1. Introduction
1.1 The Motivation: Beyond Human Capability
For humans, horizontal movement is easy. Humanoid robots have recently advanced to human-level flat land traversing capabilities. By comparison, humans are significantly limited in vertical mobility. Humanoid robots have an opportunity to advance far beyond human capabilities in vertical mobility in the near future, and this would solve a myriad of complex problems.
1.2 Background
Researchers and engineers have been interested in the problem of robot vertical mobility for many years. Many have studied the problem by observing how it is solved in nature; an example of such an attempt, Festo’s BionicKangaroo, is shown in Figure 1.2.1 below.
Figure 1.2.1: Festo’s BionicKangaroo.
Most look at the problem of vertical mobility as a means for more efficient horizontal movement, because jumping can be an efficient way to move horizontally. Few have approached the problem as a way to significantly improve robots vertical mobility, which is a closer comparison to flying robots than horizontally moving robots. The few examples that have studied the problem of significant vertical mobility—such as Boston Dynamics’ Sand Flea Robot shown in Figure 1.2.2 below—have not found success beyond the prototype stage. What is missing in this problem area is an approach that focuses on extreme vertical movement using efficient, low-cost methods that are easy to reproduce.
Figure 1.2.2: Boston Dynamics’ Sand Flea Robot.
2. Problem Statement
2.1 The Problem: Humanoid Robots are Bad at Moving Vertically
Robots that require vertical mobility typically fly. But this poses a problem for humanoid robots. Humanoid robots are typically very dense in order to fit all of their required components (battery, sensors, stability structures, etc). This density prohibits them from flying to augment their vertical mobility. Yet, superhuman vertical mobility is an important requirement for humanoid robots to succeed in the areas we need them to. Humanoid robots should be able to move from the ground to hard-to-reach areas repeatedly and with ease. This is a vital skill for many tasks, including 1) traversing rough or uneven surfaces or 2) reaching remote areas.
2.2 A Complex Problem
Vertical mobility for humanoid robots relies on jumping, or; exerting an amount of mechanical force that is multiple times greater than the weight the body that is doing the exerting. Mechanical force or power is typically limited by the physical trade-off between force and velocity. This necessitates a power-amplifying mechanism to enable an acceleration large enough to execute a successful jump exhibiting the phases shown in Figure 2.2.1 below.
To repeatedly execute successful jumps, autonomous robots must be able to:
- Reach high accelerations,
- execute multiple jumps without human intervention, and
- execute multiple jumps with little degradation over time.
Figure 2.2.1: Jumping phases.
Achieving the above capabilities requires a powerful robot with a specific type of coordination in which the robot can identify and otherwise correct itself to a jumping position no matter how it lands. The robot must also be physically capable of withstanding repeated impacts, with the mechanism remaining stable enough to provide predictable output between iterations.
3. Mechanism
3.1 The Path: Mechanical Advantage
To succeed against the problem described in Section 2, a mechanism must maximize mechanical advantage to enable a larger, almost disproportionate jump height response. Specifically, the mechanism must be optimized to output maximal vertical force. A mechanism that can output a vertical force multiple times its weight must be a significant force multiplier. Specifically, it must have a mechanical advantage greater than 1, but more likely in the range of 3-5. The classic example of a force multiplier is a pulley system, shown in Figure 3.1.1.
Figure 3.1.1: Pulley system.
3.2 A Successful Mechanism
3.2.1 Inspiration from Nature.
Our chosen mechanism will utilize the flea (order: Siphonaptera) as a source of inspiration:
Figure 3.2.1.1: Kinematic breakdown of flea jumping mechanism.
Flea jumps are powered by a spring-like mechanism in the leg structure that leverages significant mechanical advantage to enable force-multiplying jumps to launch it many multiple times its height. The force from flea jumps start from the tarsus (the lower hind leg) and launch using the contact between the tibia (calf/foot) and ground.
Our mechanism will be similar to the one pictured above, with some added constraints:
- Our mechanism will make use of guide rails, so the main focus will be maximizing vertical force output.
- Our jump-height to mechanism-weight ratio will be much smaller than the flea’s, which can be upwards of 200.
