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174
CHOMP: Covariant Hamiltonian Optimization for Motion Planning
"... Popular high-dimensional motion planning algorithms seem to pay an overly high price in terms of trajectory quality for their performance. In domains sparsely populated by obstacles, the heuristics used by sampling-based planners to navigate narrow passages can be needlessly complex; furthermore, ad ..."
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Cited by 18 (5 self)
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Popular high-dimensional motion planning algorithms seem to pay an overly high price in terms of trajectory quality for their performance. 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 converges over a wider range of input paths and is able to optimize higher- order dynamics of trajectories than previous path optimization strategies. As a result, CHOMP can be used as a standalone motion planner in many real-world planning queries. The effectiveness of our proposed method is demonstrated in manipulation planning for a 6-DOF robotic arm as well as in trajectory generation for a walking quadruped robot. 1
Advanced Perception, Navigation and Planning for Autonomous In-Water Ship Hull Inspection
"... Inspection of ship hulls and marine structures using autonomous underwater vehicles has emerged as a unique and challenging application of robotics. The problem poses rich questions in physical design and operation, perception and navigation, and planning, driven by difficulties arising from the aco ..."
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Cited by 16 (13 self)
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Inspection of ship hulls and marine structures using autonomous underwater vehicles has emerged as a unique and challenging application of robotics. The problem poses rich questions in physical design and operation, perception and navigation, and planning, driven by difficulties arising from the acoustic environment, poor water quality and the highly complex structures to be inspected. In this paper, we develop and apply algorithms for the central navigation and planning problems on ship hulls. These divide into two classes, suitable for the open, forward parts of a typical monohull, and for the complex areas around the shafting, propellers and rudders. On the open hull, we have integrated acoustic and visual mapping processes to achieve closed-loop control relative to features such as weld-lines and biofouling. In the complex area, we implemented new large-scale planning routines so as to achieve full imaging coverage of all the structures, at a high resolution. We demonstrate our approaches in recent operations on naval ships. 1
Control design along trajectories with sums of squares programming. Under review
, 2013
"... Abstract — Motivated by the need for formal guarantees on the stability and safety of controllers for challenging robot control tasks, we present a control design procedure that explicitly seeks to maximize the size of an invariant “funnel” that leads to a predefined goal set. Our certificates of in ..."
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Cited by 14 (10 self)
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Abstract — Motivated by the need for formal guarantees on the stability and safety of controllers for challenging robot control tasks, we present a control design procedure that explicitly seeks to maximize the size of an invariant “funnel” that leads to a predefined goal set. Our certificates of invariance are given in terms of sums of squares proofs of a set of appropriately defined Lyapunov inequalities. These certificates, together with our proposed polynomial controllers, can be efficiently obtained via semidefinite optimization. Our approach can handle time-varying dynamics resulting from tracking a given trajectory, input saturations (e.g. torque limits), and can be extended to deal with uncertainty in the dynamics and state. The resulting controllers can be used by space-filling feedback motion planning algorithms to fill up the space with significantly fewer trajectories. We demonstrate our approach on a severely torque limited underactuated double pendulum (Acrobot) and provide extensive simulation and hardware validation. I.
Robust online motion planning with regions of finite time invariance
- In Proceedings of the Workshop on the Algorithmic Foundations of Robotics
, 2012
"... Abstract In this paper we consider the problem of generating motion plans for a nonlinear dynamical system that are guaranteed to succeed despite uncertainty in the environment, parametric model uncertainty, disturbances, and/or errors in state estimation. Furthermore, we consider the case where the ..."
