ClimberBot
Comparing gait efficiencies in a quadrupedal climbing robot
Overview
During the fall of 2020, two fellow students- Phil Cotter and Mike Schoder- and I designed a quadrupedal climbing robot to measure the efficiency of climbing gaits. Why? Seeing a natural transition point from walking to running as driven by cost of transport (COT) in many animals, we were curious if the same held true for alternating and bounding climbing gaits.
The project consisted of two main deliverables: (1) a simulation that would, in turn, determine the hardware and controller design of (2) a physical experimentation set-up. Although we collaborated on all aspects of the product, I was the main designer of the mechanical robot.
The robot consists of two 2-DOF legs, a metal & polymer 3D printer body, ad plastic arms. The shoulder remained fixed to eliminate an additional DOF. ClimberBot was attached to two tensioned ropes and employed Petzl ascenders to prevent backward movement. Finally, ClimberBot utilized a cartesian PID controller with a 9-degree Bezier curve to define the trajectory of each leg.
Simulation results showed that the alternating gait displayed a lower cost of transport at all speeds than the bounding gait. However, experimentation led to opposite results; bounding was more efficient than alternating. Experimental limitations in friction and motor power, especially at lower speeds, likely led to these results. To mitigate friction, future work should investigate a robot design that can grasp & ungrasp the rope, which would eliminate any sliding friction along the ascent.
Alternating Climbing Gait
Bounding Climbing Gait
Motivation
Many animals exhibit vertical climbing (“scansorial”) behavior in order to avoid predators, access food sources, or find shelter. Quadrupedal animals display different speed-dependent climbing gaits similar to standard, horizontal locomotive gaits.
In designing quadrupedal robots to operate in more diverse and useful environments, is there anything to be learned from the climbing behavior of animals?
Research Question:
Inspired by Alexander’s 1984 paper “Walking and Running”, is there a speed crossover point between the alternating and bounding gaits of a vertical climbing quadrupedal robot from a cost of transport (COT) perspective?
Hypotheses:
As the commanded vertical ascent speed increases, there will be a crossover point where the bounding gait becomes more efficient than alternating.
The alternating gait will be more efficient at lower speeds, while the bounding gait will be more efficient at higher speeds.
Simulation
Methods
Goal: model alternating and bounding gaits in order to identify an optimal torque trajectory and understand the theoretical behavior of the robot.
The simulation used a planar model and was further simplified to reduce degrees of freedom and avoid singularities. Model constraints:
Impulse force constraint on foot
Impulse constraint on hand (bounding) and spring-damper constraint on hand (alternating)
Impulse force constraint at the hip joint in the vertical direction during retraction (alternating only) Spring-damper joint limits
Model Simplification: Full model with 4-DOF has many local optima, making optimization-based dynamic simulation challenging. In, addition, the closed-chain kinematic constraints result in a singularity at a 90-degree knee joint angle. A simplified model to use two members only and a single joint/motor
Results
More energy was required for the bounding gait at all speeds investigated
Bounding gait has a clear energy optimal speed (~0.5 m/s) for this robot, whereas alternating gait COT is relatively flat
Ignores real torque limitations (bounding) and controller tracking limitations (alternating)
Experimentation
Methods
Hardware:
Used 2x 4-linkage legs, 3D-printed appendages, and Petzl Tibloc progress capture devices to construct the robot
2x vertical ropes were held in tension for the robot to climb and a counterweight was used to decrease the required load on motors
Control:
Cartesian PID controller used to prescribe leg motion
9-degree Bezier curve use to define the trajectory of each leg
Legs are perfectly in phase (bounding) or out of phase (alternating)
Number of “strides” set to 8 given rope length limitation
Procedure:
Run each gait over a range of speeds (0.04-0.25m/s)
Measure total hand-height traveled for each speed
Compute input energy for each run
Compare the cost of transport between gait types
Results
Legs were able to approximate the desired cartesian trajectory but were limited by friction and controller performance.
At very low speeds and very high speeds, the feet would produce “jerky,” unpredictable movement
Bounding was more efficient than alternating at all speeds from a cost-of-transport perspective
Overcoming friction one leg at a time required more energy
The tendency of the body to rotate during alternating increased friction and the amount of control input required to maintain the desired trajectory
