Navigating in search and rescue environments is challenging, since a variety of terrains has to be considered. Hybrid driving-stepping locomotion, as provided by our robot Momaro, is a promising approach. Similar to other locomotion methods, it incorporates many degrees of freedom---offering high flexibility but making planning computationally expensive for larger environments. We propose a navigation planning method, which unifies different levels of representation in a single planner. In the vicinity of the robot, it provides plans with a fine resolution and a high robot state dimensionality. With increasing distance from the robot, plans become coarser and the robot state dimensionality decreases. We compensate this loss of information by enriching coarser representations with additional semantics. Experiments show that the proposed planner provides plans for large, challenging scenarios in feasible time.
Planning for systems with high-dimensional motion flexibility quickly reaches its limits for larger environments since the search space grows exponentially. Similar to multiresolution planning, several approaches utilize multiple representations with different planning dimensionalities to decrease planning complexity. @cite_5 generate an initial plan in a low-dimensional search space and replan in the high-dimensional search space by only considering those states that are part of the low-dimensional plan. @cite_4 plan a path in a low-dimensional search space and only switch to high-dimensional planning in those areas where low-dimensional planning cannot find a solution. Similarly, @cite_9 plan in 2D and switch to high-dimensional planning in the robot vicinity and at key points. As described for multiresolution planning, planning with multiple robot configuration dimensionalities might lead to wrong or bad plans, since a low-dimensional robot representation might assess challenging situations wrongly.
@cite_5 @cite_9 @cite_4
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Path planning is often a high-dimensional computationally-expensive planning problem as it requires reasoning about the kinodynamic constraints of the robot and collisions of the robot with the environment. However, large regions of the environment are typically benign enough that a much faster low-dimensional planning combined with a local path following controller suffice. Planning with Adaptive Dimensionality that was recently developed makes use of this observation and iteratively constructs and searches a state-space consisting of mainly low-dimensional states. It only introduces regions of high-dimensional states into the state-space where they are necessary to ensure completeness and bounds on sub-optimality. However, due to its iterative nature, the approach relies on running a series of weighted A* searches. In this paper, we introduce and apply to Planning with Adaptive Dimensionality a simple but very effective incremental version of weighted A* that reuses its previously generated search tree if available. On the theoretical side, the new algorithm preserves guarantees on completeness and bounds on sub-optimality. On the experimental side, it speeds up 3D (x,y,heading) path planning with a full-body collision checking by up to a factor of 5. Our results also show that it tends to be much faster than applying alternative incremental graph search techniques such as D* to Planning with Adaptive Dimensionality. Multirobot path planning is difficult because the full configuration space of the system grows exponentially with the number of robots. Planning in the joint configuration space of a set of robots is only necessary if they are strongly coupled, which is often not true if the robots are well separated in the workspace. Therefore, we initially plan for each robot separately, and only couple sets of robots after they have been found to interact, thus minimizing the dimensionality of the search space. We present a general strategy called subdimensional expansion, which dynamically generates low dimensional search spaces embedded in the full configuration space. We also present an implementation of subdimensional expansion for robot configuration spaces that can be represented as a graph, called M*, and show that M* is complete and finds minimal cost paths. Navigating in search and rescue environments is challenging, since a variety of terrains has to be considered. Hybrid driving-stepping locomotion, as provided by our robot Momaro, is a promising approach. Similar to other locomotion methods, it incorporates many degrees of freedom—offering high flexibility but making planning computationally expensive for larger environments. We propose a navigation planning method, which unifies different levels of representation in a single planner. In the vicinity of the robot, it provides plans with a fine resolution and a high robot state dimensionality. With increasing distance from the robot, plans become coarser and the robot state dimensionality decreases. We compensate this loss of information by enriching coarser representations with additional semantics. Experiments show that the proposed planner provides plans for large, challenging scenarios in feasible time. We believe the core of handling the complexity of coordinated multiagent search lies in identifying which subsets of robots can be safely decoupled, and hence planned for in a lower dimensional space. Our work, as well as those of others take that perspective. In our prior work, we introduced an approach called subdimensional expansion for constructing low-dimensional but sufficient search spaces for multirobot path planning, and an implementation for graph search called M*. Subdimensional expansion dynamically increases the dimensionality of the search space in regions featuring significant robot-robot interactions. In this paper, we integrate M* with Meta-Agent Constraint-Based Search (MA-CBS), a planning framework that seeks to couple repeatedly colliding robots allowing for other robots to be planned in low-dimensional search space. M* is also integrated with operator decomposition (OD), an A*-variant performing lazy search of the outneighbors of a given vertex. We show that the combined algorithm demonstrates state of the art performance. This