RBE 595 Space and Planetary Robotics Lecture 7

RBE 595: Space and Planetary Robotics Lecture 7 Professor Marko B Popovic A term 2019

Lunar rovers Luna With increased confidence from the success of their Sputnik missions, the Soviet Union launched 24 Luna spacecrafts to the Moon, between 1959 and 1976. 15 were successful, each designed as either an orbiter or lander, and accomplished many firsts in space exploration. They also performed many experiments, studying the Moon's chemical composition, gravity, temperature, and radiation. Luna 1 missed its intended impact with the Moon and became the first spacecraft to fall into orbit around the Sun. In 1959, the second Luna mission successfully impacted the lunar surface, becoming the first man-made object to reach another world. Luna 3 orbited the Moon later that year, and returned the first photographs of its far side, which can never be seen from Earth. The Soviet Union soon learned to build spacecrafts which could perform soft landings on the lunar surface, and send back panoramic photos from their landing sites. Lunas 17 and 21 even carried roving vehicles which roamed around on the Moon's terrain. Another major achievement of the Luna program was the ability to collect samples of lunar soil and return them to Earth, by 1970. However, these accomplishments were overshadowed by the U. S. Apollo missions which had already placed humans on the Moon by this time.

Lunokhod (Russian: Луноход, "Moonwalker") was a series of Soviet robotic lunar rovers designed to land on the Moon between 1969 and 1977. The 1969 Lunokhod 1 A (Lunokhod 0, Lunokhod No. 201) was destroyed during launch, the 1970 Lunokhod 1 and the 1973 Lunokhod 2 landed on the moon and Lunokhod 3 (Lunokhod No. 205, planned for 1977) was never launched. The successful missions were in operation concurrently with the Zond and Luna series of Moon flyby, orbiter and landing missions. The Lunokhods were transported to the lunar surface by Luna spacecraft, which were launched by Proton-K rockets. The moon lander part of the Luna spacecraft for Lunokhods were similar to the ones for sample return missions. Not until the 1997 Mars Pathfinder was another remote-controlled vehicle put on an extraterrestrial body. In 2010, nearly forty years after the 1971 loss of signal from Lunokhod 1, the NASA Lunar Reconnaissance Orbiter photographed its tracks and final location, and researchers, using a telescopic pulsed-laser rangefinder, detected the robot's retroreflector.

Lunokhod was the first roving remote-controlled robot to land on another world.

Luna 17 was launched on November 10, 1970. After reaching Earth parking orbit, the final stage of Luna 17's launching rocket fired to place it into a trajectory towards the Moon (November 10, 1970). After two course correction manoeuvres (on November 12 and 14) it entered lunar orbit on November 15, 1970. The spacecraft soft-landed on the Moon in the Sea of Rains on November 17, 1970. The lander had dual ramps from which the payload, Lunokhod 1, could descend to the lunar surface. To be able to work in vacuum a special fluoride based lubricant was used for the mechanical parts and the electric motors (one in each wheel hub) were enclosed in pressurized containers. The rover ran during the lunar day, stopping occasionally to recharge its batteries via the solar panels. At night the rover hibernated until the next sunrise, heated by the radioisotope heater unit. Lunokhod 1 was a lunar vehicle formed of a tub-like compartment with a large convex lid on eight independently powered wheels. Its length was 2. 3 meters. Lunokhod 1 was equipped with a cone-shaped antenna, a highly directional helical antenna, four television cameras, and special extendable devices to impact the lunar soil for density measurements and mechanical property tests. An X-ray spectrometer, an X-ray telescope, Cosmic Ray Detector, and a Laser device were also included. The vehicle was powered by batteries which were recharged during the lunar day by a solar cell array mounted on the underside of the lid. During the lunar nights, the lid was closed and a polonium-210 heat source kept the internal components at operating temperature.

The rover stood 135 cm (4 ft 5 in) tall and had a mass of 840 kg (1, 850 lb). It was about 170 cm (5 ft 7 in) long and 160 cm (4 ft 11 in) wide and had eight wheels each with an independent suspension, motor and brake. The rover had two speeds, approximately 1 and 2 km/h (0. 6 and 1. 2 mph). Payload: Cameras (two TV & four panoramic telephotometers) RIFMA X-ray fluorescence spectrometer RT-1 X-ray telescope Pr. OP odometer/penetrometer RV-2 N radiation detector TL laser retroreflector During its 322 Earth days of operations, Lunokhod 1 traveled 10. 5 km (6. 5 miles) and returned more than 20, 000 TV images and 206 high-resolution panoramas. In addition, it performed twenty-five soil analyses with its RIFMA x-ray fluorescence spectrometer and used its penetrometer at 500 different locations.

