Stop Teaching Robots to Move Like Us

Okay, hear me out. Almost every humanoid demo I watch carries the same unstated assumption: the goal is to move like a person. Walk like us, reach like us, turn a doorknob like us. That makes a great video. I think it's the wrong spec.

The humanoid form has a real argument behind it. The world is effectively a human-shaped API. Stair risers fit our legs, door handles sit at hip height, and tools are sized for our hands. A robot that conforms to that API can walk into an existing building without anyone renovating it. Boston Dynamics makes the same case when it calls the humanoid form factor a useful design for robots working in a world designed for people^[1].

That is an argument about the interface, though, not the implementation. In software we'd describe it as the difference between honoring an API contract and porting the legacy codebase, bugs included. Human motion limits are legacy constraints. Tendons, ligaments, blood vessels, nerves, and a tight evolutionary energy budget produced them. A robot has none of those, so let's work out what copying them costs.

“It is comparatively easy to make computers exhibit adult level performance on intelligence tests or playing checkers, and difficult or impossible to give them the skills of a one-year-old when it comes to perception and mobility.”

Moravec's paradox is usually read as "movement is hard." I read it slightly differently: movement is hard for us to specify, because we evaluate it against our own bodies. We reach for our own motion as the reference implementation even when it's just one point in a much bigger design space.

1. Our joints are a compromise

Human joints are limited by bone contact, ligament tension, and the soft tissue that has to stretch across them. Clinical reference values from the AAOS and later normative studies put the numbers roughly here^[3][4]. The right-hand column shows the choices open to an actuated revolute joint that has none of those tissues to protect.

None of the right-hand column is science fiction. Industrial arms have had high-range and continuous wrist axes for decades. The new part is humanoid builders openly treating human limits as optional. Boston Dynamics described its electric Atlas this way:

“Atlas may resemble a human form factor, but we are equipping the robot to move in the most efficient way possible to complete a task, rather than being constrained by a human range of motion. Atlas will move in ways that exceed human capabilities.”

Here's why that's the right call, in math.

2. Workspace: where can the hand actually go?

Start with the simplest useful model: a planar two-link arm, like a shoulder and an elbow. With link lengths $l_1, l_2$ and joint angles $\theta_1, \theta_2$, forward kinematics gives the hand position ^[5]:

The distance from shoulder to hand depends only on the elbow, which comes straight from the law of cosines:

With equal links ($l_1 = l_2 = 1$) and a human elbow capped near $145^\circ$, the hand can never come closer to the shoulder than

A ±180° elbow reaches $r_{\min} = |l_1 - l_2| = 0$, and a continuous shoulder sweeps that annulus all the way around. Figure 1 shows the gap.

Real humans cover some of that gap with the extra shoulder degrees of freedom, by leaning, and by stepping. That's the point, though. We pay for reach with whole-body motion. A robot limited like us pays the same tax in balance, energy, and time, for no reason except that we set the limits.

3. Singularities and the locked elbow

The Jacobian maps joint velocities to hand velocities, $\dot{\mathbf{x}} = J(\boldsymbol\theta)\,\dot{\boldsymbol\theta}$. For the two-link arm, with the shorthand $s_{12} = \sin(\theta_1+\theta_2)$:

Yoshikawa's manipulability measure ^[6] tells you how freely the hand can move in every direction from a given pose:

Manipulability peaks at $\theta_2 = \pm 90^\circ$ and goes to zero at $0^\circ$, the fully extended arm. Humans live on the edge of that singularity all the time. We lock our elbows to carry groceries and our knees to stand in line. That's actually clever. Through the static relation

a radial load on a straight arm needs almost no joint torque because the skeleton carries it. Robots can and should use the same trick. The difference is that a human can only approach the singularity from one side. A bidirectional elbow can pass through it and switch between the elbow-up and elbow-down solutions of inverse kinematics, picking whichever branch has better manipulability or clearance for the next task.

4. Smoothness is a human tax

When people reach from one point to another, the hand follows a remarkably consistent bell-shaped velocity profile. Flash and Hogan showed it matches the trajectory that minimizes integrated squared jerk ^[7]:

For a move of distance $D$ over time $T$, with $\tau = t/T$, the optimum is a quintic polynomial:

Why would biology optimize for that? Harris and Wolpert offered a compelling answer: motor noise scales with the size of the neural command, so abrupt, high-force commands make movements less accurate ^[8]. Smoothness is how a noisy controller buys precision. It's a workaround for our hardware.

