Mojo5 - Enhancing Performance with More Powerful Batteries (11)

 

Mojo5 - with power bank battery

Welcome back to the "Totally Not Evil Robot Army" blog. In this 11th installment of the Mojo5 series, we’re going to dive into a crucial aspect of building robust quadruped robots: using more powerful batteries to drive hobby servos. Specifically, we'll explore how increasing the available amperage and voltage can significantly improve the performance of underpowered servos and the considerations needed to ensure safe and efficient operation.

The Problem with Underpowered Servos

Building a quadruped robot like Mojo5 with cheap hobby servos often leads to performance issues. Many of these servos, such as the MG995, are slow and lack the torque needed for dynamic movements. Even with a 5V power supply, these servos can become wobbly and unreliable, especially under load. This is where upgrading to more powerful batteries comes into play.

The Limitations of the Original Power Configuration

Initially, Mojo5 used a 5V 12000mAh power bank. While this power source had a high capacity, it was limited to a maximum output of 3A. Given that the MG995 servos have a stall current rating of up to 3A each, the total current demand for the robot could easily exceed 20A during peak operation. This significant shortfall in available current was a primary cause of the robot's poor performance.

Upgrading the Power Source: LiPo Batteries

Based on previous discussions and experiments, we found that using a more powerful battery can drastically improve servo performance. Upgrading to a LiPo battery with a 2200mAh capacity, 7.4V voltage, and a 50C discharge rating provides the needed boost. This battery can supply well over the 20A needed by the servos, addressing the current limitations of the previous power source.

Considerations for Over-Volting

1. Risk of Burnout: Exceeding the servo’s voltage rating does carry a risk of burnout. However, anecdotal evidence suggests that slight over-volting is generally safe if monitored properly. Implementing a voltage regulator could limit the current capacity, which might be counterproductive. In general voltage regulators on servo power sources are not recommended.

2. Separate Circuits for Different Servos: For servos with lower voltage ratings, such as the MG90 (max 6V), consider creating a separate circuit to avoid over-volting. This will add an additional circuit which can be problematic. For my experiments with Mojo5, I used the same circuit.

Practical Application: Experimenting

Initial Setup

1. Battery Connection: Connect the 7.4V 50C LiPo battery directly to the power bus of the PCA9685 servo driver, bypassing capacitors and regulators. This setup ensures the servos receive power directly.

2. Handling Large Wires: Safely connecting XT-60 battery connectors and their thick 12 AWG wires to smaller electronics is challenging. Using a bare copper PCB or prototyping PCBs with multiple copper lines can provide a more robust connection. Soldering all wires together is an ugly but space-efficient solution.

Not Recommended!

In this experiment, I took the short cut and soldered the large wires directly in to a dupont connector. The connector was connected directly to the servo bus. This is not a recommended practice! I better connection with larger wires is recommended. In this particular case, as long as all of the servo motors do not stall, then only brief seconds of +20A current would be expected.  Current greater than 7A for sustained periods of time would destroy the connectors.

Experiment Results

After connecting the 7.4V battery:

• Servo Performance: There was a noticeable improvement in servo actuation. The MG995 servos operated better, with no immediate burnout.
• Heat Management: Monitoring the temperature of connectors and wires is crucial. Using a finger-test method (keeping fingers on components for one minute) can help identify safe current levels. If components become too hot to touch, reduce the current.

To visualize the improvement, I have embedded a short video showing Mojo5's performance with the original 5V power bank versus the upgraded 7.4V LiPo battery. Notice the difference in servo response time and stability.

Long-Term Solutions

While the initial experiments are promising, long-term solutions require more robust hardware:

1. Custom Servo Driver Board: Developing a servo driver board with better connectors and thicker traces can handle higher currents more efficiently. This would replace the PCA9685 board, which is not designed for high current loads.
2. Current Monitoring: Implementing current measurements and safety features like e-fuses can prevent overcurrent situations and protect your components.

Conclusion

Upgrading to more powerful batteries can significantly enhance the performance of underpowered servos in your DIY robots. While there are risks associated with over-volting, careful monitoring and proper hardware can mitigate these risks. As we continue to push the boundaries of DIY robotics, sharing these experiences and solutions will help us all build more capable and reliable robots.

Mojo5 - Mirrored Servo Control for Opposite Side Legs (#10)

Mojo5 - Two Legs with Symmetric Control

Introduction to Mirrored Servo Control (Symmetric Control)

One of the primary challenges in developing Mojo5 was ensuring synchronized movements between the servos on opposite sides of the robot. To achieve this, we employed a straightforward yet effective approach: mirroring the servo movements by reflecting the target angles.