Lunokhod 2 (vehicle 8 ЕЛ№ 204) was the second and more advanced of two unmanned lunar rovers landed on the Moon by the Soviet Union as part of the Lunokhod program. The launcher put the spacecraft into Earth parking orbit on January 8, 1973, followed by translunar injection. On January 12, 1973, Luna 21 was braked into a 90 by 100 km (56 by 62 miles) lunar orbit. The Luna 21 spacecraft landed on the Moon and deployed the second Soviet lunar rover, Lunokhod 2. The primary objectives of the mission were to collect images of the lunar surface, examine ambient light levels to determine the feasibility of astronomical observations from the Moon, perform laser ranging experiments from Earth, observe solar X-rays, measure local magnetic fields, and study mechanical properties of the lunar surface material. The landing occurred on January 15, 1973 in Le Monnier crater at 25. 85 degrees N, 30. 45 degrees E. Lunokhod 2 was equipped with three slow-scan television cameras, one mounted high on the rover for navigation, which could return high resolution images at different rates— 3. 2, 5. 7, 10. 9 or 21. 1 seconds per frame (not frames per second). These images were used by a five-man team of controllers on Earth who sent driving commands to the rover in real time. There were four panoramic cameras mounted on the rover.

Power was supplied by a solar panel on the inside of a round hinged lid which covered the instrument bay, which would charge the batteries when opened. A polonium-210 radioactive heat source was used to keep the rover warm during the long lunar nights. Scientific instruments included a soil mechanics tester, Solar X-ray experiment, an astrophotometer to measure visible and ultraviolet light levels, a magnetometer deployed in front of the rover on the end of a 2. 5 m (8 ft 2 in) boom, a radiometer, a photodetector (Rubin-1) for laser detection experiments, and a French-supplied laser corner reflector. Payload[edit] Cameras (three TV & four panoramic telephotometers) RIFMA-M X-ray fluorescence spectrometer X-ray telescope PROP odometer/penetrometer RV-2 N-LS radiation detector TL laser retroreflector AF-3 L UV/visible astrophotometer SG-70 A magnetometer Rubin 1 photodetector Lunokhod 2 operated for about 4 months, covered 42 km (26 miles) of terrain, including hilly upland areas and rilles (rille = a fissure or narrow channel on the moon's surface), and held the record for the longest distance of surface travel of any extraterrestrial vehicle until 2014. It sent back 86 panoramic images and over 80, 000 TV pictures. Many mechanical tests of the surface, laser ranging measurements, and other experiments were completed during this time.

Lunar Roving Vehicle The Lunar Roving Vehicle (LRV) is a battery-powered fourwheeled rover used on the Moon in the last three missions of the American Apollo program (15, 16, and 17) during 1971 and 1972. They are popularly known as "Moon buggies", a play on the words "dune buggy". Built by Boeing, each LRV weighed 210 kg, could carry two astronauts, equipment and lunar samples, and had a designed top speed of 13 km/h. They were transported to the Moon folded up in the Lunar Module's Quadrant 1 Bay. After being unpacked, they were driven an average distance of 30 km on each of the three missions, without major incident. These three LRVs remain on the Moon.

The Moon-buggy was a one hp vehicle in total. Each of the four wheels had a 0. 25 electric motor made by Delco. The moon-buggies and the test models were built by Boeing at a cost of $38, 000. In today’s dollars that equates to roughly $285 million. The total distance travelled by all three LRVs was about 56 miles. In theory, each could have gone that far on the battery power on-board. A repair to a fender was made to a moon-buggy during Apollo 17. Astronauts Cernan and Schmidt used duct tape to fix it. This was caught on video. The repair did not work and fell apart after an hour. A second duct tape repair with a clamp was made. https: //www. youtube. com/watch? time_continue=9&v=5 c. Kpzp 358 F 4 https: //www. youtube. com/watch? time_continue=1&v=Tqg. HCN 4 A 0 b 0

