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.
Robot motion planning has been tackled with search, sampling and optimization methods. Recently, optimization algorithms have gained popularity, due to the existence of fast general-purpose software and the possibility to easily integrate many different constraints in the problem. One of the state-of-the-art algorithms is sequential quadratic programming, which is used by SNOPT @cite_23 for general-purpose optimization, but also by trajectory-optimization libraries @cite_1 , and trajectory optimization research on legged robots @cite_20 . Projected conjugate-gradient methods such as CHOMP @cite_6 have also been proposed for the problem. The gradient-descent methods we evaluate in this paper are related to CHOMP in the sense that they also do (pre-conditioned) gradient descent. However, as in @cite_1 we use penalties for constraints, thus being able to consider general non-linear constraints on robot postures or motion.
@cite_20 @cite_1 @cite_6 @cite_23
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Existing high-dimensional motion planning algorithms are simultaneously overpowered and underpowered. In domains sparsely populated by obstacles, the heuristics used by sampling-based planners to navigate “narrow passages” can be needlessly complex; furthermore, additional post-processing is required to remove the jerky or extraneous motions from the paths that such planners generate. In this paper, we present CHOMP, a novel method for continuous path refinement that uses covariant gradient techniques to improve the quality of sampled trajectories. Our optimization technique both optimizes higher-order dynamics and is able to converge over a wider range of input paths relative to previous path optimization strategies. In particular, we relax the collision-free feasibility prerequisite on input paths required by those strategies. As a result, CHOMP can be used as a standalone motion planner in many real-world planning queries. We demonstrate the effectiveness of our proposed method in manipulation planning for a 6-DOF robotic arm as well as in trajectory generation for a walking quadruped robot. Traditional motion planning approaches for multilegged locomotion divide the problem into several stages, such as contact search and trajectory generation. However, reasoning about contacts and motions simultaneously is crucial for the generation of complex whole-body behaviors. Currently, coupling theses problems has required either the assumption of a fixed gait sequence and flat terrain condition, or nonconvex optimization with intractable computation time. In this letter, we propose a mixed-integer convex formulation to plan simultaneously contact locations, gait transitions, and motion, in a computationally efficient fashion. In contrast to previous works, our approach is not limited to flat terrain nor to a prespecified gait sequence. Instead, we incorporate the friction cone stability margin, approximate the robot's torque limits, and plan the gait using mixed-integer convex constraints. We experimentally validated our approach on the HyQ robot by traversing different challenging terrains, where nonconvexity and flat terrain assumptions might lead to suboptimal or unstable plans. Our method increases the motion robustness while keeping a low computation time. We present a new optimization-based approach for robotic motion planning among obstacles. Like CHOMP (Covariant Hamiltonian Optimization for Motion Planning), our algorithm can be used to find collision-free trajectories from naA¯ve, straight-line initializations that might be in collision. At the core of our approach are (a) a sequential convex optimization procedure, which penalizes collisions with a hinge loss and increases the penalty coefficients in an outer loop as necessary, and (b) an efficient formulation of the no-collisions constraint that directly considers continuous-time safety Our algorithm is implemented in a software package called TrajOpt. We report results from a series of experiments comparing TrajOpt with CHOMP and randomized planners from OMPL, with regard to planning time and path quality. We consider motion planning for 7 DOF robot arms, 18 DOF full-body robots, statically stable walking motion for the 34 DOF Atlas humanoid robot, and physical experiments with the 18 DOF PR2. We also apply TrajOpt to plan curvature-constrained steerable needle trajectories in the SE(3) configuration space and multiple non-intersecting curved channels within 3D-printed implants for intracavitary brachytherapy. Details, videos, and source code are freely available at: http: rll.berkeley.edu trajopt ijrr. In this paper, a new method is presented for motion planning in dynamic environments, that is, finding a trajectory for a robot in a scene consisting of both static and dynamic, moving obstacles. We propose a practical algorithm based on a roadmap that is created for the static part of the scene. On this roadmap, an approximately time-optimal trajectory from a start to a goal configuration is computed, such that the robot does not collide with any moving obstacle. The trajectory is found by performing a two-level search for a shortest path. On the local level, trajectories on single edges of the roadmap are found using a depth-first search on an implicit grid in state-time space. On the global level, these local trajectories are coordinated using an A sup * -search to find a global trajectory to the goal configuration. The approach is applicable to any robot type in configuration spaces with any dimension, and the motions of the dynamic obstacles are unconstrained, as long as they are known beforehand. The approach has been implemented for both free-flying and articulated robots in three-dimensional workspaces, and it has been applied to multirobot motion planning, as well. Experiments show that the method achieves interactive performance in complex environments.