letter presents latent sampling-based motion planning (L-SBMP), a methodology toward computing motion plans for complex robotic systems by learning a plannable latent representation. Recent works in control of robotic systems have effectively leveraged local, low-dimensional embeddings of high-dimensional dynamics. In this letter, we combine these recent advances with techniques from sampling-based motion planning (SBMP) in order to design a methodology capable of planning for high-dimensional robotic systems beyond the reach of traditional approaches (e.g., humanoids, or even systems where planning occurs in the visual space). Specifically, the learned latent space is constructed through an autoencoding network, a dynamics network, and a collision checking network, which mirror the three main algorithmic primitives of SBMP, namely state sampling, local steering, and collision checking. Notably, these networks can be trained through only raw data of the system's states and actions along with a supervising collision checker. Building upon these networks, an RRT-based algorithm is used to plan motions directly in the latent space —we refer to this exploration algorithm as learned latent RRT. This algorithm globally explores the latent space and is capable of generalizing to new environments. The overall methodology is demonstrated on two planning problems, namely a visual planning problem, whereby planning happens in the visual (pixel) space, and a humanoid robot planning problem. Path planning quickly becomes computationally hard as the dimensionality of the state-space increases. In this paper, we present a planning algorithm intended to speed up path planning for high-dimensional state-spaces such as robotic arms. The idea behind this work is that while planning in a high-dimensional state-space is often necessary to ensure the feasibilityof the resulting path, large portions of the path have a lower-dimensional structure. Based on this observation, our algorithm iteratively constructs a state-space of an adaptive dimensionality--a state-space that is high-dimensional only where the higher dimensionality is absolutely necessary for finding a feasible path. This often reduces drastically the size of the state-space, and as a result, the planning time and memory requirements. Analytically, we show that our method is complete and is guaranteed to find a solution if one exists, within a specified suboptimality bound. Experimentally, we apply the approach to 3D vehicle navigation (x, y, heading), and to a 7 DOF robotic arm on the Willow Garage’s PR2 robot. The results from our experiments suggest that ourmethod can be substantially faster than some of the state-of-the-art planning algorithms optimized for those tasks. Abstract Planning optimal paths for large numbers of robots is computationally expensive. In this paper, we introduce a new framework for multirobot path planning called subdimensional expansion, which initially plans for each robot individually, and then coordinates motion among the robots as needed. More specifically, subdimensional expansion initially creates a one-dimensional search space embedded in the joint configuration space of the multirobot system. When the search space is found to be blocked during planning by a robot–robot collision, the dimensionality of the search space is locally increased to ensure that an alternative path can be found. As a result, robots are only coordinated when necessary, which reduces the computational cost of finding a path. We present the M ⁎ algorithm, an implementation of subdimensional expansion that adapts the A ⁎ planner to perform efficient multirobot planning. M ⁎ is proven to be complete and to find minimal cost paths. Simulation results are presented that show that M ⁎ outperforms existing optimal multirobot path planning algorithms. This paper presents the first randomized approach to kinodynamic planning (also known as trajectory planning or trajectory design). The task is to determine control inputs to drive a robot from an ini ial configuration and velocity to a goal configuration and velocity while obeying physically based dynamical models and avoiding obstacles in the robot’s environment. The authors consider generic systems that express the nonlinear dynamics of a robot in terms of the robot’s high-dimensional configuration space. Kinodynamic planning is treated as a motion-planning problem in a higher dimensional state space that has both first-order differential constraints and obstacle-based global constraints. The state space serves the same role as the configuration space for basic path planning; however, standard randomized path-planning techniques do not directly apply to planning trajectories in the state space. The authors have developed a randomized planning approach that is particularly tailored to trajectory plannin... Enabling robots to accomplish sophisticated tasks requires enhancing their capability to plan at multiple levels of discrete and continuous abstractions. Toward this goal, the proposed approach couples the ability of sampling-based motion planning to handle the complexity arising from high-dimensional robotic systems, nonlinear dynamics, and collision avoidance with the ability of discrete planning to handle discrete specifications. The approach makes it possible to specify tasks via Linear Temporal Logic (LTL) and automatically computes collision-free and dynamically-feasible motions that enable the robot to carry out assigned tasks. While discrete planning guides sampling-based motion planning, the latter feeds back information to further refine the guide and advance the search. Sampling is also used in the discrete space to shorten the length of the discrete plans and to expand the search toward new discrete states. Experiments with high-dimensional dynamical robot models performing various LTL tasks show significant computational speedups over related work. Planning with kinodynamic constraints is often required for mobile robots operating in cluttered, complex environments. A common approach is to use a two-dimensional (2-D) global planner for long range planning, and a short range higher dimensional planner or controller capable of satisfying all of the constraints on motion. However, this