Please solve problem 2, include matlab code. the equation is Tf - T0 = T = 10 sec; qi(T0) = 10 degrees, (dq(t)/dt), t=t0=0 and d^2q(t)/dt^2 t = t0 =0

the free acting at the enton, F,.. 10 N. F.-0,r,.. a Dwus6eHywal sear or result The follow ing question is for your estra eredit If you have tise, wok on ia 0 Obain the joint angles of all the singular configarations by solving the deoit of the Jacobian matrix. Skeich singular configuratios and determine in which dinection the endpoint cannot be moved with a non-zero velocity Problem 2 Trajectory Planning: Find a suitable trajectory (determine the minimum order of the polynomial based on the following specifications: The initial/starting time is to, the final time is ty with t- = -10 sec; qdlo)-10, dan r-o-o and "fqiuur-e-0; the corresponding coditios are, 100, 0, 0. Plot the position, velocity and acceleration trajectory when to 0 and T 10 sec (You may use MATLAB.) Problem 3 Trajectory Planning: Often, a trajectory is assigned by specifying a sequence of desired points (via-points) without indication on the velocity in these points. For example, consider the following via-points and corresponding q's to=0 t, = 4 ts 10 In these cases, the "most suitable" values for the velocities must be automatically computed. This assignment is quite simple with heuristic rules such as zero initial and final value velocity, i.e da/dt-0 at to and t while at other (intermediate) points the assignment is dqi/dt = 0 sign(vut sign(vk-1), or the free acting at the enton, F,.. 10 N. F.-0,r,.. a Dwus6eHywal sear or result The follow ing question is for your estra eredit If you have tise, wok on ia 0 Obain the joint angles of all the singular configarations by solving the deoit of the Jacobian matrix. Skeich singular configuratios and determine in which dinection the endpoint cannot be moved with a non-zero velocity Problem 2 Trajectory Planning: Find a suitable trajectory (determine the minimum order of the polynomial based on the following specifications: The initial/starting time is to, the final time is ty with t- = -10 sec; qdlo)-10, dan r-o-o and "fqiuur-e-0; the corresponding coditios are, 100, 0, 0. Plot the position, velocity and acceleration trajectory when to 0 and T 10 sec (You may use MATLAB.) Problem 3 Trajectory Planning: Often, a trajectory is assigned by specifying a sequence of desired points (via-points) without indication on the velocity in these points. For example, consider the following via-points and corresponding q's to=0 t, = 4 ts 10 In these cases, the "most suitable" values for the velocities must be automatically computed. This assignment is quite simple with heuristic rules such as zero initial and final value velocity, i.e da/dt-0 at to and t while at other (intermediate) points the assignment is dqi/dt = 0 sign(vut sign(vk-1), or