Step planning is becoming an increasingly important research topic for humanoid robots. Most cost functions for step planning in the literature are designed based on terrain information. The energy cost to perform each step action is usually ignored. In walking, energy consumption depends on gait features such as step length and width. In this paper, we use three simple and intuitive energy cost functions for different step lengths, widths, and the turning angle. These functions are inspired by literature on human walking energy analysis, and the function parameters are tuned to match computed costs for optimal humanoid walking motions obtained by simulation. The energy cost and the terrain cost are combined to obtain an optimal step planning sequence using A* search.

Although there has been great progress in robot grasp planning, automatically generated grasp sets using a quality metric are not as robust as human-generated grasp sets when applied to real problems. Most previous research on grasp quality metrics has focused on measuring the quality of established grasp contacts after grasping, but it is difficult to reproduce the same planned final grasp configuration with a real robot hand, which makes the quality evaluation less useful in practice. In this study, we focus more on the grasping process, which usually involves changes in contact and object location, and explore the efficacy of using dynamic simulation in estimating the likely success or failure of a grasp in the real environment. Among many factors that can possibly affect the result of grasping, we particularly investigated the effect of considering object dynamics and pose uncertainty on the performance in estimating the actual grasp success rates measured from experiments. We observed that considering both dynamics and uncertainty improved the performance significantly, and when applied to automatic grasp set generation, this method generated more stable and natural grasp sets compared with a commonly used method based on kinematic simulation and force-closure analysis.

In this paper new grasp quality measures considering both object dynamics and pose uncertainty are proposed. Dynamics of the object is incorporated into our grasping simulation to capture the change of its pose and contact points during grasping. Pose uncertainty is considered by running multiple simulations starting from slightly different initial poses sampled from a probability distribution model. A simple robotic grasping strategy is simulated and the quality score of the resulting grasp is evaluated from the simulation result. The effectiveness of the new quality measures on predicting the actual grasp success rate is shown through a real robot experiment.

We propose a fast physically-based simulation system for skeleton-driven deformable body characters. Our system can generate realistic motions of self-propelled deformable body characters by considering the two-way interactions among the skeleton, the deformable body, and the environment in the dynamic simulation. It can also compute the passive jiggling behavior of a deformable body driven by a kinematic skeletal motion. We show that a well-coordinated combination of: (1) a reduced deformable body model with nonlinear finite elements, (2) a linear-time algorithm for skeleton dynamics, and (3) explicit integration can boost simulation speed to orders of magnitude faster than existing methods, while preserving modeling accuracy as much as possible. Parallel computation on the GPU has also been implemented to obtain an additional speedup for complicated characters. Detailed discussions of our engineering decisions for speed and accuracy of the simulation system are presented in the article. We tested our approach with a variety of skeleton-driven deformable body characters, and the tested characters were simulated in real time or near real time.

This paper describes Newton and quasi-Newton optimization algorithms for dynamics-based robot movement generation. The robots that we consider are modeled as rigid multibody systems containing multiple closed loops, active and passive joints, and redundant actuators and sensors. While one can, in principle, always derive in analytic form the equations of motion for such systems, the ensuing complexity, both numeric and symbolic, of the equations makes classical optimization-based movement-generation schemes impractical for all but the simplest of systems. In particular, numerically approximating the gradient and Hessian often leads to ill-conditioning and poor convergence behavior. We show in this paper that, by extending (to the general class of systems described above) a Lie theoretic formulation of the equations of motion originally developed for serial chains, it is possible to recursively evaluate the dynamic equations, the analytic gradient, and even the Hessian for a number of physically plausible objective functions. We show through several case studies that, with exact gradient and Hessian information, descent-based optimization methods can be forged into an effective and reliable tool for generating physically natural robot movements.

We present the cyclic coordinate descent (CCD) algorithm for optimizing quadratic objective functions on SE(3), and apply it to a class of robot sensor calibration problems. Exploiting the fact that SE(3) is the semidirect product of SO(3) and /spl Rfr//sup 3/, we show that by cyclically optimizing between these two spaces, global convergence can be assured under a mild set of assumptions. The CCD algorithm is also invariant with respect to choice of fixed reference frame (i.e., left invariant, as required by the principle of objectivity). Examples from camera calibration confirm the simplicity, efficiency, and robustness of the CCD algorithm on SE(3), and its wide applicability to problems of practical interest in robotics.

The paper presents a class of Newton-type algorithms for the optimization of robot motions that take into account the dynamics. Using techniques from the theory of Lie groups and Lie algebras, the equations of motion of a rigid multibody system can be formulated in such a way that both the first and second derivatives of the dynamic equations with respect to arbitrary joint variables can be computed analytically. The result is that one can formulate the exact gradient and Hessian of an objective function involving the dynamics, and develop efficient second-order Newton-type optimization algorithms for generating optimal robot motions. The methodology is illustrated with a nontrivial example.