The Lunar Roving Vehicle had a mass of 460 pounds (210 kg), and was designed to hold a payload of 1, 080 pounds (490 kg). This resulted in weights in the approximately one-sixth g on the lunar surface of 77 pounds-force (35 kgf) empty and 260 pounds-force (116 kgf) fully loaded. The frame was 10 feet (3. 0 m) long with a wheelbase of 7. 5 feet (2. 3 m). The height of the vehicle was 3. 6 feet (1. 1 m). The frame was made of 2219 aluminum alloy tubing welded assemblies and consisted of a three-part chassis that was hinged in the center so it could be folded up and hung in the Lunar Module Quadrant 1 bay, which was kept open to space by omission of the outer skin panel. It had two side-by-side foldable seats made of tubular aluminum with nylon webbing and aluminum floor panels. An armrest was mounted between the seats, and each seat had adjustable footrests and a Velcro-fastened seat belt. A large mesh dish antenna was mounted on a mast on the front center of the rover. The suspension consisted of a double horizontal wishbone with upper and lower torsion bars and a damper unit between the chassis and upper wishbone. Fully loaded, the LRV had a ground clearance of 14 inches (36 cm). https: //en. wikipedia. org/wiki/Double_wishbone_suspe nsion#/media/File: Double_wishbone_Suspension. gif

The wheels were designed and manufactured by General Motors Defense Research Laboratories in Santa Barbara, California. “Resilient wheel“ consisted of a spun aluminum hub and a 32 inches (81 cm) diameter, 9 inches (23 cm) wide tire made of zinc-coated woven 0. 033 inches (0. 84 mm) diameter steel strands attached to the rim and discs of formed aluminum. Titanium chevrons covered 50% of the contact area to provide traction. Inside the tire was a 25. 5 inches (65 cm) diameter bump stop frame to protect the hub. Dust guards were mounted above the wheels. Each wheel had its own electric drive made by Delco, a direct current (DC) series-wound motor capable of 0. 25 horsepower (190 W) at 10, 000 rpm, attached to the wheel via an 80: 1 harmonic drive, and a mechanical brake unit. Each wheel could free-wheel in case of drive failure.

Lunar soil is the fine fraction of the regolith found on the surface of the Moon. Its properties can differ significantly from those of terrestrial soil. The physical properties of lunar soil are primarily the result of mechanical disintegration of basaltic and anorthositic rock, caused by continual meteoric impacts and bombardment by solar and interstellar charged atomic particles over years. The process is largely one of mechanical weathering in which the particles are ground to finer and finer size over time. The term lunar soil is often used interchangeably with lunar regolith, but typically refers to only the finer fraction of regolith, that which is composed of grains 1 cm in diameter or less. Lunar dust generally connotes even finer materials than lunar soil. There is no official definition of what size fraction constitutes "dust"; some place the cutoff at less than 50 μm in diameter, while others at less than 10 μm. Due to myriad meteorite impacts (with velocities in the range of 20 km/s), the lunar surface is covered with a thin layer of dust. The dust is electrically charged and sticks to any surface it comes in contact with. The density of lunar regolith is about 1. 5 g/cm 3. The soil becomes very dense beneath the top layer of regolith. Other factors which may affect the properties of lunar soil include large temperature differentials, the presence of a hard vacuum, and the absence of a significant lunar magnetic field, thereby allowing charged solar wind particles to continuously hit the surface of the Moon. There is some evidence that the Moon may have a tenuous atmosphere of moving dust particles constantly leaping up from and falling back to the Moon's surface ("Moon fountain“), giving rise to a "dust atmosphere" that looks static but is composed of dust particles in constant motion.

Mars rovers A Mars rover is an automated motor vehicle that propels itself across the surface of the planet Mars upon arrival. Rovers have several advantages over stationary landers: they examine more territory, and they can be directed to interesting features, they can place themselves in sunny positions to weather winter months, and they can advance the knowledge of how to perform very remote robotic vehicle control. • Mars 2, Prop-M rover, 1971, Mars 2 landing failed taking Prop-M with it. The Mars 2 and 3 spacecraft from the USSR had identical 4. 5 kg Prop-M rovers. They were to move on skis while connected to the landers with cables. • Mars 3, Prop-M rover, 1971, lost when Mars 3 lander stopped communicating about 20 seconds after landing. • Sojourner rover, Mars Pathfinder, landed successfully on July 4, 1997. Communications were lost on September 27, 1997. • Beagle 2, Planetary Undersurface Tool, lost with Beagle 2 on deployment from Mars Express in 2003. A compressed spring mechanism was designed to allow movement across the surface at a rate of 1 cm per 5 seconds and to burrow into the ground and collect a subsurface sample in a cavity in its tip. • Spirit (MER-A), Mars Exploration Rover, launched on June 10, 2003 and landed successfully on January 4, 2004. Nearly 6 years after the original mission limit, Spirit had covered a total distance of 7. 73 km (4. 80 mi) but its wheels became trapped in sand. Around January 26, 2010, NASA conceded defeat in its efforts to free the rover and stated that it would now function as a stationary science platform. The last communication received from the rover was on March 22, 2010, and NASA ceased attempts to re-establish communication on May 25, 2011.

