Trajectory optimization and posture generation are hard problems in robot locomotion, which can be non-convex and have multiple local optima. Progress on these problems is further hindered by a lack of open benchmarks, since comparisons of different solutions are difficult to make. In this paper we introduce a new benchmark for trajectory optimization and posture generation of legged robots, using a pre-defined scenario, robot and constraints, as well as evaluation criteria. We evaluate state-of-the-art trajectory optimization algorithms based on sequential quadratic programming (SQP) on the benchmark, as well as new stochastic and incremental optimization methods borrowed from the large-scale machine learning literature. Interestingly we show that some of these stochastic and incremental methods, which are based on stochastic gradient descent (SGD), achieve higher success rates than SQP on tough initializations. Inspired by this observation we also propose a new incremental variant of SQP which updates only a random subset of the costs and constraints at each iteration. The algorithm is the best performing in both success rate and convergence speed, improving over SQP by up to 30 in both criteria. The benchmark's resources and a solution evaluation script are made openly available.
This paper describes a collection of optimization algorithms for achieving dynamic planning, control, and state estimation for a bipedal robot designed to operate reliably in complex environments. To make challenging locomotion tasks tractable, we describe several novel applications of convex, mixed-integer, and sparse nonlinear optimization to problems ranging from footstep placement to whole-body planning and control. We also present a state estimator formulation that, when combined with our walking controller, permits highly precise execution of extended walking plans over non-flat terrain. We describe our complete system integration and experiments carried out on Atlas, a full-size hydraulic humanoid robot built by Boston Dynamics, Inc.  The Pascal Visual Object Classes (VOC) challenge is a benchmark in visual object category recognition and detection, providing the vision and machine learning communities with a standard dataset of images and annotation, and standard evaluation procedures. Organised annually from 2005 to present, the challenge and its associated dataset has become accepted as the benchmark for object detection. This paper describes the dataset and evaluation procedure. We review the state-of-the-art in evaluated methods for both classification and detection, analyse whether the methods are statistically different, what they are learning from the images (e.g. the object or its context), and what the methods find easy or confuse. The paper concludes with lessons learnt in the three year history of the challenge, and proposes directions for future improvement and extension. Direct methods for trajectory optimization are widely used for planning locally optimal trajectories of robotic systems. Many critical tasks, such as locomotion and manipulation, often involve impacting the ground or objects in the environment. Most state-of-the-art techniques treat the discontinuous dynamics that result from impacts as discrete modes and restrict the search for a complete path to a specified sequence through these modes. Here we present a novel method for trajectory planning of rigid-body systems that contact their environment through inelastic impacts and Coulomb friction. This method eliminates the requirement for a priori mode ordering. Motivated by the formulation of multi-contact dynamics as a Linear Complementarity Problem for forward simulation, the proposed algorithm poses the optimization problem as a Mathematical Program with Complementarity Constraints. We leverage Sequential Quadratic Programming to naturally resolve contact constraint forces while simultaneously optimizing a trajectory that satisfies the complementarity constraints. The method scales well to high-dimensional systems with large numbers of possible modes. We demonstrate the approach on four increasingly complex systems: rotating a pinned object with a finger, simple grasping and manipulation, planar walking with the Spring Flamingo robot, and high-speed bipedal running on the FastRunner platform. In this paper we tackle the problem of visually predicting surface friction for environments with diverse surfaces, and integrating this knowledge into biped robot locomotion planning. The problem is essential for autonomous robot locomotion since diverse surfaces with varying friction abound in the real world, from wood to ceramic tiles, grass or ice, which may cause difficulties or huge energy costs for robot locomotion if not considered. We propose to estimate friction and its uncertainty from visual estimation of material classes using convolutional neural networks, together with probability distribution functions of friction associated with each material. We then robustly integrate the friction predictions into a hierarchical (footstep and full-body) planning method using chance constraints, and optimize the same trajectory costs at both levels of the planning method for consistency. Our solution achieves fully autonomous perception and locomotion on slippery terrain, which considers not only friction and its uncertainty, but also collision, stability and trajectory cost. We show promising friction prediction results in real pictures of outdoor scenarios, and planning experiments on a real robot facing surfaces with different friction.