approach is incomplete and can result in oscillations and the inability to find a path to the goal. In this paper we present an approach to solving this problem by combining the global and local path planning problem into a single search using a combined 2-D and higher dimensional state-space. Advanced modern humanoid robots often have complex manipulators with a large number of degrees of freedom. Thus, motion planning for such manipulators is a very computationally challenging problem. However, often robotic manipulators allow the wrist degrees of freedom to be controlled independently from the configuration of the rest of the arm. In this paper we show how to split the high dimensional planning problem into two lower-dimensional sub-problems—planning for the main arm joints and planning for the wrist joints, without losing guarantees on completeness. This approach is an extension of our previously developed framework for planning with adaptive dimensionality. Experimentally, we show that this approach is very effective in speeding up planning for robotic arms on Willow Garage’s PR2 platform. We compare our algorithm with several popular alternative approaches for performing motion planning for robotic arms. The results we observe illustrate that our algorithm provides a good balance between planning time, planning success rate, path consistency, and path quality. We present a novel optimization-based motion planning algorithm for high degree-of-freedom (DOF) robots in dynamic environments. Our approach decomposes the high-dimensional motion planning problem into a sequence of low-dimensional sub-problems. We compute collision-free and smooth paths using optimization-based planning and trajectory perturbation for each sub-problem. The overall algorithm does not require a priori knowledge about global motion or trajectories of dynamic obstacles. Rather, we compute a conservative local bound on the position or trajectory of each obstacle over a short time and use the bound to incrementally compute a collision-free trajectory for the robot. The high-DOF robot is treated as a tightly coupled system, and we incrementally use constrained coordination to plan its motion. We highlight the performance of our planner in simulated environments on robots with tens of DOFs. In this paper, we develop an online motion planning approach which learns from its planning episodes (experiences) a graph, an Experience Graph. On the theoretical side, we show that planning with Experience graphs is complete and provides bounds on suboptimality with respect to the graph that represents the original planning problem. Experimentally, we show in simulations and on a physical robot that our approach is particularly suitable for higher-dimensional motion planning tasks such as planning for two armed mobile manipulation. Many mundane manipulation tasks such as picking and placing various objects in a kitchen are highly repetitive. It is expected that robots should be capable of learning and improving their performance with every execution of these repetitive tasks. This work focuses on learning from experience for motion planning. Our approach relies on a graphsearch method for planning that builds an Experience Graph online to represent the high-level connectivity of the free space used for the encountered planning tasks. The planner uses the Experience graph to accelerate its planning whenever possible and gracefully degenerates to planning from scratch if no previous planning experiences can be reused. Planning with Experience graphs is complete and it provides bounds on suboptimality with respect to the graph that represents the original planning problem. Related work in (Jiang and Kallmann 2007) takes a database of motion plans and uses an RRT to draw the search towards a similar path to the new query. Our approach may use parts of many prior paths (not just one) and provides bounds on solution quality, unlike the above work. We provide results showing Experience Graphs can significantly improve the performance of a high-dimensional full-body planner for the PR2 robot. For more details refer to the full paper ( 2012). Abstract Safe and efficient path planning for mobile robots in large dynamic environments is still a challenging research topic. In order to plan collision-free trajectories, the time component of the path must be explicitly considered during the search. Furthermore, a precise planning near obstacles and in the vicinity of the robot is important. This results in a high computational burden of the trajectory planning algorithms. However, in large open areas and in the far future of the path, the planning can be performed more coarsely. In this paper, we present a novel algorithm that uses a hybrid-dimensional multi-resolution state × time lattice to efficiently compute trajectories with an adaptive fidelity according to the environmental requirements. We show how to construct this lattice in a consistent way and define the transitions between regions of different granularity. Finally, we provide some experimental results, which prove the real-time capability of our approach and show its advantages over single-dimensional single-resolution approaches. Finding asymptotically-optimal paths in multi-robot motion planning problems could be achieved, in principle, using sampling-based planners in the composite configuration space of all of the robots in the space. The dimensionality of this space increases with the number of robots, rendering this approach impractical. This work focuses on a scalable sampling-based planner for coupled multi-robot problems that provides asymptotic optimality. It extends the dRRT approach, which proposed building roadmaps for each robot and searching an implicit roadmap in the composite configuration space. This work presents a new method, dRRT* , and develops theory for scalable convergence to optimal paths in multi-robot problems. Simulated experiments indicate dRRT* converges to high-quality paths while scaling to higher numbers of robots where the naive approach fails. Furthermore, dRRT* is applicable to high-dimensional problems, such as planning for robot manipulators ABSTRACT The configuration space is a fundamental concept that is widely used in algorithmic robotics. Many