Reachable Sets for Safe, Real-Time Manipulator Trajectory Design

Holmes, Patrick D.; Kousik, Shreyas; Raz, Daphna; Barbalata, Corina; Johnson-Roberson, Matthew; Vasudevan, Ram

doi:10.15607/rss.2020.xvi.100

Cited by 31 publications

(40 citation statements)

References 30 publications

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“…The purpose of this article is to establish the foundation of RTD as a provably safe and persistently feasible planner. These techniques can also be extended and applied to dynamic environments (Vaskov et al, 2019a), fast robots such as autonomous vehicles (Vaskov et al, 2019b), aerial robots (Kousik et al, 2019), and manipulator arms (Holmes et al, 2020). In summary, the RTD framework can serve as a useful lens to address the challenges of safe, real-time robot trajectory design.…”

Section: Discussionmentioning

confidence: 99%

Bridging the gap between safety and real-time performance in receding-horizon trajectory design for mobile robots

Kousik

Vaskov

Fan

et al. 2020

The International Journal of Robotics Research

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To operate with limited sensor horizons in unpredictable environments, autonomous robots use a receding-horizon strategy to plan trajectories, wherein they execute a short plan while creating the next plan. However, creating safe, dynamically feasible trajectories in real time is challenging, and planners must ensure persistent feasibility, meaning a new trajectory is always available before the previous one has finished executing. Existing approaches make a tradeoff between model complexity and planning speed, which can require sacrificing guarantees of safety and dynamic feasibility. This work presents the Reachability-based Trajectory Design (RTD) method for trajectory planning. RTD begins with an offline forward reachable set (FRS) computation of a robot’s motion when tracking parameterized trajectories; the FRS provably bounds tracking error. At runtime, the FRS is used to map obstacles to parameterized trajectories, allowing RTD to select a safe trajectory at every planning iteration. RTD prescribes an obstacle representation to ensure that obstacle constraints can be created and evaluated in real time while maintaining safety. Persistent feasibility is achieved by prescribing a minimum sensor horizon and a minimum duration for the planned trajectories. A system decomposition approach is used to improve the tractability of computing the FRS, allowing RTD to create more complex plans at runtime. RTD is compared in simulation with rapidly-exploring random trees and nonlinear model-predictive control. RTD is also demonstrated in randomly crafted environments on two hardware platforms: a differential-drive Segway and a car-like Rover. The proposed method is safe and persistently feasible across thousands of simulations and dozens of real-world hardware demos.

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Section: Discussionmentioning

confidence: 99%

Bridging the gap between safety and real-time performance in receding-horizon trajectory design for mobile robots

Kousik

Vaskov

Fan

et al. 2020

The International Journal of Robotics Research

Self Cite

View full text Add to dashboard Cite

show abstract

“…However, this approach is often too computationally demanding to be run online for complex systems. To ease the computational burden, constraints are often only enforced on trajectories of finite horizon, such as in sequential trajectory planning [4], [5] and model-predictive control [1], [6]. Since these methods only enforce constraints along partial trajectories, guaranteeing safety requires additional conditions to be met.…”

Section: A Related Workmentioning

confidence: 99%

Safe Value Functions

Massiani¹,

Heim²,

Solowjow³

et al. 2021

Preprint

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The relationship between safety and optimality in control is not well understood, and they are often seen as important yet conflicting objectives. There is a pressing need to formalize this relationship, especially given the growing prominence of learning-based methods. Indeed, it is common practice in reinforcement learning to simply modify reward functions by penalizing failures, with the penalty treated as a mere heuristic. We rigorously examine this relationship, and formalize the requirements for safe value functions: value functions that are both optimal for a given task, and enforce safety. We reveal the structure of this relationship through a proof of strong duality, showing that there always exists a finite penalty that induces a safe value function. This penalty is not unique, but upperunbounded: larger penalties do not harm optimality. Although it is often not possible to compute the minimum required penalty, we reveal clear structure of how the penalty, rewards, discount factor, and dynamics interact. This insight suggests practical, theory-guided heuristics to design reward functions for control problems where safety is important.

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“…A repulsive velocity can be applied to any rigid body whenever it collides with any obstacle based on a physical simulator. Reachable sets are used for safe and real-time trajectory design in [10], but the reachability analysis has to be offline. Some optimal controllers handle the obstacles by mixed integer programming which is known to be a NP-hard problem [30].…”

Section: Motion Planning For Manipulationmentioning

confidence: 99%

A Quadratic Programming Approach to Manipulation in Real-Time Using Modular Robots

Liu,

Yim

2021

Preprint

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Motion planning in high-dimensional space is a challenging task. In order to perform dexterous manipulation in an unstructured environment, a robot with many degrees of freedom is usually necessary, which also complicates its motion planning problem. Real-time control brings about more difficulties in which robots have to maintain the stability while moving towards the target. Redundant systems are common in modular robots that consist of multiple modules and are able to transformed into different configurations with respect to different needs. Different from robots with fixed geometry or configurations, the kinematics model of a modular robotic system can alter as the robot reconfigures itself, and developing a generic control and motion planning approach for such systems is difficult, especially when multiple motion goals are coupled. A new manipulation planning framework is developed in this paper. The problem is formulated as a sequential linearly constrained quadratic program (QP) that can be solved efficiently. Some constraints can be incorporated into this QP, including a novel way to approximate environment obstacles. This solution can be used directly for real-time applications or as an off-line planning tool, and it is validated and demonstrated on the CKBot and SMORES-EP modular robot platforms.

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Reachable Sets for Safe, Real-Time Manipulator Trajectory Design

Cited by 31 publications

References 30 publications

Bridging the gap between safety and real-time performance in receding-horizon trajectory design for mobile robots

Bridging the gap between safety and real-time performance in receding-horizon trajectory design for mobile robots

Safe Value Functions

A Quadratic Programming Approach to Manipulation in Real-Time Using Modular Robots

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