A robot's limits are different: torque, current, heat, structural stiffness. If the binding constraint is peak acceleration $a_{\max}$, differentiate the quintic twice and you find the minimum-jerk profile peaks at $\ddot x_{\max} = \tfrac{10}{\sqrt3}\,D/T^2$. Solve for the fastest allowed duration of each strategy:

The ratio is $2 / 2.40 \approx 0.83$. On the same actuators, the time-optimal move finishes about 17% sooner. Across a shift of repetitive pick-and-place, that's a real throughput difference, and it came from dropping a borrowed constraint.

One honest caveat: pure bang-bang has unbounded jerk, which excites structural resonance and wears gearboxes. In practice you plan jerk-limited S-curves. Those limits come from the machine's actual stiffness, though, not from a nervous system it doesn't have.

5. Infinite wrists and the regrasp problem

Take a boring task: unscrew a jar lid through a total angle $\Theta$. If the wrist has a usable range $\theta_r$, the number of release-and-regrip cycles is

A human forearm offers roughly $\theta_r \approx 160^\circ$ of combined pronation and supination ^[3]. For ten turns ($\Theta = 3600^\circ$):

Every regrasp costs time, adds a chance to drop the object, and makes perception re-confirm the grip. A continuous wrist removes that whole failure mode. That's a better outcome than a better regrasp policy.

6. Legs are a great answer to the wrong question

The standard way to compare locomotion across animals and machines is the dimensionless cost of transport, going back to Gabrielli and von Kármán ^[9]:

This is the energy spent to move one unit of weight one unit of distance. Collins, Ruina, Tedrake, and Wisse reported a specific energetic cost of transport of about 0.2 for human walking and for their passive-dynamics-inspired Cornell biped, versus an estimated 3.2 for Honda's ASIMO ^[10]. On a hard floor, a rolling wheel's cost is bounded below by its rolling-resistance coefficient, typically around 0.01.

Legs win on stairs, rubble, and gaps. On the flat hallway between them, a wheel is at least an order of magnitude cheaper. Nature couldn't evolve a free-spinning axle, but we can build one. Wheel-legged systems like the wheeled ANYmal already switch between rolling and stepping with whole-body control ^[11]. The human gait is one gait. It shouldn't be the only one.

7. A design vocabulary for non-human motion

If we stop treating the human body as the reference implementation, what do we design with instead? Here is my working list. The mathematical glue for most of it is redundancy resolution. When a robot has more joints than the task needs, the general solution for joint velocities is ^[12]

The first term does the task. The second term projects any secondary objective $\dot{\boldsymbol\theta}_0$ into the null space, so it moves the body without disturbing the hand. That second term is where non-human motion lives.

Then there's the far end of the spectrum: bodies that aren't rigid links at all. Soft and continuum robots, inspired by octopus arms and elephant trunks, trade discrete joints for continuous deformation and can squeeze through gaps no jointed arm fits ^[13]. A human-shaped robot won't become an octopus, but a humanoid's hand or gripperdoesn't need to be a hand.

8. The one place human motion still wins: around humans

This is the counterweight, and it matters. Near people, motion is also communication. Dragan, Lee, and Srinivasa draw a useful distinction between predictable motion, which matches what an observer expects given a known goal, and legible motion, which lets an observer infer the goal quickly ^[14]. A robot that spins its torso 180° without warning is efficient and terrifying at the same time.

The systems answer is one I'd give for any platform: separate the public contract from the internal implementation. When people are in the loop, the robot should run a legible, human-readable motion profile. When the aisle is empty, it should switch to whatever the actuators allow. Treat human-likeness as a mode, not a limit.

Where this leaves us

Match the world's interface. Don't inherit the body's constraints. The shape of a humanoid buys compatibility with stairs, doors, and tools. Its motion should be designed from first principles: workspace, manipulability, actuator limits, and energy per meter.

I'm still working through the second-order effects here, especially how learned policies trained on human motion capture might quietly re-import the limits we're trying to drop. If you're building in this space and think I've got something wrong, I'd genuinely love to hear it. The best whiteboard sessions start with someone telling me I'm wrong.