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Cited by 14 (6 self)
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Abstract In this paper we consider the problem of generating motion plans for a nonlinear dynamical system that are guaranteed to succeed despite uncertainty in the environment, parametric model uncertainty, disturbances, and/or errors in state estimation. Furthermore, we consider the case where these plans must be generated online, because constraints such as obstacles in the environment may not be known until they are perceived (with a noisy sensor) at runtime. Previous work on feedback motion planning for nonlinear systems was limited to offline planning due to the computational cost of safety verification. Here we take a trajectory library approach by designing controllers that stabilize the nominal trajectories in the library and pre-computing regions of finite time invariance (“funnels”) for the resulting closed loop system. We leverage sums-of-squares programming in order to efficiently compute funnels which take into account bounded disturbances and uncertainty. The resulting funnel library is then used to sequentially compose motion plans at runtime while ensuring the safety of the robot. A major advantage of the work presented here is that by explicitly taking into account the effect of uncertainty, the robot can evaluate motion plans based on how vulnerable they are to disturbances. We demonstrate our method on a simulation of a plane flying through a two dimensional forest of polyg-onal trees with parametric uncertainty and disturbances in the form of a bounded “cross-wind”. 1
Path planning for non-circular micro aerial vehicles in constrained environments
- In IEEE Int. Conf. on Rob. & Aut
, 2013
"... Abstract — Operating micro aerial vehicles (MAVs) outside of the bounds of a rigidly controlled lab environment, specifically one that is unstructured and contains unknown obstacles, poses a number of challenges. One of these challenges is that of quickly determining an optimal (or nearly so) path f ..."
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Cited by 14 (2 self)
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Abstract — Operating micro aerial vehicles (MAVs) outside of the bounds of a rigidly controlled lab environment, specifically one that is unstructured and contains unknown obstacles, poses a number of challenges. One of these challenges is that of quickly determining an optimal (or nearly so) path from the MAVs current position to a designated goal state. Past work in this area using full-size unmanned aerial vehicles (UAVs) has predominantly been performed in benign environments. However, due to their small size, MAVs are capable of operating in indoor environments which are more cluttered. This requires planners to account for the vehicle heading in addition to its spatial position in order to successfully navigate. In addition, due to the short flight times of MAVs along with the inherent hazards of operating in close proximity to obstacles, we desire the trajectories to be as cost-optimal as possible. Our approach uses an anytime planner based on A ⋆ that performs a graph search on a four-dimensional (4-D) (x,y,z,heading) lattice. This allows for the generation of close-to-optimal trajectories based on a set of precomputed motion primitives along with the capability to provide trajectories in real-time allowing for onthe-fly re-planning as new sensor data is received. We also account for arbitrary vehicle shapes, permitting the use of a noncircular footprint during the planning process. By not using the overly conservative circumscribed circle for collision checking, we are capable of successfully finding optimal paths through cluttered environments including those with narrow hallways. Analytically, we show that our planner provides bounds on the sub-optimality of the solution it finds. Experimentally, we show that the planner can operate in real-time in both a simulated and real-world cluttered environments. I.
LQR-RRT ∗ : Optimal Sampling-Based Motion Planning with Automatically Derived Extension Heuristics
"... Abstract — The RRT ∗ algorithm has recently been proposed as an optimal extension to the standard RRT algorithm [1]. However, like RRT, RRT ∗ is difficult to apply in problems with complicated or underactuated dynamics because it requires the design of a two domain-specific extension heuristics: a d ..."
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Cited by 14 (1 self)
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Abstract — The RRT ∗ algorithm has recently been proposed as an optimal extension to the standard RRT algorithm [1]. However, like RRT, RRT ∗ is difficult to apply in problems with complicated or underactuated dynamics because it requires the design of a two domain-specific extension heuristics: a distance metric and node extension method. We propose automatically deriving these two heuristics for RRT ∗ by locally linearizing the domain dynamics and applying linear quadratic regulation (LQR). The resulting algorithm, LQR-RRT ∗ , finds optimal plans in domains with complex or underactuated dynamics without requiring domain-specific design choices. We demonstrate its application in domains that are successively torquelimited, underactuated, and in belief space. I.
Sampling-based coverage path planning for inspection of complex structures
- In Proceedings of the International Conference on Automated Planning and Scheduling
, 2012
"... We present several new contributions in sampling-based cov-erage path planning, the task of finding feasible paths that give 100 % sensor coverage of complex structures in obstacle-filled and visually occluded environments. First, we establish a framework for analyzing the probabilistic completeness ..."
