Consider the robot tool moves from point w to point w in tool configuration space over...

 

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Consider the robot tool moves from point w¹ to point w² in tool configuration space over an interval of time [T₁ T₂]. Suppose a cubic polynomial w(t) is used for the segment {w¹, w²} as w(t) = e(t - T₁)³ + f(t-T₁)² + g(t-T₁) +h, T₁ ≤ t ≤ T₁+T₂ Assuming the tool is to start out from point w at time T₁ with velocity v¹ and end up to point w² at time T₂ with velocity v², find the equation Bx = y, where x = [e.f.g. h]" is the vector of unknown polynomial coefficients and B and y are to be determined, to represent the constraints on the polynomial coefficients. Consider the robot tool moves from point w¹ to point w² in tool configuration space over an interval of time [T₁ T₂]. Suppose a cubic polynomial w(t) is used for the segment {w¹, w²} as w(t) = e(t - T₁)³ + f(t-T₁)² + g(t-T₁) +h, T₁ ≤ t ≤ T₁+T₂ Assuming the tool is to start out from point w at time T₁ with velocity v¹ and end up to point w² at time T₂ with velocity v², find the equation Bx = y, where x = [e.f.g. h]" is the vector of unknown polynomial coefficients and B and y are to be determined, to represent the constraints on the polynomial coefficients.

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