Animation as a Trajectory Optimization Problem

Paper One (Spacetime Constraints)

This is an example response. To add your own response, click on 'Edit' above. Paragraphs are separated with just a blank line. This paper is interesting because... It is flawed because ... I didn't understand the following bits... Open problems are ... -- Michiel van de Panne

In “spacetime constraints” paper, it presents a neat method for animation, using physics model and some objective functions, and then letting system automatically figure out how the motion should be performed. Having said that, the performance of the approach still heavily depends on constraints set by users; and moreover, finding an appropriate objective function and whereby solving for optima are also quite challenging. As it said “the realism of simulation comes at the expense of control.” In “particle” method, it mentions SQP solver, so it would be good if we can reveal a little bit about how it works. -- Steven Chang

(Spacetime Constraints) I didn’t read very carefully but it’s amazing that the program can understand commands such like “don’t waste energy” or “come down hard enough to splatter whatever you land on”. What I’m curious is that how could the program know what the animators mean? There must have some patterns that should follow. So then the program can do only what it has been taught to do which limits its performance. Thus it still needs much human efforts to define such constraints with the program. The ultimate goal on this research area might be building the system that realizes generating animation by what-you-say-is-what-you-get model. But seems it has a long way to go.-- Zhangbo Liu

First of all, this paper is a fun read just because of its age. I was 6 1/2 years old when this was written. I love the mention of "acceleration by array processors" and how systems with less than 1000 variables are solved in "under 10 minutes". So old! Another nice property regarding the generation of this paper is its wording. Perhaps it is due to the novelty of SIGGRAPH as a conference at the time, but this paper reads more like a good textbook than a conference paper (i.e., it provides a nice introductory example, works through the details and really assumes little prior knowledge). Anyways, while reading the paper, the two questions that were outstanding in my head were "does this apply to human figures with more than four DOF?" and "Yes, optimization is cool, but what function do you minimize and what constraints do you put in?". Indeed, both of these are still (see my comments on the next paper) open problems and are areas for active research. The jumping Luxo result is nice, which shows immediate application of the technique to motions of low dimensional figures. One final note is that I quite enjoy the fact that they used LISP to develop their math compiler and runtime system. -- KenRose

(Spacetime constraints) A very good paper in my view, which is I believe being used later on in different works. The main problem is that they refer to motion data but their example is using particles which have significantly less degrees of freedom. So the challenge is to apply it to motion capture data (which is illustrated in the other paper). -- Hagit Schechter

How does it scale, if we have to deal with this crazy high dimensional optimization problem? especially for more complex systems like human characters... Then again, I wonder what you could pull off today, given that this was published nearly 20 years ago. It seems impressive for the time, and it's obviously an interesting approach to the problem of partially automating motion of characters. --Christopher Batty

It's a cool idea, but as Christopher mentioned, it scales very poorly. Discretization scales exponentially in dimension (so here, 3 spatial dimensions, 1 for time => ~TN^3 multiplied by however many joints/limbs you have). It doesn't really matter how sparse the matrices are, this is going to be a massive linear system to solve. -- Daniel Eaton

Paper Two (Synthesizing Human Motion)

Another paper. Please add your comments below.

This “Synthesizing …” paper presents an interesting approach to generate realistic motions by solving the optimization problem in a low-dimensional space. Projecting human motions onto an abstract low-dimensional space is based on the observations that many dynamic human motions can be adequately represented with only five to ten degrees of freedom. However, after watching the movie, I am wondering whether this is surely adequate for some complex motions other than jumping, walking and those presented in the movie. Similar to first paper in that animators also have to select a set of motions as references, I think the performance could still be an issue; but they also use IK solver to enforce the kinematics constraints, so the result should be more accurate and realistic. -- Steven Chang

(Synthesizing Human Motion) Once I’ve read the Neuroanimator [Grzeszczuk et al. 1998] and it was very interesting. I think this paper did the similar work as that one. There do have several methods of using low dimension physically-based model to emulate and control higher dimension physically-based models. But a common issue I think is to balance the realistic effect and the computational workload. PS: I tried several times to watch the video but I didn’t observe obvious difference among the motion under 2, 5 and 10 dimensions.-- Zhangbo Liu

I regard this paper an excellent sequel to the Spacetime Constraints paper. The background section nicely explains other work in the area of dimensionality reduction and use of optimization for synthesizing motion. Sadly, the state of the art still seems to be "high dimensions are hard" due to a variety of reasons (contact forces, objective functions with torque, system size, etc.). I like their objective function since it really only depends on three parameters (w_T, w_A and w_P), which is simple enough for a human to manipulate. While reading the paper, I thought that it would be nice if the user didn't have to specify which motions from the database that are similar to the desired motion. Indeed, the authors also pointed this out in the Discussion section at the end. -- KenRose

(Synthesizing physically realistic human motion) The paper combines different works in the field and synthesizes into one that makes a lot of sense to me. The first comment that I have is related to selecting the basis motions, currently done by the user. My question is, have there been related works to compute the best basis motions, opposed to having the user select them? The second comment is related to their statement that in general they got less reliable motion when running the optimization in higher dimensions. They do not provide a good explanation for that (after all – that is un-intuitive), and I wonder if someone can come up with an explanation for that. -- Hagit Schechter

This seems to be one approach to overcoming scalability difficulties of original space-time constraints paper. It's frustrating that the method is fairly slow AND there is no guarantee of convergence for motions that diverge somewhat from the training data, but it is nifty that it can sometimes generalize beyond the input data. As an animation physics guy I like the idea of combining equations of motion with models from motion capture as they do here The claim that the lower dimensional representation increases the naturalness of the optimized result is intriguing. I wonder if there's an intuitive explanation of why this might be the case, eg. The low dimensional model encompasses the natural motion defined in the database, but by optimizing with a larger number of dimensions it allows more flexibility for the mathematical/physics constraint optimization to take over causing greater divergence from "natural" looking motion. -Christopher Batty

It would be great if the presenters could do a quick refresher on SQP. The optimization problem these authors pose is similar to the one posed in the paper presented by Christopher, last week (low-dimensional control signals) though, this paper is a year older. What does the expression "sparse sketch" mean? Is that just the mocap data? -- Daniel Eaton