• Opportunity (MER-B), Mars Exploration Rover, launched on July 7, 2003 and landed on January 25, 2004. Opportunity surpassed the previous records for longevity at 5, 352 sols (5498 Earth days from landing to mission end; 15 Earth years or 8 Martian years) and covered a total distance of 40. 25 km (25. 01 mi). The rover sent its last status on 10 June 2018 when a global 2018 Mars dust storm blocked the sunlight needed to recharge its batteries. After hundreds of attempts to reactivate the rover, NASA declared the mission complete on February 13, 2019. • Curiosity of the Mars Science Laboratory (MSL) mission by NASA, was launched November 26, 2011 and landed at the Aeolis Palus plain near Aeolis Mons (informally "Mount Sharp") in Gale Crater on August 6, 2012. The Curiosity rover is still operational as of September 18, 2019. The global topography of Mars, overlain with locations of Mars landers and rovers. Coloring of the base map indicates relative elevations, based on data from the Mars Orbiter Laser Altimeter on NASA's Mars Global Surveyor. Reds and pinks are higher elevation (+3 km to +8 km); yellow is 0 km; greens and blues are lower elevation (down to − 8 km). Whites (>+12 km) and browns (>+8 km) are the highest elevations. Axes are latitude and longitude; note poles are not shown.

The Viking missions to Mars Each spacecraft consisted of an orbiter and lander. The landers were sterilized before launch to prevent contamination of Mars with organisms from Earth. Their objectives were to obtain highly detailed pictures of the Martian surface, learn about its composition, and search for life. Viking 1 was launched on Aug. 20, 1975, followed later that year on Sep. 9 by Viking 2. After searching for flat, level areas, the spacecraft deployed their landers, brought safely to the ground using parachutes and retro-thrusters which prevented a dangerous high-speed impact. Viking 1 landed on the western slope of Chryse Planitia (the Plains of Gold) at 22. 3 degrees N latitude, 48. 0 degrees longitude. Viking 2 landed on Utopia Planitia; 47. 6 degrees N latitude, 225. 7 degrees W. longitude. Over the next four years, the orbiters mapped 97% of the Martian surface and relayed information from the landers back to Earth.

The Viking landers monitored Martian weather, regular dust storms, and returned high-resolution color photos which revealed interesting geologic features. Their analysis of Mars' soil found no evidence of life, though unexpected chemical activity was observed. The Viking missions did discover water in both solid and vapor form, which suggests that life may have existed on the planet many years ago. Tallest planetary mountain in the Solar System (discovered by US Mariner 9 in 1971. Olympus Mons is a shield volcano 624 km (374 mi) in diameter (approximately the same size as the state of Arizona), 25 km (16 mi) high, and is rimmed by a 6 km (4 mi) high scarp. A caldera 80 km (50 mi) wide is located at the summit of Olympus Mons.

Sojourner was the Mars Pathfinder robotic Mars rover that landed on July 4, 1997 and explored Mars for around three months. It has front and rear cameras and hardware to conduct several scientific experiments. Designed for a mission lasting 7 sols, with possible extension to 30 sols, it was in fact active for 83 sols. The base station had its last communication session with Earth at 3: 23 a. m. Pacific Daylight Time on September 27, 1997. The rover needed the base station to communicate with Earth, despite still functioning at the time communications ended. 11. 5 kilograms (25 lb) Sojourner traveled a distance of just over 100 metres (330 ft) by the time communication was lost. It was instructed to stay stationary until October 5, 1997 (sol 91) and then drive around the lander.

