Safe path planning is a crucial component in autonomous robotics. The many approaches to find a collision free path can be categorically divided into trajectory optimisers and sampling-based methods. When planning using occupancy maps, the sampling-based approach is the prevalent method. The main drawback of such techniques is that the reasoning about the expected cost of a plan is limited to the search heuristic used by each method. We introduce a novel planning method based on trajectory optimisation to plan safe and efficient paths in continuous occupancy maps. We extend the expressiveness of the state-of-the-art functional gradient optimisation methods by devising a stochastic gradient update rule to optimise a path represented as a Gaussian process. This approach avoids the need to commit to a specific resolution of the path representation, whether spatial or parametric. We utilise a continuous occupancy map representation in order to define our optimisation objective, which enables fast computation of occupancy gradients. We show that this approach is essential in order to ensure convergence to the optimal path, and present results and comparisons to other planning methods in both simulation and with real laser data. The experiments demonstrate the benefits of using this technique when planning for safe and efficient paths in continuous occupancy maps.
Optimisation is a widely used approach for finding feasible paths, where the planned path is the local extrema of a pre-defined arbitrary cost function. Loosely speaking, the cost function captures the costs and penalties associated with a configuration-space state, e.g. distance from obstacles. Khatib pioneered the use of artificial potential field for collision avoidance @cite_28 . (CHOMP) utilises covariate gradients from a precomputed obstacle cost to minimise the trajectory's obstacle and smoothness functionals @cite_2 . The (STOMP) planner uses noisy perturbations to perform optimisation under constraints where the cost functional is non-differentiable @cite_1 . Both CHOMP and STOMP commit to a waypoint representation which require to trade-off expressiveness with computational costs. proposed the Gaussian process motion planner which uses a Gaussian process generated by linear time varying stochastic differential equations for path representation @cite_10 . perform trajectory optimisation in a (RKHS) @cite_17 . However, all these methods fall short when planning using occupancy maps as discussed in section .
@cite_28 @cite_1 @cite_2 @cite_10 @cite_17
2019965290 2099893201 2161819990 2095905067
We present a new approach to motion planning using a stochastic trajectory optimization framework. The approach relies on generating noisy trajectories to explore the space around an initial (possibly infeasible) trajectory, which are then combined to produced an updated trajectory with lower cost. A cost function based on a combination of obstacle and smoothness cost is optimized in each iteration. No gradient information is required for the particular optimization algorithm that we use and so general costs for which derivatives may not be available (e.g. costs corresponding to constraints and motor torques) can be included in the cost function. We demonstrate the approach both in simulation and on a mobile manipulation system for unconstrained and constrained tasks. We experimentally show that the stochastic nature of STOMP allows it to overcome local minima that gradient-based methods like CHOMP can get stuck in. 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. In this paper, we present CHOMP (covariant Hamiltonian optimization for motion planning), a method for trajectory optimization invariant to reparametrization. CHOMP uses functional gradient techniques to iteratively improve the quality of an initial trajectory, optimizing a functional that trades off between a smoothness and an obstacle avoidance component. CHOMP can be used to locally optimize feasible trajectories, as well as to solve motion planning queries, converging to low-cost trajectories even when initialized with infeasible ones. It uses Hamiltonian Monte Carlo to alleviate the problem of convergence to high-cost local minima (and for probabilistic completeness), and is capable of respecting hard constraints along the trajectory. We present extensive experiments with CHOMP on manipulation and locomotion tasks, using seven-degree-of-freedom manipulators and a rough-terrain quadruped robot. Many real-world tasks require fast planning of highly dynamic movements for their execution in real-time. The success often hinges on quickly finding one of the few plans that can achieve the task at all. A further challenge is to quickly find a plan which optimizes a desired cost. In this paper, we will discuss this problem in the context of catching small flying targets efficiently. This can be formulated as a non-linear optimization problem where the desired trajectory is encoded by an adequate parametric representation. The optimizer generates an energy-optimal trajectory by efficiently using the robot kinematic redundancy while taking into account maximal joint motion, collision avoidance and local minima. To enable the resulting method to work in real-time, examples of the global planner are generalized using nearest neighbour approaches, Support Vector Machines and Gaussian process regression, which are compared in this context. Evaluations indicate that the presented method is highly efficient in complex tasks such as ball-catching.