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Cited by 12 (2 self)
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We present several new contributions in sampling-based cov-erage path planning, the task of finding feasible paths that give 100 % sensor coverage of complex structures in obstacle-filled and visually occluded environments. First, we establish a framework for analyzing the probabilistic completeness of a sampling-based coverage algorithm, and derive results on the completeness and convergence of existing algorithms. Sec-ond, we introduce a new algorithm for the iterative improve-ment of a feasible coverage path; this relies on a sampling-based subroutine that makes asymptotically optimal local im-provements to a feasible coverage path based on a strong gen-eralization of the RRT ∗ algorithm. We then apply the algo-rithm to the real-world task of autonomous in-water ship hull inspection. We use our improvement algorithm in conjunc-tion with redundant roadmap coverage planning algorithm to produce paths that cover complex 3D environments with un-precedented efficiency.
Revising Motion Planning under Linear Temporal Logic Specifications
- in Partially Known Workspaces. IEEE International Conference on Robotics and Automation
, 2013
"... Abstract — In this paper we propose a generic framework for real-time motion planning based on model-checking and revision. The task specification is given as a Linear Temporal Logic formula over a finite abstraction of the robot motion. A preliminary motion plan is first generated based on the init ..."
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Cited by 11 (4 self)
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Abstract — In this paper we propose a generic framework for real-time motion planning based on model-checking and revision. The task specification is given as a Linear Temporal Logic formula over a finite abstraction of the robot motion. A preliminary motion plan is first generated based on the initial knowledge of the system model. Then real-time information obtained during the runtime is used to update the system model, verify and further revise the motion plan. The implementation and revision of the motion plan are performed in real-time. This framework can be applied to partially-known workspaces and workspaces with large uncertainties. Computer simulations are presented to demonstrate the efficiency of the framework. I.
FIRM: Sampling-based Feedback Motion Planning Under Motion Uncertainty and Imperfect Measurements
"... In this paper we present FIRM (Feedback-based Information RoadMap), a multi-query approach for planning under uncertainty, that is a belief-space variant of Probabilistic Roadmap Methods (PRMs). The crucial feature of FIRM is that the costs associated with the edges are independent of each other, an ..."
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Cited by 11 (5 self)
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In this paper we present FIRM (Feedback-based Information RoadMap), a multi-query approach for planning under uncertainty, that is a belief-space variant of Probabilistic Roadmap Methods (PRMs). The crucial feature of FIRM is that the costs associated with the edges are independent of each other, and in this sense it is the first method that generates a graph in belief space that preserves the optimal substructure property. From a practical point of view, FIRM is a robust and reliable planning framework. It is robust since the solution is a feedback and there is no need for expensive replanning. It is reliable because accurate collision probabilities can be computed along the edges. In addition, FIRM is a scalable framework, where the complexity of the planning framework. As a concrete instantiation of FIRM, we adopt Stationary Linear Quadratic Gaussian (SLQG) controllers as belief stabilizers and introduce the so-called SLQG-FIRM. In SLQG-FIRM we focus on kinematic systems and then extend to dynamical systems by sampling in the equilibrium space. We investigate the performance of SLQG-FIRM in different scenarios.
Planning periodic persistent monitoring trajectories for sensing robots in gaussian random fields
- In Robotics and Automation (ICRA), 2013 IEEE International Conference on
, 2013
"... Abstract — This paper considers the problem of planning a trajectory for a sensing robot to best estimate a time-changing Gaussian Random Field in its environment. The robot uses a Kalman filter to maintain an estimate of the field value, and to compute the error covariance matrix of the estimate. A ..."
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Cited by 11 (3 self)
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Abstract — This paper considers the problem of planning a trajectory for a sensing robot to best estimate a time-changing Gaussian Random Field in its environment. The robot uses a Kalman filter to maintain an estimate of the field value, and to compute the error covariance matrix of the estimate. A new randomized path planning algorithm is proposed to find a periodic trajectory for the sensing robot that tries to minimize the largest eigenvalue of the error covariance matrix over an infinite horizon. The algorithm is proven to find the minimum infinite horizon cost cycle in a graph, which grows by successively adding random points. The algorithm leverages recently developed methods for periodic Riccati recursions to efficiently compute the infinite horizon cost of the cycles, and it uses the monotonicity property of the Riccati recursion to efficiently compare the cost of different cycles without explicitly computing their costs. The performance of the algorithm is demonstrated in numerical simulations. I.
