Optimization with trajectory sensitivity considerations

Byrne, P.C.; Burke, Mark E.

doi:10.1109/tac.1976.1101182

Cited by 36 publications

(3 citation statements)

References 7 publications

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“…[13] demonstrates the potential for improved feedforward control to enhance disturbance rejection for controllers with both feedback and feedforward terms. [3] and [9] introduce methods similar to those in this paper to optimize trajectory sensitivity for linear time invariant systems. [4] and [5] alexanderansari2011@u .…”

Section: Introductionmentioning

confidence: 99%

Minimal parametric sensitivity trajectories for nonlinear systems

Ansari

Murphey

2013

2013 American Control Conference

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Ahstract-Trajectory optimization techniques can be used to minimize error norms on both state and controls with respect to a reference. However, without sufficient control authority, resulting controllers can be sensitive to variations in model parameters. This paper presents a method to incorporate parametric sensitivity in optimal control calculations to develop optimally insensitive trajectories which can be better tracked under open loop and limited gain feedback conditions. As it builds on existing nonlinear optimal control theory, the approach can be easily implemented and applies to a variety of system types. The effectiveness of the technique is demonstrated using a simplified vehicle model. Controllers developed are capable of tracking highly aggressive and dynamically infeasible paths while minimizing sensitivity to variations in modeled friction.

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Section: Introductionmentioning

confidence: 99%

Minimal parametric sensitivity trajectories for nonlinear systems

Ansari

Murphey

2013

2013 American Control Conference

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“…This assumption implies that the proposed desensitisation method penalises an approximate sensitivity rather than the true sensitivity. It is interesting to note that similar approximations have been made in the past regarding applications of desensitisation techniques to the linear quadratic regulator problem in [21,22]. By setting (∂K k /∂α i ) = 0, the equation for the desensitised optimal gain is given by…”

Section: Discrete Ekfmentioning

confidence: 88%

Desensitised Kalman filtering

Karlgaard

Shen

2013

IET Radar, Sonar & Navigation

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“…The potential for improved feedforward control to enhance disturbance rejection for controllers with both feedback and feedforward terms is demonstrated in Singer and Seering (1990). Methods similar to those presented in this paper but restricted to linear time invariant systems are discussed in Byrne and Burke (1976) and Kreindler (1969). In Chen et al (2009) and Fernandes de Paula and Henrique Carvalho de Ferreira (2011), H ∞ methods for controller sensitivity minimization are derived for linear and time-discretized systems.…”

Section: Introductionmentioning

confidence: 95%

Minimum sensitivity control for planning with parametric and hybrid uncertainty

Ansari

Murphey

2015

The International Journal of Robotics Research

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This paper introduces a method to minimize norms on nonlinear trajectory sensitivities during open-loop trajectory optimization. Specifically, we derive new parametric sensitivity terms that measure the variation in nonlinear (continuous-time) trajectories due to variations in model parameters, and hybrid sensitivities, which account for variations in trajectory caused by sudden transitions from nominal dynamics to alternative dynamic modes. We adapt continuous trajectory optimization to minimize these sensitivities while only minimally changing a nominal trajectory. We provide appended states, cost, and linearizations, required so that existing open-loop optimization methods can generate minimally sensitive feedforward trajectories. Although there are several applications for sensitivity optimization, this paper focuses on robot motion planning, where popular sample-based planners rely on local trajectory generation to expand tree/graph structures. While such planners often use stochastic uncertainty propagation to model and reduce uncertainty, this paper shows that trajectory uncertainty can be reduced by minimizing first-order sensitivities. Simulated vehicle examples show parametric sensitivity optimization generates trajectories optimally insensitive to parametric model uncertainty. Similarly, minimizing hybrid sensitivities reduces uncertainty in crossing mobility hazards (e.g. rough terrain, sand, ice). Examples demonstrate the process yields a planner that uses approximate hazard models to automatically and optimally choose when to avoid hazardous terrain and when controls can be adjusted to traverse hazards with reduced uncertainty. Sensitivity optimization offers a simple alternative to stochastic simulation and complicated uncertainty modeling for nonlinear systems.

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Optimization with trajectory sensitivity considerations

Cited by 36 publications

References 7 publications

Minimal parametric sensitivity trajectories for nonlinear systems

Minimal parametric sensitivity trajectories for nonlinear systems

Desensitised Kalman filtering

Minimum sensitivity control for planning with parametric and hybrid uncertainty

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