model is infeasible or unbounded

Hi there,

I have built up a simple trajectory optimization model which minimize the acceleration rate given fixed initial time step and speed, and final time step and speed. The model itself looks straightforward and the lp file I output looks fine to me. Nevertheless, Gurobipy still say the model is infeasible and unbounded. Below is my code and lp output. Thank you very much for you time and help. 

def trajectory(initialSpeed, finalSpeed, timesteps, distance):
    m = gp.Model("trajectory")
    # claim speed variable set
    v0 = m.addVars(timesteps,vtype = GRB.CONTINUOUS, name = "speed")
    # define objective function, minimize the accelration rate
    obj = gp.quicksum((v0[i + 1] - v0[i]) * (v0[i + 1] - v0[i]) for i in range(len(v0) - 1))
    m.setObjective(obj, GRB.MINIMIZE)

    # acceleration capacity limit for a vehicle
    m.addConstrs((v0[i + 1] - v0[i] <= 2 for i in range(len(v0)-1)), name ="upperacc")
    m.addConstrs((v0[i + 1] - v0[i] >= -1.4 for i in range(len(v0) - 1)), name="loweracc")

    # fixed initial speed and final speed
    m.addLConstr(v0[0], GRB.EQUAL, initialSpeed, name ="initialSpeed")
    m.addLConstr(v0[len(v0)-1], GRB.EQUAL, finalSpeed, name ="finalSpeed")
    
    # speed limits
    m.addConstrs((v0[i] <=30 for i in range(len(v0))) , name ="upperspeedlimits")
    m.addConstrs((v0[i] >=0 for i in range(len(v0))) , name = "lowerspeedlimits")
    m.addConstr(gp.quicksum(v0[i] for i in range(len(v0))) == distance, name = "distance")
    m.write("test.lp")

    m.optimize()

    for v in m.getVars():
        print('%s %g' % (v.varName, v.x))
    print('Obj: %g' % m.objVal)
    
#test run
trajectory(25,10,15,200)
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LP FILE

\ Model trajectory
\ LP format - for model browsing. Use MPS format to capture full model detail.
Minimize
 [ - 4 speed[0] * speed[1] + 2 speed[0] ^2 + 4 speed[1] ^2
   - 4 speed[1] * speed[2] + 4 speed[2] ^2 - 4 speed[2] * speed[3]
   + 4 speed[3] ^2 - 4 speed[3] * speed[4] + 4 speed[4] ^2
   - 4 speed[4] * speed[5] + 4 speed[5] ^2 - 4 speed[5] * speed[6]
   + 4 speed[6] ^2 - 4 speed[6] * speed[7] + 4 speed[7] ^2
   - 4 speed[7] * speed[8] + 4 speed[8] ^2 - 4 speed[8] * speed[9]
   + 4 speed[9] ^2 - 4 speed[9] * speed[10] + 4 speed[10] ^2
   - 4 speed[10] * speed[11] + 4 speed[11] ^2 - 4 speed[11] * speed[12]
   + 4 speed[12] ^2 - 4 speed[12] * speed[13] + 4 speed[13] ^2
   - 4 speed[13] * speed[14] + 2 speed[14] ^2 ] / 2 
Subject To
 upperacc[0]: - speed[0] + speed[1] <= 2
 upperacc[1]: - speed[1] + speed[2] <= 2
 upperacc[2]: - speed[2] + speed[3] <= 2
 upperacc[3]: - speed[3] + speed[4] <= 2
 upperacc[4]: - speed[4] + speed[5] <= 2
 upperacc[5]: - speed[5] + speed[6] <= 2
 upperacc[6]: - speed[6] + speed[7] <= 2
 upperacc[7]: - speed[7] + speed[8] <= 2
 upperacc[8]: - speed[8] + speed[9] <= 2
 upperacc[9]: - speed[9] + speed[10] <= 2
 upperacc[10]: - speed[10] + speed[11] <= 2
 upperacc[11]: - speed[11] + speed[12] <= 2
 upperacc[12]: - speed[12] + speed[13] <= 2
 upperacc[13]: - speed[13] + speed[14] <= 2
 loweracc[0]: - speed[0] + speed[1] >= -1.4
 loweracc[1]: - speed[1] + speed[2] >= -1.4
 loweracc[2]: - speed[2] + speed[3] >= -1.4
 loweracc[3]: - speed[3] + speed[4] >= -1.4
 loweracc[4]: - speed[4] + speed[5] >= -1.4
 loweracc[5]: - speed[5] + speed[6] >= -1.4
 loweracc[6]: - speed[6] + speed[7] >= -1.4
 loweracc[7]: - speed[7] + speed[8] >= -1.4
 loweracc[8]: - speed[8] + speed[9] >= -1.4
 loweracc[9]: - speed[9] + speed[10] >= -1.4
 loweracc[10]: - speed[10] + speed[11] >= -1.4
 loweracc[11]: - speed[11] + speed[12] >= -1.4
 loweracc[12]: - speed[12] + speed[13] >= -1.4
 loweracc[13]: - speed[13] + speed[14] >= -1.4
 initialSpeed: speed[0] = 25
 finalSpeed: speed[14] = 10
 upperspeedlimits[0]: speed[0] <= 30
 upperspeedlimits[1]: speed[1] <= 30
 upperspeedlimits[2]: speed[2] <= 30
 upperspeedlimits[3]: speed[3] <= 30
 upperspeedlimits[4]: speed[4] <= 30
 upperspeedlimits[5]: speed[5] <= 30
 upperspeedlimits[6]: speed[6] <= 30
 upperspeedlimits[7]: speed[7] <= 30
 upperspeedlimits[8]: speed[8] <= 30
 upperspeedlimits[9]: speed[9] <= 30
 upperspeedlimits[10]: speed[10] <= 30
 upperspeedlimits[11]: speed[11] <= 30
 upperspeedlimits[12]: speed[12] <= 30
 upperspeedlimits[13]: speed[13] <= 30
 upperspeedlimits[14]: speed[14] <= 30
 lowerspeedlimits[0]: speed[0] >= 0
 lowerspeedlimits[1]: speed[1] >= 0
 lowerspeedlimits[2]: speed[2] >= 0
 lowerspeedlimits[3]: speed[3] >= 0
 lowerspeedlimits[4]: speed[4] >= 0
 lowerspeedlimits[5]: speed[5] >= 0
 lowerspeedlimits[6]: speed[6] >= 0
 lowerspeedlimits[7]: speed[7] >= 0
 lowerspeedlimits[8]: speed[8] >= 0
 lowerspeedlimits[9]: speed[9] >= 0
 lowerspeedlimits[10]: speed[10] >= 0
 lowerspeedlimits[11]: speed[11] >= 0
 lowerspeedlimits[12]: speed[12] >= 0
 lowerspeedlimits[13]: speed[13] >= 0
 lowerspeedlimits[14]: speed[14] >= 0
 distance: speed[0] + speed[1] + speed[2] + speed[3] + speed[4] + speed[5]
   + speed[6] + speed[7] + speed[8] + speed[9] + speed[10] + speed[11]
   + speed[12] + speed[13] + speed[14] = 200
Bounds
End

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