Reader Guide and Prerequisites

Physical AI Systems is written as an independent, self-contained textbook for advanced undergraduate students, graduate researchers, and practicing systems engineers who wish to build machines that safely couple learned intelligence to physical matter and energy.

Readers will bring different strengths from machine learning, embedded systems, or mechanics. The book introduces the concepts needed to reason about their interactions without requiring specialist training in every contributing discipline. This guide distinguishes the shared starting background from material introduced in the text and suggests where readers with different backgrounds can concentrate their attention.

The Technical Baseline

The main text assumes a shared foundation in programming, machine learning, and basic mathematics. The following preparation supports reading the explanations and following the short calculations:

• Programming & Systems: Readers should be able to read and write Python functions, follow data through a program, and recognize that execution takes time and uses memory. Familiarity with C or C++, pointers, and memory allocation is useful for optional implementation work.
• Machine Learning Intuition: Readers should recognize the difference between training a model and using it to make predictions, and be familiar with arrays or tensors as model inputs and outputs. Experience with a particular framework is unnecessary.
• Foundational Physics & Mathematics: Readers should be comfortable with basic algebra, vectors and matrices, and single-variable calculus (rates of change). Physical AI relies directly on freshman Newtonian mechanics:
  • Newton’s second law for linear and rotational systems (\(F = ma\), \(\tau = I \alpha\)).
  • Kinetic energy and stopping distance napkin math (\(E_k = \frac{1}{2} m v^2\), \(d_{\text{stop}} \approx v\,\tau_{\text{delay}} + \frac{v^2}{2a_{\text{brake}}}\)).
  • Basic electrical power and heating (\(P = I_{\text{phase}}^2 R_{\text{phase}}\)). Advanced differential geometry, Lie group continuous control theory, and formal reachability analysis are deliberately not required; their mathematical treatments are collected in the volume appendices.

This preparation supports reasoning about the complete system. Specialized control theory, detailed robotics mathematics, and low-level implementation expertise are not starting requirements for the main explanation.

Disciplinary Reading Pathways

Readers approach physical AI from different engineering traditions. The published sequence develops a shared systems perspective; readers can give additional attention to the interactions least familiar from their own background:

• For Machine Learning Practitioners: Focus on the physical consequences of computation. A machine continues moving while its model processes an observation. Pay close attention to The Physical Body for motion and braking constraints, Physical Data and Policy Training for endogenous feedback and compounding drift (\(\mathcal{O}(T^2 \epsilon)\)), Closed-Loop Evaluation for closed-loop reality, Safety Enforcement for checking proposed actions before execution, and Silicon Placement for computing resources that affect timing.
• For Embedded Systems & Silicon Architects: Focus on how learned computation contributes to decisions that the machine must carry out on time. Pay close attention to The Causal Boundary for the proposal boundary, Sensor Perception for how sensory observations inform decisions, Spatial Memory for spatial belief representations, Grounded Intent and Trajectory Planning for trajectory synthesis, and Silicon Placement for system-on-chip (SoC) memory bus contention and thermal limits.
• For Roboticists & Control Engineers: Focus on closing the physical loop around learned models. Pay close attention to The Causal Boundary for limits on what a model may command, The Nervous System for timing and communication between components, Supervisory Intervention for human authority handshakes and bumpless transfer, Adversarial Verification for hardware-in-the-loop fault injection, and Deployment Release for the structured evidence needed to judge readiness for release.

These points of emphasis supplement a sequential reading rather than replace it, because the book’s argument lies in how each discipline connects to the rest of the machine.

What the Book Introduces

The book starts from the physical and computational relationships needed to explain a system’s behavior. Specialized concepts enter through the problems they help solve, with their assumptions and limits made explicit. The main text develops the following ideas from that shared foundation:

• Proposals and permission to act: The text explains how a learned model can propose an action while a separate component determines whether that action may reach the body.
• Checks under physical limits: The explanation connects proposed actions to available space and machine motion, stating the assumptions under which a check can help.
• Timing across components: The text develops how components that operate at different rates exchange results and coordinate their work, and why delays matter to the physical response.
• Observations and motion: The explanation relates positions and directions described by sensors and models to movements of the body, including how sudden changes in commanded motion affect the mechanical response.
• Evidence for release: The text explains how to connect a claim about system behavior to supporting evidence and identify what that evidence leaves unresolved.

Detailed proofs, specialized notation, and implementation layouts provide optional depth. The main explanation retains the mechanism, assumptions, and engineering consequence so that following the systems argument does not depend on pursuing that detail.

How to Read the Numbers

Every number in this book carries one of five labels, four categories of evidence and one for design choices, and its label decides what it may be used for.

• Measured: A calibrated observation of a particular machine. It names its instrument, its operating conditions, its sample count, and, for a distribution, the percentile it reports. Only a measured number, or a number derived from measured ones, can support a safety margin.
• Derived: Computed from measured numbers through a stated physical or statistical model. It carries that model’s assumptions and the propagated uncertainty of its inputs.
• Datasheet: A manufacturer’s rating under the manufacturer’s conditions. It says what to expect and what to test, and it is not evidence about the unit on the bench.
• Illustrative: Selected to show arithmetic or scaling. It supports no margin, timeout, or release decision.

A budget or requirement, such as a lease duration or a clearance margin, belongs to none of the four. It is a design decision, labeled chosen, and it means something only when it is checked against the measured or derived number it must fit, as a chosen lease is checked against the derived ceiling on pre-brake delay.

A worked design in this book shows a decision procedure. When its inputs are illustrative, the decision it reaches is illustrative too. It shows how the machine’s speed, lease, or verdict would be set, and it would bind a real machine only after the inputs it names are measured.

When a number decides something, such as a speed limit, a timeout, or a release, the book keeps it as a limit record with six elements: the value or distribution; the operating conditions under which it holds (payload, temperature, supply voltage, surface, concurrent workload, firmware); the measurement uncertainty; the engineering margin between the operating target and the breakdown threshold; the detector that catches an excursion while the machine runs; and its provenance, meaning its label and the instrument or model that produced it. A limit holds only under its stated conditions. When wear, heat, a new payload, or a new build changes them, the limit must be established again before it is reused.

Worked examples label each number’s category once, at first use. A result holds under the assumptions stated with its example and nowhere else. A bound from finitely many trials holds under its sampling assumptions and proves nothing beyond them, and a measured percentile describes the tested workload, not a worst case. In a release argument each premise also has a status: established (measured or derived), assumed, decided by accountable judgment, unsupported, or outside the threat model. Deployment Release and The Epistemic Frontier use these statuses.

What We Deliberately Omit

The book focuses on how learned computation, physical mechanisms, and execution systems work together. That focus limits the depth of its treatment in neighboring fields:

• Exhaustive Robotic Kinematic Derivations: The main text does not develop long derivations for every manipulator configuration. The relevant systems concern is what movements a machine can make and which physical limits constrain them.
• Deep Learning Theory: The book does not provide a comprehensive mathematical treatment of loss landscapes and optimization. Learning mechanisms matter here through the behavior they produce and the demands they place on the physical system.
• Framework and Tool Tutorials: The book does not teach particular robotics middleware, simulators, or training frameworks. Software matters here through its effect on timing, memory, and evidence.

These boundaries leave the essential mechanisms and their consequences in the systems argument. They limit exhaustive specialist treatment without making familiarity with that treatment a prerequisite for following the book.