Sojourner has solar panels and a non-rechargeable battery, which allowed limited nocturnal operations. Once the batteries were depleted, it could only operate during the day. The batteries are lithium-thionyl chloride (Li. SOCl 2) and could provide 150 watt-hours. The batteries also allowed the health of the rover to be checked while enclosed in the cruise stage while en route to Mars. 0. 22 square meters of solar cells could produce a maximum of about 15 watts on Mars, depending on conditions. The cells were Ga. As/Ge (Gallium Arsenide/Germanium) and capable of about 18 percent efficiency. They could survive down to about − 140° Celsius (− 220 °F). Its central processing unit (CPU) is an 80 C 85 with a 2 MHz clock, addressing 64 Kbytes of memory. It has four memory stores; the previously mentioned 64 Kbytes of RAM (made by IBM) for the main processor, 16 Kbytes of radiation-hardened PROM (made by Harris), 176 Kbytes of non-volatile storage (made by Seeq Technology), and 512 Kbytes of temporary data storage (made by Micron). The electronics were housed inside the Warm Electronics Box inside the rover. It communicated with the base station with 9, 600 baud radio modems. The practical rate was closer to 2, 600 baud with a theoretical range of about half a kilometer. The rover could travel out of range of the lander, but its software would need to be changed to that mode. Under normal driving, it would periodically send a "heartbeat" message to the lander. The UHF radio modems worked similar to walkie-talkies, but sent data, not voice. It could send or receive, but not both at same time, which is known as half-duplex. The data was communicated in bursts of 2 kilobytes. The rover had three cameras: 2 monochrome cameras in front, and a color camera in the rear. Each front camera had an array 484 pixels high by 768 wide. The optics consisted of a window, lens, and field flattener. The window was made of sapphire, while the lens objective and flattener were made of zinc selenide. The rover was imaged on Mars by the base station's IMP camera system, (Imager for Mars Pathfinder, a camera on board the Mars Pathfinder lander)which also helped determine where the rover should go.

Opportunity , also known as MER-B (Mars Exploration Rover – B) or MER-1, and nicknamed "Oppy", is a robotic rover that was active on Mars from 2004 until the middle of 2018. Launched on July 7, 2003, as part of NASA's Mars Exploration Rover program, it landed in Meridiani Planum on January 25, 2004, three weeks after its twin Spirit (MER-A) touched down on the other side of the planet. With a planned 90 -sol duration of activity (slightly more than 90 Earth days), Spirit functioned until it got stuck in 2009 and ceased communications in 2010, while Opportunity was able to stay operational for 5111 sols after landing, maintaining its power and key systems through continual recharging of its batteries using solar power, and hibernating during events such as dust storms to save power. This careful operation allowed Opportunity to exceed its operating plan by 14 years, 46 days (in Earth time), 55 times its designed lifespan. By June 10, 2018, when it last contacted NASA, the rover had traveled a distance of 45. 16 kilometers (28. 06 miles). Mission highlights included the initial 90 -sol mission, finding extramartian meteorites such as Heat Shield Rock (Meridiani Planum meteorite), and over two years of exploring and studying Victoria crater. The rover survived moderate dust storms and in 2011 reached Endeavour crater, which has been described as a "second landing site". The Opportunity mission is considered one of NASA's most successful ventures.

Due to the planetary 2018 dust storm on Mars, Opportunity ceased communications on June 10 and entered hibernation on June 12, 2018. It was hoped it would reboot once the weather cleared, but it did not, suggesting either a catastrophic failure or that a layer of dust had covered its solar panels. NASA hoped to re-establish contact with the rover, citing a windy period that could potentially clean off its solar panels. On February 13, 2019, NASA officials declared that the Opportunity mission was complete, after the spacecraft had failed to respond to over 1, 000 signals sent since August 2018. Spirit and Opportunity are twin rovers, each a six-wheeled, solar-powered robot standing 1. 5 meters (4. 9 ft) high, 2. 3 meters (7. 5 ft) wide, and 1. 6 meters (5. 2 ft) long and weighing 180 kilograms (400 lb). Six wheels on a rockerbogie system enable mobility. Each wheel has its own motor, the vehicle is steered at front and rear and was designed to operate safely at tilts of up to 30 degrees. Maximum speed is 5 centimeters per second (2. 0 in/s) although average speed was about a fifth of this (0. 89 centimeters per second (0. 35 in/s)). Both Spirit and Opportunity have pieces of the fallen World Trade Center's metal on them that were "turned into shields to protect cables on the drilling mechanisms".