Technical Implementation

To implement the mirroring effect, we introduced a boolean parameter in our Servo structure to indicate whether a servo should be mirrored. The adjustment is applied directly in the servo control function.

void moveServo(const Servo& servo, int pos) {

  pos = max(servo.minPos, min(pos, servo.maxPos));

  int pulseWidth =  map(pos, servo.minPos, servo.maxPos, servo.minPWM, servo.maxPWM);

  pca9685.setPWM(servo.num, 0, pulseWidth);

    if (servo.mirror) {

        pos = 180 - pos;  // Adjust the position if mirroring is needed

    }

    pos = max(servo.minPos, min(pos, servo.maxPos));

    int pulseWidth =  map(pos, servo.minPos, servo.maxPos, servo.minPWM, servo.maxPWM);

    pca9685.setPWM(servo.num, 0, pulseWidth);

}

the following structure is used to define all the elements of the servo

struct Servo {

  uint8_t num;

  int minPos;

  int maxPos;

  int minPWM;

  int maxPWM;

  int minRange;

  int maxRange;

  int minRangePWM;

  int maxRangePWM;

  bool mirror;  //true => adjust IK if opposite side

};

The results of this code are directly observed in the output for the Pulse Width Modulation (pwm) values that are sent to the servos.  Here you can see the servo values are 'reflected' or 'mirrored', symmetrical to one another:

Mojo5 - Symmetric control - pwm values over a rectangle gait

Practical Application and Results

In our setup, the mirror effect (symmetric control) is particularly useful for maintaining symmetry in the leg movements. This approach simplifies the inverse kinematics (IK) calculations, as the same code can be used for both sides of the robot with the mirrored adjustment applied where necessary only at the servo control.

To illustrate this concept, we've embedded a short video demonstrating the addition of a leg from the opposite side of Mojo5. The IK calculations are identical, but the servo angles are adjusted by reflecting the target angles, resulting in a mirrored motion that maintains the robot's symmetry.

Insights on Mirrored Movements

Creating a mirrored movement (symmetric control) for servos is crucial for several reasons:

• Symmetry and Balance: Ensuring that both sides of the robot move in a symmetrical manner is essential for maintaining balance, especially in quadruped robots. Asymmetrical movements can lead to instability and erratic behavior.

• Simplified Coding: By mirroring movements, the same IK code can be reused for both sides, reducing complexity and the potential for errors. This makes the development process more efficient and the codebase easier to maintain. The servo angles are simply adjusted because all servos turn counter-clockwise and have a 0 to 180° range based on their orientation. Servos on the opposite side face differently, so this mirroring adjustment is necessary.

• Consistent Gait Patterns: Symmetrical leg movements are vital for creating smooth and natural-looking gait patterns. Mirroring helps in achieving uniform step lengths and timings, which are important for the robot's locomotion.

Summary

The mirroring technique (symmetric control) we've implemented in Mojo5 represents a significant simplification in controlling symmetrical movements in quadruped robots. By introducing a boolean flag in the servo structure and adjusting the servo angles accordingly, we achieve mirrored movements without duplicating the IK code. This not only enhances the efficiency of our development process but also ensures more consistent and predictable robotic movements.

Mojo5 - Inverse Kinematics in Motion (#9)

I've recently implemented an inverse kinematics (IK) solution to enhance the precision and control of robotic leg movements. Our primary experiment involved programming the leg to execute a simple rectangular movement pattern, with a focus on maintaining accuracy and consistency. Here, I will share some intriguing geometrical observations and challenges we encountered.

Intended Path and Test Setup

For this test, the robot leg will start in the (0,-130) position. Moving clockwise, It steps backward (in my case more positive, note the inverted x axis) to the (50, -130) position. Next up by 25mm to the top. At this time I use a different z position, but it is hard to see. the motion continues around in a rectangle ending at the start.

Planned path for simple gait test. starting at the center bottom

Video Analysis

In the bolow short video, the robot steps through the gait path. The leg is mounted above the table and horizontal to the table, not in a typical robot position. I have traced each step of the path, with a small dot at the end of the foot.

