Long distance walking record

The broad goal of the Ranger project [12] is to develop a reliable robot capable of walking long distances on minimal amounts of energy. We set ourselves the goal of making Ranger walk a marathon distance of 26.2 miles or 42.2 kilometers, without falling down, without stopping, and without recharging.

The feat of walking a marathon was achieved in stages. Ranger was built in the fall of 2006 [58]. In December 2006, it walked 1 km or 0.6 mi non-stop with a TCOT of 1.6 [9], setting a legged distance record then. Further improvements in the hardware and walking controller led to longer walks. In April 2008, it walked 9 km or 5.6 mi with a TCOT of 0.6 [10]. In July 2010, it walked 23 km or 14.3 mi with a TCOT of 0.49 [11].

On 1-2 May 2011, before we had implemented all steps of the optimization in the energy-effective controller presented earlier in this paper, Ranger walked 40.5 miles or 65 kilometers, non-stop, and on a single battery charge (beating BigDog’s record of 12.6 mi set in 2008 by more than a factor of 3). Ranger took 186,076 steps at a leisurely pace of 2.12 kilometers per hour or 1.32 miles per hour to set this distance record. The total energy consumption for Ranger for this walk was 493 watt-hours1. For this ultra- marathon Ranger had a TCOT of 0.28. As noted, this was later reduced to TCOT = 0.19. Thus, we believe Ranger could now walk (0.28/0.19)*65 km = 95 km on a single charge, well over two full marathons.

1_{Electricity costs 11.2 cents per kilo-watt-hour in United States for the year 2011. Ranger’s 493 watt-}

Figure 7.4: Ranger’s ultra-marathon walk. On 1-2 May 2011 [12], Ranger walked non-stop for 40.5 miles (65 km) on Cornell’s Barton Hall track without recharging or being touched by a human. Some of the crew that worked on Ranger are shown walking behind Ranger during the 65 km walk. Basic data are in the table below.

Total steps 186,076

Total time 110,942 s (= 30 hrs 49 min 2 sec)

Number of laps 307.75

Lap distance 212 m (= 0.132 miles)

Total distance 65,243 m (= 65.24 km = 40.54 mi)

Average time per step 0.6 s

Average distance per step 0.35 m (= 13.78 in)

Average speed 0.59 m/s (= 2.12 km/h = 1.32 mph)

Total power 16 W

Power used by motors 11.3 W

Power used by computers and sensors 4.7 W

Total energy used 493 watt-hours

Battery 25.9 V Li-ion

Total robot mass 9.91 kg (= 21.85 lb)

Battery mass 2.8 kg (= 6.3 lb)

Total cost of transport (TCOT) 0.28 (later lowered to 0.19)

Table 7.2: Statistics of Ranger’s 40.5 mile ultra-marathon walk on 1-2 May 2011.

CHAPTER 8

CONCLUDING REMARKS

8.1

Thesis summary

This thesis presented a model based control design framework for bipedal robots that combines energy efficiency with stability and demonstrated its application on the custom built bipedal robot called the Ranger.

First in chapter 2, we give a peek at our control design algorithm that starts with a hi-fidelity robot model, and proceeds with a trajectory generator to get the nominal gait and finally a stabilizing controller that stabilizes the nominal gait. We applied our stabilizing controller idea to balance of a simple inverted pendulum with a controller bandwidth slower than the characteristic time scale of the system.

In chapter 3, we presented a model for the robot and its actuators. In chapter 4, we presented bench experiments that helped fit the parameters of the assumed model. In particular, we found that the simple ideal DC motor description inadequate. The motor brush resistance was almost twice than what was reported by the manufacturer and there was substantial brush-commutator contact resistance. The gear-box had a load dependent friction which we approximated as a current dependent friction.

In chapter 5, we formulated an energy-optimal trajectory control problem. Our en- ergy metric was the total cost of transport (TCOT) and is defined as the energy used per weight per unit distance travelled. We decoupled the motion of the foot of the swinging leg in single stance phase (that does the ground clearance) from the rest of the walk. These helped us write the TCOT as a sum of COT to power the computers and others electronics, COT for foot-flip and COT for walking. We considered minimization of

the various COT’s as a function of step length and step velocity. The COT to run the computers and electronics is step velocity dependent and favors fast speeds. The COT for foot-flip is step length dependent and favors big steps. The COT for walking has a strong step time dependence and favors walking at the natural frequency of the swing legs. After summing the COT we found that minimum TCOT is 0.163 (Total Watts= 10.2) and occurs at a step length of 0.48 m and step velocity of 0.77 m/s. In the optimal solution, 49 % of the energy goes to power the computer and electronics, 23% is used to do the foot-flip for ground clearance and the rest 28 % is used in taking a step.

Next, we turn to implementation on the robot. In the later half of chapter 5, we re-parameterized the optimal solution with the goal of simplifying the control represen- tation. Our approximate representation yields the nominal trajectory and reduces the original 126 parameters in the fine grid solution to about 15 parameters while increasing the cost by about 7%. In order to stabilize the nominal trajectory, we first motivated an energy based control of a 2-D point-mass model of walking in chapter 6. The central idea here is that we are interested in regulating the kinetic energy of the robot’s center of mass in the upright position. We identify two means of doing so; using an ankle push- off control and using step length control. Further analysis reveals that ankle push-off control works best to regulate slow walking while step length works best to regulate fast walking.

Using the approximate coarse-grid controller representation (chapter 5) and the sta- bilizing control ideas (chapter 6), we implement the simulation based controller on the biped platform Ranger. We show that using our control framework Ranger walks sta- bly with a TCOT of 0.19 (about 14 % more than the fine grid optimal solution), more energy-efficient than any legged robot built-to-date. Also, using a slightly less energy- efficient version of approximate controller than the one presented here, Ranger walked

non-stop for 40.5 miles or 65 km on a single battery charge, setting a legged robot dis- tance record.