We present a new time integrator for articulated body dynamics. We formulate the governing equations of the dynamics using only the position variables and then recast the position-based articulated dynamics as an optimization problem. Our reformulation allows us to integrate the dynamics in a fully implicit manner without computing high-order derivatives. Therefore, under arbitrarily large timestep sizes, we observe highly stable behaviors using an off-the-shelf numerical optimizer. Moreover, we show that the accuracy of our time integrator can increase by using a high-order collocation method. We show that each iteration of optimization has a complexity of O(N ) using the Quasi-Newton method or O(N 2 ) using Newton's method, where N is the number of links of the articulated model. Finally, our method is highly parallelizable and can be accelerated using a Graphics Processing Unit (GPU). We highlight the efficiency and stability of our method on different benchmarks and compare the performance with prior articulated body dynamics simulation methods based on the Newton-Euler equation. Using a larger timestep size, our method achieves up to 4 times speedup on a single-core CPU. With GPU acceleration, we observe an additional 3 − 6 times speedup over a 4-core CPU. We give a brief overview of previous work in articulated body dynamics, time-integration schemes, and position-based dynamics. Articulated body dynamic simulation is a classic, well-studied problem in robotics. Some methods [30, 5, 29] focus on articulated bodies with general constraints, where the configurations of articulated bodies are represented using maximal coordinates.
To generate stable behaviour at large time-step sizes, Pan et al. REF propose an integrator for articulated body dynamics by using only position variables to formulate the dynamic equation.
Time Integrating Articulated Body Dynamics Using Position-Based Collocation Method
arXiv: Robotics
Engineering Computer Science