As seen in the video, the motion lacks the expected precision, influenced by several factors:

• Fixture Stability: The fixture holding the leg is unstable, contributing to erratic movements.
• Manual Marking Inaccuracy: Yellow dots indicating key positions were marked by eye, leading to imprecision.
• Servo Calibration: The calibration of the servo points was approximative. At a setting meant to be 90°, the actual angle could range between 85-95°.

Geometrical Challenges: The Skew Issue

One of the more fascinating issues we observed is the skew to the left when the leg is raised vertically. This skew is likely influenced by the constraints of the 'solution space'—the range within which the actuator operates. As a result, there is a slight warping effect in the grid area over which the leg can move.

Mojo5 Inverse Kinematics - geometric skew

Implications of the Skew

• Motor-Driven Distortions: The two servomotors, designed to drive the leg in specific rotational angles, do not guarantee a perfectly perpendicular alignment of the movement path. This introduces a mathematical distortion in the intended trajectory.
• Impact on Gait Creation: While this skew does not necessarily hinder the robot's ability to perform meaningful gaits, it highlights an essential aspect of robotic movement—geometric imperfections inherent in mechanical and software solutions.

Further Research on the Mapped or Solution Space

The space in which the robot can operates can be understood as the geometric area or volume within which the robot can effectively reach and manipulate objects. This space is defined by the following:

• Reachability: Determined by the length of the robot's arms and the range of motion of its joints. The maximum and minimum extents of each joint define the outer and inner boundaries of this space.
• Compliance: In the context of SCARA robots, the vertical compliance allows for certain movements in the vertical plane within the workspace. This selective compliance helps in absorbing forces during tasks like assembly, where vertical give is beneficial.
• Kinematic Constraints: Defined by the robot's mechanical design and the kinematic equations governing its movements. These constraints delineate the paths and patterns the robot can execute.
• Control Resolution: The precision with which the robot's controllers can position its joints also defines the resolution within the mapped space, influencing how finely the robot can maneuver within its reach.

Certainly a very interesting area of study in robotics!

Mojo5 - My Inverse Kinematics Simplified (#8)

Inverse Kinematics pictured by Dalle3, it can be much simpler!

A much simpler approach

In my previous post on Inverse Kinematics (IK), the complexity might have left some readers puzzled about whether there could be a simpler method to achieve the same results. The good news is, yes, there is a simpler way! Thanks to insights from my roboticist friend Oracid over at the French Robot Forum on Robot Maker, I've streamlined the IK calculations for our Mojo5.

Understanding the Basics

The challenge remains the same: given a target point (x, y), we need to determine the angles of the hip servo (S1) and knee servo (S2). The geometric configuration of the robot's leg has not changed; we still deal with the leg segments L1 (upper) and L2 (lower), equal in length, connected at the knee and forming two sides of a parallelogram.

Geometric Simplification

This parallelogram setup allows us to simplify our calculations considerably. The angle from the horizontal to the leg segment L1 directly provides the angle for S1, and similarly, the angle from the horizontal to the side of L2 gives us S2.

Mojo5 - simplified Inverse Kinematics

Simplified Calculation Steps

Calculate Distance D:  First, we determine the distance from the hip servo to our target (x, y) using the Pythagorean theorem:  D = sqrt(x*x + y*y).  Note D plays a very important role in the following calculations for angles alpha and beta. It is also the line that divides our parallelogram in half.

Calculate alpha:  We will use the trigonometric law of cosines. Given that we know the length of our upper leg L1 and the length of D (aka the hypotenuse), we can calculate the angle between them.  We will call this alpha:  alpha = acos(D / (2*L)).  You may notice this is the same calculation that I used previously. More importantly, this angle alpha is the same on either side of the bisection of the parallelogram by D.

Calculate beta:  We will use a much simpler approach. Also using trigonometry, we see that there is a Right Triangle formed by the Y position, X length and the hypotenuse D. it is possible to calculate this angle opposite of y and D.  beta = asin ( abs(y) / D). It must be adjusted to its reflection in the event that x < 0, this is done (in radians) by subtracting PI from beta. Now one more interesting note. The angle we just calculated is the same angle at top horizontal, this makes it more clear how this beta angle will be used in our final calculations.

Final Servo Calculations:  For S1 we can take the value of beta and subtract apha from it.  Like wise to calculate the angle for S2 and can take the value of beta and add alpha to it to find its value.

• S1 = beta - alpha
• S2 = beta + alpha

Hopefully this explaination will help in visualizing the relationships and how to calcuate the correct angles for S1 and S2.  

