Abstract:A key challenge to the widespread deployment of robotic manipulators is the need to ensure safety in arbitrary environments while generating new motion plans in real-time. In particular, one must ensure that a manipulator does not collide with obstacles, collide with itself, or exceed its joint torque limits. This challenge is compounded by the need to account for uncertainty in the mass and inertia of manipulated objects, and potentially the robot itself. The present work addresses this challenge by proposing… Show more
“…solve the family of d-degree SOS optimization problems given in Eq. (19). Now, it follows that if we show that…”
Section: Convergence Of Our Proposed Sos Programsmentioning
confidence: 85%
“…( 19) it satisfies all of the constraints of Opt. (19). Since SOS polynomials are non-negative it then follows…”
Section: Convergence Of Our Proposed Sos Programsmentioning
confidence: 95%
“…The path planning of autonomous systems is the computational problem of finding the sequence of inputs that moves a given object from an initial condition to a target set while avoiding obstacles. Computing optimal paths is a well researched subject, with a broad range of practical uses ranging from the navigation of UAVs [18] to the precise movements of robotic manipulators [19].…”
Section: A Application To Path Planning and Obstacle Avoidancementioning
confidence: 99%
“…( 40)) we show lim d→∞ ||J * d − min 1≤i≤m g i || L ∞ (Λ,R) = 0. Note, the solutions, {J d } d∈N , to Opts (19) and (22) provide inner sublevel set approximations as shown in Eq. ( 38).…”
Section: Convergence Of Our Proposed Sos Programsmentioning
confidence: 99%
“…d ∑ SOS , s i,1 (x)∈ d ∑ SOS , s i, j,2 (x)∈ d ∑ SOS , s i,3 (x)∈ d ∑ SOS , s 4 (x)∈ d ∑ SOSfor all i, j ∈{1, ..., m}.In a similar way to how we tightened Opt (13). to get Opt (19). we next tighten Opt (15).…”
“…solve the family of d-degree SOS optimization problems given in Eq. (19). Now, it follows that if we show that…”
Section: Convergence Of Our Proposed Sos Programsmentioning
confidence: 85%
“…( 19) it satisfies all of the constraints of Opt. (19). Since SOS polynomials are non-negative it then follows…”
Section: Convergence Of Our Proposed Sos Programsmentioning
confidence: 95%
“…The path planning of autonomous systems is the computational problem of finding the sequence of inputs that moves a given object from an initial condition to a target set while avoiding obstacles. Computing optimal paths is a well researched subject, with a broad range of practical uses ranging from the navigation of UAVs [18] to the precise movements of robotic manipulators [19].…”
Section: A Application To Path Planning and Obstacle Avoidancementioning
confidence: 99%
“…( 40)) we show lim d→∞ ||J * d − min 1≤i≤m g i || L ∞ (Λ,R) = 0. Note, the solutions, {J d } d∈N , to Opts (19) and (22) provide inner sublevel set approximations as shown in Eq. ( 38).…”
Section: Convergence Of Our Proposed Sos Programsmentioning
confidence: 99%
“…d ∑ SOS , s i,1 (x)∈ d ∑ SOS , s i, j,2 (x)∈ d ∑ SOS , s i,3 (x)∈ d ∑ SOS , s 4 (x)∈ d ∑ SOSfor all i, j ∈{1, ..., m}.In a similar way to how we tightened Opt (13). to get Opt (19). we next tighten Opt (15).…”
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