Robust online motion planning via contraction theory and convex optimization
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...A similar new approach, based on contraction theory and convex optimization, allows computation of error bounds that can then define safe tubes around a nominal dynamic trajectory computable online [18]....
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...Approaches making use of robust MPC schemes are not widely used in robotics (yet), but tube and funnel approaches have recently been explored for robust robot motion planning [17], [18], [19]....
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..., a standard sampling-based planner [18], [19]) that computes a nominal input u∗ online (i....
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...We solve the resulting problem using the SNOPT solver [32]....
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...Specifically, due to the difficulty of constructing invariant tubes and associated tracking controllers for nonlinear systems [10], most existing schemes for TMPC for nonlinear systems involve applying methods from linear TMPC by decomposing the dynamics into a linear and a nonlinear component (which is treated as a bounded disturbance) [11], [12]....
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