Here you can view a simplified set of C++ code:

void calcIK(float x, float y, float &s1, float &s2,) {

  float L = 70; //length mm

  float d = sqrt(x*x + y*y);

  float alpha = acos(d / (2*L));

  float beta = asin(abs(y)/d);  if(x<0)beta=(M_PI-beta); 

  s1 = ((beta - alpha) * (180.0 / M_PI));

  s2 = ((beta + alpha) * (180.0 / M_PI));

}

 

Mojo5 - Inverse Kinematics (#7)

Inverse Kinematics

At first glance, one might think that Inverse Kinematics (IK) boils down to simple trigonometry. However, determining the appropriate angles is merely scratching the surface. The real challenge lies in considering the physical arrangement of servos, the reference frame, and the constraints tied to both the servo capabilities and their placement. Collectively, these factors embody the essence of Inverse Kinematics.

For  Mojo5, I've chosen to use two MG995 servos, arranged in a stack. One servo is responsible for the 'hip' motion, and the other controls the 'knee.' The crux of IK in this setup is to map a target position within the coordinate plane to specific angles for these servos. To streamline the calculations, I've made a series of strategic design decisions. The lengths of the leg segments, L1 and L2, are set to be equal, each measuring 70mm. The hip servo is positioned as the origin point of our coordinate system. The mechanism for the knee is somewhat intricate, primarily because the servo controlling it is not mounted directly on the leg. Additionally, I've introduced a concept of 'yaw' movement along the z-axis, although, for the time being, our IK calculations will focus solely on movements within the x and y axes.

When it comes to calculating the necessary angles through IK, the approach is to visualize a triangle formed by the leg segments. Given that L1 and L2 are of equal length, this triangle is always isosceles. While this detail may seem minor at first, it becomes crucial when applying the Pythagorean theorem—a^2 = b^2 + c^2—to determine the distance (D) between the endpoints of the leg segments. This distance is key to assessing the feasibility of reaching a given target (x, y) position. To ensure reachability, D must not exceed the sum of the lengths of the two leg segments, or in other words, D <= 2*L.

Calculating the Hip Angle (Theta1)

To determine the hip angle, one must sum two distinct angles. The initial angle is formed between the horizontal axis and the target point (x,y) at the end of line D in our coordinate system. This can be calculated using the ArcTangent function, specifically arctan2(y/x) in standard practices. However, in my application, I employ arctan2(-y/x). The choice to use a negative y value due to my y values will consistently fall below zero. An alternative approach could involve taking the absolute value of the ArcTangent result to ensure a positive angle.

Following this, it's necessary to find the interior angle between line D and leg segment L1 within our conceptualized triangle. This angle, designated as alpha, can be determined through the law of cosines. In a simplified form, the calculation of alpha is expressed as acos(D / (2*L)). By adding alpha to the previously calculated angle, we derive the hip angle. However, there's a twist due to the servo's counterclockwise incrementation: the actual Theta1 is the supplement of the sum of alpha and our initial angle, mathematically expressed as Theta1 = 180 - (alpha + theta).

Mojo5 - Inverse Kinematics of the Hip Joint

Calculating the Knee Angle (Theta2)

To calculate the knee angle, our first step involves identifying the interior angle between the two legs, L1 and L2, which we'll refer to as beta. Once again, the law of cosines proves invaluable for this calculation. While the deeper mathematical proofs are better left to academia, the simplified formula to compute beta is given by acos((2*L^2 - D^2) / (2*L^2)). This equation allows us to calculate beta, which represents the angle between the leg segments in our model.

However, to translate this angle into a form usable by the servo mechanism, additional adjustments are necessary due to the servo being linked to the leg segments via cams. We must take the supplementary angle to beta. This supplementary angle, once processed through the cam system, achieves the effect of pulling the leg segments into the correct position but in a reversed direction. Consequently, we must employ the complement of this supplementary angle to align with the actual geometry and movement direction required by the servo mechanism. This raises an interesting question: could the calculation have been simplified to just beta minus 90 degrees?

Mojo5 - Inverse Kinematics of the Knee Joint

Moving forward

This step concludes the basic framework for the Inverse Kinematics (IK) calculation pertinent to our robotic project. It's important to note that the physical setup of the servos and the joint mechanics imposes certain limitations on movement. Preliminary observations suggest the knee joint is limited to 90 degrees of motion, while the hip joint can achieve approximately 130 degrees. These constraints are not absolute; certain hip positions may permit additional knee movement, although these specific interactions remain to be fully mapped out.