in this paper. In particular, we focus on horse gaits, which have rarely been studied in computer animation. Our work can be combined with the controller-based approaches to provide the reference trajectory that is re- quired in these approaches. Our asynchronous time warping method can effectively handle the gait transition problem. It allows a horse to change its gait arbitrarily between Walk, Am- ble, Trot, Rack, Canter and Gallop. The tran- Figure 2: Six gaits of horse locomotion. The sition begins once a user requests a larger speed dark blue and light blue regions rep- change such that the horse needs to change its resent the stance and flight phase re- gait according to zoological study. The speed spectively. changing command can be given at any phase of a horse stride. In addition, as a horse can change its gait directly from a slow-speed gait correct speed as described in Muybridge’s pho- to a fast-speed gait in the reality, our method can tographs. Note that there is no horse turning also achieve this kind of gait transition and thus motion in Muybridge’s photographs. Figure 2 results in more natural horse locomotion. shows these six gaits used in our system.