Closed form characterization of collision free velocities and confidence bounds for non-holonomic robots in uncertain dynamic environments

Gopalakrishnan, Bharath; Singh, Arun Kumar; Krishna, K. Madhava

doi:10.1109/iros.2015.7354075

Cited by 15 publications

(24 citation statements)

References 13 publications

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“…Secondly, the fixed final time paradigm of optimization (16) is not equipped to capture the effect of increase in traversal time of reaching motions due to presence of obstacles. A possible solution to this could be developed using the time scaling concepts [14]. Our current study is limited to developing and approximating an efficient solution for the computational framework, and demonstrating the homotopies and strategies that can be explained within this framework, and we do not test our predictions against real reaching data.…”

Section: Discussion and Future Workmentioning

confidence: 99%

See 1 more Smart Citation

Stochastic Optimal Control for Modeling Reaching Movements in the Presence of Obstacles: Theory and Simulation

Singh

Berman

Nisky

2018

2018 7th IEEE International Conference on Biomedical Robotics and Biomechatronics (Biorob)

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In many human-in-the-loop robotic applications such as robot-assisted surgery and remote teleoperation, predicting the intended motion of the human operator may be useful for successful implementation of shared control, guidance virtual fixtures, and predictive control. Developing computational models of human movements is a critical foundation for such motion prediction frameworks. With this motivation, we present a computational framework for modeling reaching movements in the presence of obstacles. We propose a stochastic optimal control framework that consists of probabilistic collision avoidance constraints and a cost function that tradesoff between effort and end-state variance in the presence of a signal-dependent noise. First, we present a series of reformulations to convert the original non-linear and non-convex optimal control into a parametric quadratic programming problem. We show that the parameters can be tuned to model various collision avoidance strategies, thereby capturing the quintessential variability associated with human motion. Then, we present a simulation study that demonstrates the complex interaction between avoidance strategies, control cost, and the probability of collision avoidance. The proposed framework can benefit a variety of applications that require teleoperation in cluttered spaces, including robot-assisted surgery. In addition, it can also be viewed as a new optimizer which produces smooth and probabilistically-safe trajectories under signal dependent noise.

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Section: Discussion and Future Workmentioning

confidence: 99%

“…Hence, we next reformulate these chance constraints into a tractable form and show that the reformulation naturally leads to an efficient optimization structure. Reformulating Chance Constraints: We follow [14], and substitute of P r(C t i (.)) with:…”

Section: B Optimal Controlmentioning

confidence: 99%

Stochastic Optimal Control for Modeling Reaching Movements in the Presence of Obstacles: Theory and Simulation

Singh

Berman

Nisky

2018

2018 7th IEEE International Conference on Biomedical Robotics and Biomechatronics (Biorob)

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“…becomes a very challenging problem. A workaround has been proposed in works like [14], [16], [17] where the analytical expressions for E [. ] and Var [.…”

Section: A Computational Challengementioning

confidence: 99%

Solving Chance-Constrained Optimization Under Nonparametric Uncertainty Through Hilbert Space Embedding

Gopalakrishnan

Singh

Krishna

et al. 2022

IEEE Trans. Contr. Syst. Technol.

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In this article, we present an efficient algorithm for solving a class of chance-constrained optimization under nonparametric uncertainty. Our algorithm is built on the possibility of representing arbitrary distributions as functions in Reproducing Kernel Hilbert Space (RKHS). We use this foundation to formulate chance-constrained optimization as one of minimizing the distance between a desired distribution and the distribution of the constraint functions in the RKHS. We provide a systematic way of constructing the desired distribution based on the notion of scenario approximation. Furthermore, we use the kernel trick to show that the computational complexity of our reformulated optimization problem is comparable to solving a deterministic variant of the chance-constrained optimization. We validate our formulation on two important robotic applications: 1) reactive collision avoidance of mobile robots in uncertain dynamic environments and 2) inverse-dynamics-based path-tracking of manipulators under perception uncertainty. In both these applications, the underlying chance constraints are defined over nonlinear and nonconvex functions of uncertain parameters and possibly also decision variables. We also benchmark our formulation with the existing approaches in terms of sample complexity and the achieved optimal cost highlighting significant improvements in both these metrics.

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“…It is worth pointing out that there are various heuristics for choosing the point s * . One of them which has been shown to result in low approximation errors is to choose s * from the solution space of µ s f RV O i j ≥ 0 [14]. It is easy to note that solving it is similar to solving (17).…”

Section: Time Scaled Variant Of Surrogate Constraintsmentioning

confidence: 99%

“…We also provide a computationally efficient approach for solving these complex set of inequalities. To this end, we build upon our recent series of works [14], [15], where chance constraints are substituted with a more tractable family of surrogate constraints. The solution space of each member of the family can be mapped in closed form to the probability with each the original chance constraints are satisfied.…”

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confidence: 99%

Chance constraint based multi agent navigation under uncertainty

Gopalakrishnan

Singh²,

Kaushik

et al. 2017

Proceedings of the Advances in Robotics

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Abstract. We present Probabilistic Reciprocal Velocity Obstacle or PRVO as a general algorithm for navigating multiple robots under perception and motion uncertainty. PRVO is defined as the space of velocities that ensures dynamic collision avoidance between a pair of robots with a specified probability. Our approach is based on defining chance constraints over the inequalities defined by the deterministic Reciprocal Velocity Obstacle (RVO). The computational complexity of the proposed probabilistic RVO is comparable to the deterministic counterpart. This is achieved by a series of reformulations where we first substitute the computationally intractable chance constraints with a family of surrogate constraints and then adopt a time scaling based solution methodology to efficiently characterize their solution space. Further, we also show that the solution space of each member of the family of surrogate constraints can be mapped in closed form to the probability with which the original chance constraints are satisfied and thus consequently to probability of collision avoidance. We validate our formulations through numerical simulations where we highlight the importance of incorporating the effect of motion uncertainty and the advantages of PRVO over existing formulations which handles the effect of uncertainty by using conservative bounding volumes.

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Closed form characterization of collision free velocities and confidence bounds for non-holonomic robots in uncertain dynamic environments

Cited by 15 publications

References 13 publications

Stochastic Optimal Control for Modeling Reaching Movements in the Presence of Obstacles: Theory and Simulation

Stochastic Optimal Control for Modeling Reaching Movements in the Presence of Obstacles: Theory and Simulation

Solving Chance-Constrained Optimization Under Nonparametric Uncertainty Through Hilbert Space Embedding

Chance constraint based multi agent navigation under uncertainty

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