applications in robotics, computer-aided design, and related areas can be reduced to computational problems in terms of configuration spaces. In this paper, we survey some of our recent work on solving two important challenges related to configuration spaces: how to efficiently compute an approximate representation of high-dimensional configuration spaces; and how to efficiently perform geometric proximity and motion planning queries in high-dimensional configuration spaces. We present new configuration space construction algorithms based on machine learning and geometric approximation techniques. These algorithms perform collision queries on many configuration samples. The collision query results are used to compute an approximate representation for the configuration space, which quickly converges to the exact configuration space. We also present parallel GPU-based algorithms to accelerate the performance of optimization and search computations in configuration spaces. In particular, we design efficient GPU-based parallel k -nearest neighbor and parallel collision detection algorithms and use these algorithms to accelerate motion planning. In recent years, deep generative models have been shown to 'imagine' convincing high-dimensional observations such as images, audio, and even video, learning directly from raw data. In this work, we ask how to imagine goal-directed visual plans -- a plausible sequence of observations that transition a dynamical system from its current configuration to a desired goal state, which can later be used as a reference trajectory for control. We focus on systems with high-dimensional observations, such as images, and propose an approach that naturally combines representation learning and planning. Our framework learns a generative model of sequential observations, where the generative process is induced by a transition in a low-dimensional planning model, and an additional noise. By maximizing the mutual information between the generated observations and the transition in the planning model, we obtain a low-dimensional representation that best explains the causal nature of the data. We structure the planning model to be compatible with efficient planning algorithms, and we propose several such models based on either discrete or continuous states. Finally, to generate a visual plan, we project the current and goal observations onto their respective states in the planning model, plan a trajectory, and then use the generative model to transform the trajectory to a sequence of observations. We demonstrate our method on imagining plausible visual plans of rope manipulation. Robotic manipulation involves actions where contacts occur between the robot and the objects. In this scope, the availability of physics-based engines allows motion planners to comprise dynamics between rigid bodies, which is necessary for planning this type of actions. However, physics-based motion planning is computationally intensive due to the high dimensionality of the state space and the need to work with a low integration step to find accurate solutions. On the other hand, manipulation actions change the environment and conditions further actions and motions. To cope with this issue, the representation of manipulation actions using ontologies enables a semantic-based inference process that alleviates the computational cost of motion planning. This paper proposes a manipulation planning framework where physics-based motion planning is enhanced with ontological knowledge representation and reasoning. The proposal has been implemented and is illustrated and validated with a simple example. Its use in grasping tasks in cluttered environments is currently under development. In this work, we present an approach to planning for humanoid mobility. Humanoid mobility is a challenging problem, as the configuration space for a humanoid robot is intractably large, especially if the robot is capable of performing many types of locomotion. For example, a humanoid robot may be able to perform such tasks as bipedal walking, crawling, and climbing. Our approach is to plan for all these tasks within a single search process. This allows the search to reason about all the capabilities of the robot at any point, and to derive the complete solution such that the plan is guaranteed to be feasible. A key observation is that we often can roughly decompose a mobility task into a sequence of smaller tasks, and focus planning efforts to reason over much smaller search spaces. To this end, we leverage the results of a recently developed framework for planning with adaptive dimensionality, and incorporate the capabilities of available controllers directly into the planning process. The resulting planner can also be run in an interleaved fashion alongside execution so that time spent idle is much reduced. Standard value function approaches to finding policies for Partially Observable Markov Decision Processes (POMDPs) are generally considered to be intractable for large models. The intractability of these algorithms is to a large extent a consequence of computing an exact, optimal policy over the entire belief space. However, in real-world POMDP problems, computing the optimal policy for the full belief space is often unnecessary for good control even for problems with complicated policy classes. The beliefs experienced by the controller often lie near a structured, low-dimensional subspace embedded in the high-dimensional belief space. Finding a good approximation to the optimal value function for only this subspace can be much easier than computing the full value function. We introduce a new method for solving large-scale POMDPs by reducing the dimensionality of the belief space. We use Exponential family Principal Components Analysis (Collins, Dasgupta, & Schapire, 2002) to represent sparse, high-dimensional belief spaces using small sets of learned features of the belief state. We then plan only in terms of the low-dimensional belief features. By planning in this low-dimensional space, we can find policies for POMDP models that are orders of magnitude larger than models that can be handled by conventional techniques. We demonstrate the use of this algorithm on a synthetic problem and on mobile robot navigation tasks.