Integration of Local Geometry and Metric Information in Sampling-Based Motion Planning

The efficiency of sampling-based motion planning algorithms is dependent on how well a steering procedure is capable of capturing both system dynamics and configuration space geometry to connect sample configurations. This paper considers how metrics describing local system dynamics may be combined with convex subsets of the free space to describe the local behavior of a steering function for sampling-based planners. Subsequently, a framework for using these subsets to extend the steering procedure to incorporate this information is introduced. To demonstrate our framework, three specific metrics are considered: the LQR cost-to-go function, a Gram matrix derived from system linearization, and the Mahalanobis distance of a linear-Gaussian system. Finally, numerical tests are conducted for a second-order linear system, a kinematic unicycle, and a linear-Gaussian system to demonstrate that our framework increases the connectivity of sampling-based planners and allows them to better explore the free space. For more information: Kod*lab

Joint Exploration of Local Metrics and Geometry in Sampling-based Planning

This thesis addresses how the local geometry of the workspace around a system state can be combined with local metrics describing system dynamics to improve the connectivity of the graph produced by a sampling-based planner over a fixed number of configurations. This development is achieved through generalization of the concept of the local free space to inner products other than the Euclidean inner product. This new structure allows for naturally combining the local free space construction with a locally applicable metric. The combination of the local free space with two specific metrics is explored in this work. The first metric is the quadratic cost-to-go function defined by a linear quadratic regulator, which captures the local behavior of the dynamical system. The second metric is the Mahalanobis distance for a belief state in a belief space planner. Belief space planners reason over distributions of states, called belief states, to include modeled uncertainty in the planning process. The Mahalanobis distances metric for a given belief state can be exploited to include notions of risk in local free space construction. Numerical simulations are provided to demonstrate the improved connectivity of the graph generated by a sampling-based planner using these concepts

Accessibility-Based Clustering for Efficient Learning of Locomotion Skills

For model-free deep reinforcement learning of quadruped locomotion, the initialization of robot configurations is crucial for data efficiency and robustness. This work focuses on algorithmic improvements of data efficiency and robustness simultaneously through automatic discovery of initial states, which is achieved by our proposed K-Access algorithm based on accessibility metrics. Specifically, we formulated accessibility metrics to measure the difficulty of transitions between two arbitrary states, and proposed a novel K-Access algorithm for state-space clustering that automatically discovers the centroids of the static-pose clusters based on the accessibility metrics. By using the discovered centroidal static poses as the initial states, we can improve data efficiency by reducing redundant explorations, and enhance the robustness by more effective explorations from the centroids to sampled poses. Focusing on fall recovery as a very hard set of locomotion skills, we validated our method extensively using an 8-DoF quadrupedal robot Bittle. Compared to the baselines, the learning curve of our method converges much faster, requiring only 60% of training episodes. With our method, the robot can successfully recover to standing poses within 3 seconds in 99.4% of the test cases. Moreover, the method can generalize to other difficult skills successfully, such as backflipping.</p

Accessibility-Based Clustering for Efficient Learning of Locomotion Skills

For model-free deep reinforcement learning of quadruped locomotion, the initialization of robot configurations is crucial for data efficiency and robustness. This work focuses on algorithmic improvements of data efficiency and robustness simultaneously through automatic discovery of initial states, which is achieved by our proposed K-Access algorithm based on accessibility metrics. Specifically, we formulated accessibility metrics to measure the difficulty of transitions between two arbitrary states, and proposed a novel K-Access algorithm for state-space clustering that automatically discovers the centroids of the static-pose clusters based on the accessibility metrics. By using the discovered centroidal static poses as the initial states, we can improve data efficiency by reducing redundant explorations, and enhance the robustness by more effective explorations from the centroids to sampled poses. Focusing on fall recovery as a very hard set of locomotion skills, we validated our method extensively using an 8-DoF quadrupedal robot Bittle. Compared to the baselines, the learning curve of our method converges much faster, requiring only 60% of training episodes. With our method, the robot can successfully recover to standing poses within 3 seconds in 99.4% of the test cases. Moreover, the method can generalize to other difficult skills successfully, such as backflipping

Regression-based motion planning

This thesis explores two novel approaches to sample-based motion planning that utilize regressions as continuous function approximations to reduce the memory cost of planning. The first approach, Field Search Trees (FST) provides a solution for single-start planning by iteratively building local regressions of the cost-to-arrive function. The second approach, the Regression Complex (RC), constructs a complex of cells with each cell containing a regression of the distance between any two points on its boundary, creating a useful data structure for any start and goal planning query. We provide formal definitions of both approaches and experimental results of running the algorithms on different simulated robot systems. We conclude that regression-based motion planning provides key advantages over traditional sample-based motion planning in certain cases, but more work is required to extend these approaches into higher dimensional configuration spaces

Active Mapping and Robot Exploration: A Survey

Simultaneous localization and mapping responds to the problem of building a map of the environment without any prior information and based on the data obtained from one or more sensors. In most situations, the robot is driven by a human operator, but some systems are capable of navigating autonomously while mapping, which is called native simultaneous localization and mapping. This strategy focuses on actively calculating the trajectories to explore the environment while building a map with a minimum error. In this paper, a comprehensive review of the research work developed in this field is provided, targeting the most relevant contributions in indoor mobile robotics.This research was funded by the ELKARTEK project ELKARBOT KK-2020/00092 of the Basque Government