Solar arrays generate about 140 watts for up to fourteen hours per sol, while rechargeable lithium ion batteries stored energy for use at night. Opportunity's onboard computer uses a 20 MHz RAD 6000 CPU with 128 MB of DRAM, 3 MB of EEPROM, and 256 MB of flash memory. The rover's operating temperature ranges from − 40 to +40 °C (− 40 to 104 °F) and radioisotope heaters provide a base level of heating, assisted by electrical heaters when necessary. A gold film and a layer of silica aerogel provides insulation. Communications depend on an omnidirectional low-gain antenna communicating at a low data rate and a steerable high-gain antenna, both in direct contact with Earth. A low gain antenna is also used to relay data to spacecraft orbiting Mars. Opportunity was 'driven' by several operators throughout its mission, including JPL roboticist Vandi Verma who also co-wrote the PLEXIL command language used in its software.

The rover uses a combination of solar cells and a rechargeable chemical battery. This class of rover has two rechargeable lithium batteries, each composed of 8 cells with 8 amp-hour capacity. At the start of the mission the solar panels could provide up to around 900 watt-hours (Wh) to recharge the battery and power system in one Sol, but this could vary due to a variety of factors. In Eagle crater the cells were producing about 840 Wh, but by Sol 319 in December 2004, it had dropped to 730 Wh. Like Earth, Mars has seasonal variations that reduce sunlight during winter. However, since the Martian year is longer than that of the Earth, the seasons fully rotate roughly once every 2 Earth years. By 2016, MER-B had endured seven Martian winters, during which times power levels drop which can mean the rover avoids doing activities that use a lot of power. During its first winter power levels dropped to under 300 Wh per day for two months, but some later winters were not as bad. Another factor that can reduce received power is dust in the atmosphere, especially dust storms. Dust storms have occurred quite frequently when Mars is closest to the Sun. [48] Global dust storms in 2007 reduced power levels for Opportunity and Spirit so much they could only run for a few minutes each day. Due to the 2018 dust storms on Mars, Opportunity entered hibernation mode on June 12, but it remained silent after the storm subsided in early October. https: //www. youtube. com/watch? v=Cub. Xtc. QLma 0

Homework 3 Dynamics of autonomous Moon rover and biped robot (A) In this problem you will consider autonomous rover dynamics on Moon. Rover moves using wheels that utilize force of friction to accelerate and deaccelerate. You may assume that coefficient of friction between wheels and lunar soil (say lunar regolith) is 0. 20. What is the maximal magnitude of acceleration or de-acceleration of the rover if wheels are not slipping? (B) Consider now that road is rocky and uneven and that autonomous rover could “understand” that there is potentially damaging obstacle only when it is 5 m in front of rover. For precaution, in case that obstacle is such that it cannot be avoided by maneuver, the rover speed is such that it allows rover to come to full stop, before colliding or falling in obstacle, with half the maximal de-aceleration you obtained in part (A). What is the maximal speed of rover? (C) Estimate the required motive power of engine when rover is moving at maximal speed you obtained in part (B). Assume that rover wheels, 15 cm wide, dig 5 cm deep track on lunar soil. For this calculation it is fine to consider only gravitational potential energy of lunar soil “digging”. Assume that engine efficiency is 0. 2 (i. e. output rover’s mechanical power divided with engine input power).

(D) If 2 m by 2 m solar panel has 0. 3 transmission efficiency (not 0. 5, as one would hope say because of dust collecting on panel) how long one should charge battery for every km that rover travel with maximal allowed speed? Assume most ideal conditions for solar panel (i. e. sun rays are perpendicular to its surface) during battery charging. (E) What is the average speed of rover (assuming also time for charging)? (F) Consider now walking robot, say biped, on Moon. Do you expect that it may be more or less energy efficient than rover on wheels? Why yes or why no? (G) Consider that biped robot has same maximal speed as you obtained in part (B). Consider that all assumptions here are same as in part (C) except that tracks are now only 25% of what you had in part (C). What is required motive power of engine so biped could move with that maximal speed? (H) But let’s be careful! Imagine that biped robot has 1 m tall legs and that its entire mass may be considered as point like, located just on top of legs. For obtained maximal speed, is robot walking or running? Think about normal force, it can be expressed as weight (on Martian surface) minus mass times radial acceleration of point like mass in respect to ground foot contact point. For which speed one should expect walk run transition based on this considerations? For real robot or astronaut at which speed would you expect this transition to happen? (I) Do you expect biped robots to walk or run on Moon if they are to move in most energy efficient manner per distance travelled?