3.2.2 Description of Proposed Mechanism
The mechanism will be composed of 2 systems: (i) the jumper and (ii) the guide rail. This will restrict jumping to 1 degree of freedom (DOF); vertical. The guide rail will be composed of top and bottom plates held together by 2 vertical rails. The top and bottom plates will be held in place with the bottom plate resting on the ground. Our mechanism with sliding output, henceforth referred to as the “jumper”, will be constrained between the top plate, bottom plate and guide rails. At a high level, our initial jumper mechanism design comprises 8 links with a cam device driven by a DC motor as one of the links. This cam-DC motor link will in turn drive a torsion spring. This torsion spring will be connected through the linkage structure which will multiply the force inputted by the cam-DC motor link. (See Section 5 for a detailed description of our mechanism)
4. Proposed Scope
As detailed in Section 2.2, the primary challenge that our team will face in the development of this mechanism is balancing the forces required to achieve high output distances with the structural and positional requirements needed to enable repeated jumps. Our project scope is defined with this driving factor in mind:
- While most flea-inspired mechanisms focus on free motion along multiple DOFs, we are limiting the motion of our mechanism to one DOF (vertical) to simplify the requirements of defining a successful jump. This will be achieved using a superstructure anchored by guide rails that will further ground our jumper mechanism.
- To enable quick position reset, the mechanism will be designed to return to a singular base state after every jump. The mechanism superstructure and quick operational behavior will work in tandem to enable such a state.
- To lessen the forces required to induce a successful jump, the sliding jumper in our mechanism will be designed to house as few electrical and hardware components as possible. Ideally, we will be able to solely house our driving DC motor and linkages within the jumper structure, with all necessary electrical and power input coming in from a fixed electronics box on the superstructure via lengthy wire connections. This goal will be adjusted based on what we find is practically possible during our design process.
4.1 Initial Design
We will start our design process by developing a series of mechanism concepts that utilize unique kinematic approaches to achieve the goals defined in Section 2 and our stated operational scope of 1 DOF in the translational vertical direction. Given our goal of achieving high jumping distance, we will emphasize conducting robust motion analysis on our linkage designs through computational methods in order to optimize link lengths and behaviors. As we work to flesh these designs out as physical mechanical concepts in CAD, special attention will be paid to the mechanical properties of the mechanism—primarily the load-bearing “foot” link and the spring-loading link—to ensure their strength and robustness. We will do this using force analysis via hand calculations and FEA simulations.
4.2 Prototyping and Fabrication
The iterative nature of our design process will extend into our fabrication stage. Our prototypes will be constructed of linkages laser-cut to precise lengths, structurally-optimized 3D-printed elements, and off-the-shelf components such as linear bushings. We will initially create non-functional prototypes, moving to functional prototypes after ensuring desired and predictable motion output. We will evaluate the success of each design by measuring actual forces and distances that the device produces and overall robustness in operation. Material choices will likely change through both the initial design process and prototyping stage, as will link lengths and geometries.
The most potentially-gating part of our project will be the superstructure and its components—with our implementation of vertical guide rails, we may need to introduce metal components into our design to support our mechanism and counter any moments that it may generate in order to maintain a 1 DOF condition. This may require machining, with a remote chance of us looking at potential production lead times depending on the complexity of our designs. Machined components may also be necessary for load-bearing components in our linkage system depending on the results of our structural analysis.
The key to a successful initial prototype is optimizing towards a design that finds as many flaws as possible with the least amount of construction time required. We will take this approach and cut corners as much as possible in the initial prototype while maintaining the ability to test the key design aspects.
5. Preliminary Design
The linkage mechanism shown in Figure 5.0.1 depicts both its jumping and loading state. The mechanism centers around a cam device driven by a DC motor (link 8), which drives a torsion spring (connected by links 4 and 2). The stretched torsion spring stores energy, and due to the legs compressing (links 1 through 4), the angle between link 6 and 1 compresses. Once the cam passes the torsion spring, it snaps back to its original jumping state and triggers the jump. Link 7 is the output link and will be attached to the mounting plate of the rail system, which serves as ground. Note that more torsion springs can be added at other joints to increase the stored energy for better jump height. There are two half-joints in this linkage: the contact between the cam and spring and the contact between link 1 and ground. The mechanism is intended to stay Grashof, with link lengths to be determined through iterative computational methods due to the complexity of the system. The mechanism is also intended to have 1 DOF, confirmed with the Gruebler equation below:
Figure 5.0.1: Kinematic diagram for cam-loaded linkage mechanism.